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85,100 | Topological abelian group Haar measure Discrete Fourier transform Dirichlet character Amenable group Von Neumann's conjecture Pontryagin duality Kronecker's theorem on diophantine approximation Almost periodic function Bohr compactification Wiener's tauberian theorem | List of harmonic analysis topics | 0.783047 |
85,101 | This is a list of harmonic analysis topics. See also list of Fourier analysis topics and list of Fourier-related transforms, which are more directed towards the classical Fourier series and Fourier transform of mathematical analysis, mathematical physics and engineering. | List of harmonic analysis topics | 0.783047 |
85,102 | Continuous Fourier transform Fourier inversion theorem Plancherel's theorem Convolution Convolution theorem Positive-definite function Poisson summation formula Paley-Wiener theorem Sobolev space Time–frequency representation Quantum Fourier transform | List of harmonic analysis topics | 0.783047 |
85,103 | Periodic function Trigonometric function Trigonometric polynomial Exponential sum Dirichlet kernel Fejér kernel Gibbs phenomenon Parseval's identity Parseval's theorem Weyl differintegral Generalized Fourier series Orthogonal functions Orthogonal polynomials Empirical orthogonal functions Set of uniqueness | List of harmonic analysis topics | 0.783047 |
85,104 | Thermal alkyl shifts, similar to hydride shifts, must proceed antarafacially. Here the geometry of the transition state is prohibitive, but an alkyl group, due to the nature of its orbitals, can invert its geometry, form a new bond with the back lobe of its sp3 orbital, and therefore proceed via a suprafacial shift. ... | Sigmatropic reaction | 0.783046 |
85,105 | In principle, all sigmatropic shifts can occur with either a retention or inversion of the geometry of the migrating group, depending upon whether the original bonding lobe of the migrating atom or its other lobe is used to form the new bond. In cases of stereochemical retention, the migrating group translates without ... | Sigmatropic reaction | 0.783046 |
85,106 | The importance of Herbrand interpretations is that, if any interpretation satisfies a given set of clauses S then there is a Herbrand interpretation that satisfies them. Moreover, Herbrand's theorem states that if S is unsatisfiable then there is a finite unsatisfiable set of ground instances from the Herbrand universe... | Herbrand interpretation | 0.783046 |
85,107 | In 1962, Donald Caspar and Aaron Klug published an article on the geometry of viral capsids that applied and expanded upon concepts from Goldberg and Fuller. H.S.M. Coxeter published an article in 1971 covering much of the same information. | Goldberg–Coxeter construction | 0.783045 |
85,108 | The Goldberg–Coxeter construction or Goldberg–Coxeter operation (GC construction or GC operation) is a graph operation defined on regular polyhedral graphs with degree 3 or 4. It also applies to the dual graph of these graphs, i.e. graphs with triangular or quadrilateral "faces". The GC construction can be thought of a... | Goldberg–Coxeter construction | 0.783045 |
85,109 | The chemistry of acid dyes is complex and diverse. Most acid dyes are related in basic structure to the following: Anthraquinone type: Many acid dyes are synthesized from chemical intermediates that form anthraquinone-like structures as their final state. Many blue dyes have this structure as their basic shape. The str... | Acid dye | 0.783044 |
85,110 | The theorem holds for quantum states in a Hilbert space of any dimension. For simplicity, consider the deleting transformation for two identical qubits. If two qubits are in orthogonal states, then deletion requires that | 0 ⟩ A | 0 ⟩ B | A ⟩ C → | 0 ⟩ A | 0 ⟩ B | A 0 ⟩ C {\displaystyle |0\rangle _{A}|0\rangle _{B}|A\r... | Quantum no-deleting theorem | 0.783043 |
85,111 | Physicist Arun K. Pati along with Samuel L. Braunstein proved this theorem. The no-deleting theorem, together with the no-cloning theorem, underpin the interpretation of quantum mechanics in terms of category theory, and, in particular, as a dagger symmetric monoidal category. This formulation, known as categorical qua... | Quantum no-deleting theorem | 0.783043 |
85,112 | In physics, the no-deleting theorem of quantum information theory is a no-go theorem which states that, in general, given two copies of some arbitrary quantum state, it is impossible to delete one of the copies. It is a time-reversed dual to the no-cloning theorem, which states that arbitrary states cannot be copied. T... | Quantum no-deleting theorem | 0.783043 |
85,113 | The major fields covered by the libraries contained therein were: Elementary particle data Graphics and plotting Histograming I/O and structured data storage Numerical analysis Statistics and data analysis Detector simulation and Hadronic event generationLower-level parts of the CERN Program Library were most prominent... | CERN Program Library | 0.783042 |
85,114 | The CERN Program Library (CERNLIB) is a collection of general purpose software libraries and program modules for scientific computing, developed at the European Organization for Nuclear Research CERN. The application area of the library focuses on physics research, in particular high energy physics, involving general m... | CERN Program Library | 0.783042 |
85,115 | (In fact, uncountable Grothendieck universes provide models of set theory with the natural ∈-relation, natural powerset operation etc.). Elements of a Grothendieck universe are sometimes called small sets. The idea of universes is due to Alexander Grothendieck, who used them as a way of avoiding proper classes in algeb... | Grothendieck universe | 0.783041 |
85,116 | The formula (1) is known as Rabi formula. Now after time t the probability that the system in state | 0 ⟩ {\displaystyle |0\rangle } is given by | ⟨ 0 | ψ ( t ) ⟩ | 2 = 1 − sin 2 ( θ ) sin 2 ( ( E + − E − ) t 2 ℏ ) {\displaystyle {|\langle \ 0|\psi (t)\rangle |}^{2}=1-\sin ^{2}(\theta )\sin ^{2}\left({\frac {(E_{+}... | Rabi cycle | 0.783041 |
85,117 | In physics, the Rabi cycle (or Rabi flop) is the cyclic behaviour of a two-level quantum system in the presence of an oscillatory driving field. A great variety of physical processes belonging to the areas of quantum computing, condensed matter, atomic and molecular physics, and nuclear and particle physics can be conv... | Rabi cycle | 0.783041 |
85,118 | For example, a research paper published in 1999, by scientists from Finland's National Public Health Institute, reports the effect of environmental chemicals and changes in sex ratio over 250 years in Finland. This scientific team evaluated whether Finnish long-term data are compatible with the hypothesis that the decr... | Human sex ratio | 0.78304 |
85,119 | Another possible contributory factor is an aging population, with a higher than normal proportion of relatively elderly people, given that, due to higher differential mortality rates, the ratio of males to females reduces for each year of age. In the evolutionary biology of sexual reproduction the operational sex ratio... | Human sex ratio | 0.78304 |
85,120 | Pierre-Simon Laplace (1778) used human sex ratio as an example in his development of probability theory. He considered the statistics of almost half a million births; the statistics showed an excess of boys compared to girls. He concluded by calculation of a p-value that the excess was a real, but unexplained, effect. | Human sex ratio | 0.78304 |
85,121 | The human sex ratio at birth has been an object of study since early in the history of statistics, as it is easily recorded and a large number for sufficiently large populations. An early researcher was John Arbuthnot (1710), who in modern terms, performed statistical hypothesis testing, computing the p-value (via a si... | Human sex ratio | 0.78304 |
85,122 | For most of the 20th century in Russia (and the Soviet Union), extremely premature newborns (less than 28 weeks gestational age, or less than 1000 grams in weight, or less than 35 centimeters in length) were not counted as a live birth until they had survived for seven days; if that infant died in those first 168 hours... | Human sex ratio | 0.78304 |
85,123 | Certain idiosyncratic terms are occasionally found in the literature. For example, the term clanking replicator was once used by Drexler to distinguish macroscale replicating systems from the microscopic nanorobots or "assemblers" that nanotechnology may make possible, but the term is informal and is rarely used by oth... | Clanking replicator | 0.78304 |
85,124 | A self-replicating machine is a type of autonomous robot that is capable of reproducing itself autonomously using raw materials found in the environment, thus exhibiting self-replication in a way analogous to that found in nature. The concept of self-replicating machines has been advanced and examined by Homer Jacobson... | Clanking replicator | 0.78304 |
85,125 | In the spirit of the 1980 "Advanced Automation for Space Missions" study, the NASA Institute for Advanced Concepts began several studies of self-replicating system design in 2002 and 2003. Four phase I grants were awarded: Hod Lipson (Cornell University), "Autonomous Self-Extending Machines for Accelerating Space Explo... | Clanking replicator | 0.78304 |
85,126 | In mathematics, more precisely in operator theory, a sectorial operator is a linear operator on a Banach space, whose spectrum in an open sector in the complex plane and whose resolvent is uniformly bounded from above outside any larger sector. Such operators might be unbounded. Sectorial operators have applications in... | Sectorial operator | 0.783036 |
85,127 | Stephen Barr said about the book, "Like the famous Feynman Lectures on Physics, this book has the flavor of a good blackboard lecture". Michael Peskin's review in Classical and Quantum Gravity said, "This is quantum field theory taught at the knee of an eccentric uncle; one who loves the grandeur of his subject, has a ... | Quantum Field Theory in a Nutshell | 0.783034 |
85,128 | Based on this problem description an appropriate scope of the process is chosen. A simulation approach is chosen to model the development process. Such a model is then calibrated using empirical data and then used to conduct simulation based investigations. A detailed description of each step in general can be found in... | Software Process simulation | 0.783034 |
85,129 | In molecular biology, members of the KIN2/PAR-1/MARK kinase family of proteins are kinases that are conserved from yeast to human and share the same domain organisation: an N-terminal kinase domain and a C-terminal kinase associated domain 1 (KA1). Some members of this family also contain an UBA domain (ubiquitin-assoc... | KIN2/PAR-1/MARK kinase family | 0.783034 |
85,130 | In assessing the study methodology, an editorial in Global Change Biology stated, "An unbiased review of the literature would still find declines, but estimates based on this 'unidirectional' methodology are not credible. However, according to the authors of that review "more than half of the surveys were obtained from... | Insect biodiversity | 0.783033 |
85,131 | A total of 16 built, known also as an F.3 Interim version or F.6 Interim Version, 15 later modified to F.6 standard.Lightning T.4 Two-seat side-by-side training version, based on the F.1A; two prototypes and 20 production built, two aircraft later converted to T.5 prototypes, two aircraft later converted to T.54.Lightn... | English Electric Lightning | 0.783033 |
85,132 | The Export Lightning also retained the difficulty of maintenance, and serviceability rates suffered. The F.53 was generally well regarded by its pilots, and its adaptation to multiple roles showed the skill of its designers.In 1963, BAC Warton was working on the preliminary design of a two-seat Lightning development wi... | English Electric Lightning | 0.783033 |
85,133 | Relation – Table – Column – Row – View – Database transaction – Transaction log – history of actions executed by a database management system to guarantee ACID properties over crashes or hardware failures. Also called "transaction journal", "database log" or "binary log". Database trigger – procedural code that is auto... | Outline of databases | 0.78303 |
85,134 | History of databases – History of database management systems –: | Outline of databases | 0.78303 |
85,135 | Object database – database management system in which information is represented in the form of objects as used in object-oriented programming. Also called an "object-oriented database management system". Entity–attribute–value model – | Outline of databases | 0.78303 |
85,136 | Foreign key – referential constraint between two tables. Primary key – Superkey – set of attributes of a relation variable for which it holds that in all relations assigned to that variable, there are no two distinct tuples (rows) that have the same values for the attributes in this set. Surrogate key – unique identifi... | Outline of databases | 0.78303 |
85,137 | Database management system (DBMS) – software package with computer programs that control the creation, maintenance, and use of a database. Database connection – facility in computer science that allows client software to communicate with database server software, whether on the same machine or not. Datasource – name gi... | Outline of databases | 0.78303 |
85,138 | Database usage requirements – Database theory – encapsulates a broad range of topics related to the study and research of the theoretical realm of databases and database management systems. Database machine – or is a computer or special hardware that stores and retrieves data from a database. Also called a "back end pr... | Outline of databases | 0.78303 |
85,139 | Database security – Database activity monitoring (DAM) – database security technology for monitoring and analyzing database activity that operates independently of the database management system (DBMS) and does not rely on any form of native (DBMS-resident) auditing or native logs such as trace or transaction logs. Dat... | Outline of databases | 0.78303 |
85,140 | Relational database management system (RDBMS) – database management system (DBMS) that is based on the relational model as introduced by E. Relational model – for database management is a database model based on first-order predicate logic, first formulated and proposed in 1969 by Edgar F. Object–relational database (O... | Outline of databases | 0.78303 |
85,141 | Relational algebra – offshoot of first-order logic (and of algebra of sets), deals with a set of finitary relations (see also relation (database)) that is closed under certain operators. Relational calculus – consists of two calculi, the tuple relational calculus and the domain relational calculus, that are part of the... | Outline of databases | 0.78303 |
85,142 | Database management system – Database model – Database normalization – organizing tables based on their attributes so that the data presented can avoid having redundancy and dependency. Database storage structures – Distributed database management system – Federated database system – type of meta-database management sy... | Outline of databases | 0.78303 |
85,143 | Database languages – Data definition language – Data manipulation language – Query language – Information retrieval query language – query language used to make queries into database, where the semantics of the query are defined not by a precise rendering of a formal syntax, but by an interpretation of the most suitabl... | Outline of databases | 0.78303 |
85,144 | Database administration – work done by a database administrator, some of which may be automated. Query optimization – function of many relational database management systems in which multiple query plans for satisfying a query are examined and a good query plan is identified. Database replication – | Outline of databases | 0.78303 |
85,145 | Open Database Connectivity – Query language – Query optimizer – component of a database management system that attempts to determine the most efficient way to execute a query. Query plan – ordered set of steps used to access or modify information in a SQL relational database management system. Also called a "query exec... | Outline of databases | 0.78303 |
85,146 | Anchor Modeling – Column-oriented DBMS – database management system (DBMS) that stores data tables as sections of columns of data rather than as rows of data, like most relational DBMSs. Data Vault Modeling – HOLAP – MOLAP – stands for Multidimensional Online Analytical Processing. ROLAP – stands for Relational Online ... | Outline of databases | 0.78303 |
85,147 | Government database – collects personal information for various reasons (mass surveillance, Schengen Information System in the European Union, social security, statistics, etc.). Graph database – uses graph structures with nodes, edges, and properties to represent and store data. Knowledge base – special kind of databa... | Outline of databases | 0.78303 |
85,148 | Configuration management database – Cooperative database – holds information on customers and their transactions. Correlation database – database management system (DBMS) that is data model independent and designed to efficiently handle unplanned, ad hoc queries in an analytical system environment. Current database – c... | Outline of databases | 0.78303 |
85,149 | Cloud database – runs on a cloud computing platform, such as Amazon EC2, GoGrid and Rackspace. Collection database – collection catalog of a museum or archive implemented using a computerized database, in which the institution's objects or material are catalogued. Collective Optimization Database – open repository to e... | Outline of databases | 0.78303 |
85,150 | List of object-oriented database management systems – Comparison of object–relational database management systems – List of relational database management systems – Comparison of relational database management systems – MySQL (outline) – Document-oriented database – computer program designed for storing, retrieving, an... | Outline of databases | 0.78303 |
85,151 | Absolutely closed See H-closedAccessible See T 1 {\displaystyle T_{1}} .Accumulation point See limit point.Alexandrov topology The topology of a space X is an Alexandrov topology (or is finitely generated) if arbitrary intersections of open sets in X are open, or equivalently, if arbitrary unions of closed sets are clo... | Punctured plane | 0.783029 |
85,152 | L-space An L-space is a hereditarily Lindelöf space which is not hereditarily separable. A Suslin line would be an L-space.Larger topology See Finer topology.Limit point A point x in a space X is a limit point of a subset S if every open set containing x also contains a point of S other than x itself. This is equivalen... | Punctured plane | 0.783029 |
85,153 | {\displaystyle {\mathcal {B}}.} Thus B {\displaystyle {\mathcal {B}}} is a subbase for the topology it generates.Subbasis See Subbase.Subcover A cover K is a subcover (or subcovering) of a cover L if every member of K is a member of L.Subcovering See Subcover. Submaximal space A topological space is said to be submaxim... | Punctured plane | 0.783028 |
85,154 | We say that Y {\displaystyle Y} has the f {\displaystyle f} -strong topology if, for every subset U ⊂ Y {\displaystyle U\subset Y} , one has that U {\displaystyle U} is open in Y {\displaystyle Y} if and only if f − 1 ( U ) {\displaystyle f^{-1}(U)} is open in X {\displaystyle X} Stronger topology See Finer topology. B... | Punctured plane | 0.783028 |
85,155 | Every sequentially compact space is countably compact, and every first-countable, countably compact space is sequentially compact.Short map See metric mapSimply connected A space is simply connected if it is path-connected and every loop is homotopic to a constant map.Smaller topology See Coarser topology.Sober In a so... | Punctured plane | 0.783028 |
85,156 | S-space An S-space is a hereditarily separable space which is not hereditarily Lindelöf.Scattered A space X is scattered if every nonempty subset A of X contains a point isolated in A.Scott The Scott topology on a poset is that in which the open sets are those Upper sets inaccessible by directed joins.Second category S... | Punctured plane | 0.783028 |
85,157 | The minimum Wiener connector is useful in applications in which one wishes to learn about the relationship between a set of vertices in a graph. For example, in biology, it provides insight into how a set of proteins in a protein–protein interaction network are related, in social networks (like Twitter), it demonstrate... | Wiener connector | 0.783027 |
85,158 | Networked games and simulation tools routinely use dead reckoning to predict where an actor should be right now, using its last known kinematic state (position, velocity, acceleration, orientation, and angular velocity). This is primarily needed because it is impractical to send network updates at the rate that most ga... | Pedestrian dead reckoning | 0.783027 |
85,159 | In navigation, dead reckoning is the process of calculating the current position of a moving object by using a previously determined position, or fix, and incorporating estimates of speed, heading (or direction or course), and elapsed time. The corresponding term in biology, to describe the processes by which animals u... | Pedestrian dead reckoning | 0.783027 |
85,160 | In network theory, the Wiener connector is a means of maximizing efficiency in connecting specified "query vertices" in a network. Given a connected, undirected graph and a set of query vertices in a graph, the minimum Wiener connector is an induced subgraph that connects the query vertices and minimizes the sum of sho... | Wiener connector | 0.783027 |
85,161 | In geometry, a bitangent to a curve C is a line L that touches C in two distinct points P and Q and that has the same direction as C at these points. That is, L is a tangent line at P and at Q. | Bitangent | 0.783026 |
85,162 | In general, an algebraic curve will have infinitely many secant lines, but only finitely many bitangents. Bézout's theorem implies that an algebraic plane curve with a bitangent must have degree at least 4. The case of the 28 bitangents of a quartic was a celebrated piece of geometry of the nineteenth century, a relati... | Bitangent | 0.783026 |
85,163 | A bitangent differs from a secant line in that a secant line may cross the curve at the two points it intersects it. One can also consider bitangents that are not lines; for instance, the symmetry set of a curve is the locus of centers of circles that are tangent to the curve in two points. Bitangents to pairs of circl... | Bitangent | 0.783026 |
85,164 | Deformation of the crystal will cause variation in the size of the diffraction spot. For a cylindrically bent crystal the Bragg planes in the crystal lattice will lie on Archimedean spirals (with the exception of those orientated tangentially and radially to the curvature of the bend, which are respectively cylindrical... | Diffraction topography | 0.783025 |
85,165 | The spatial resolution achievable in topographic images can be limited by one or several of three factors: the resolution (grain or pixel size) of the detector, the experimental geometry, and intrinsic diffraction effects. First, the spatial resolution of an image can obviously not be better than the grain size (in the... | Diffraction topography | 0.783025 |
85,166 | The manifold topographic techniques can be categorized according to several criteria. One of them is the distinction between restricted-beam techniques on the one hand (such as section topography or pinhole topography) and extended-beam techniques on the other hand, which use the full width and intensity of the incomin... | Diffraction topography | 0.783025 |
85,167 | Journal of Applied Physics. AIP Publishing. 46 (7): 2845–2848. | Diffraction topography | 0.783025 |
85,168 | "The use of synchrotron edge topography to study polytype nearest neighbour relationships in SiC" (PDF). Radiation Physics and Chemistry. Elsevier BV. | Diffraction topography | 0.783025 |
85,169 | "The early days of high-resolution X-ray topography". Journal of Physics D: Applied Physics. IOP Publishing. | Diffraction topography | 0.783025 |
85,170 | Journal of Applied Physics. AIP Publishing. 29 (3): 597–598. | Diffraction topography | 0.783025 |
85,171 | Reviews Lang, A. R.: Techniques and interpretation in X-ray topography. In: Diffraction and Imaging Techniques in Materials Science (edited by Amelinckx S., Gevers R. and Van Landuyt J.) 2nd ed. | Diffraction topography | 0.783025 |
85,172 | The diffraction power of a crystalline material, and thus the intensity of the diffracted beam, changes with the type and number of atoms inside the crystal unit cell. This fact is quantitatively expressed by the structure factor. Different materials have different structure factors, and similarly for different phases ... | Diffraction topography | 0.783025 |
85,173 | When the beam hits the crystalline sample, Bragg diffraction occurs, i.e. the incident wave is reflected by the atoms on certain lattice planes of the sample, on condition that it hits those planes at the right Bragg angle. Diffraction from sample can take place either in reflection geometry (Bragg case), with the beam... | Diffraction topography | 0.783025 |
85,174 | (1999). "A new diffractometer for materials science and imaging at HASYLAB beamline G3". Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment. | Diffraction topography | 0.783025 |
85,175 | Journal of Physics D: Applied Physics. IOP Publishing. 36 (10A): A74–A78. | Diffraction topography | 0.783025 |
85,176 | Journal of Physics D: Applied Physics. IOP Publishing. 34 (10A): A47–A51. | Diffraction topography | 0.783025 |
85,177 | "μm-resolved high resolution X-ray diffraction imaging for semiconductor quality control". Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms. Elsevier BV. | Diffraction topography | 0.783025 |
85,178 | (1999-09-20). "X-ray imaging and diffraction from surface phonons on GaAs". Applied Physics Letters. | Diffraction topography | 0.783025 |
85,179 | (1998-10-19). "Visualization of 10 μm surface acoustic waves by stroboscopic x-ray topography". Applied Physics Letters. | Diffraction topography | 0.783025 |
85,180 | Interestingly, Degas was known to be in correspondence with chemist Marcellin Berthelot, considered the father of organic synthetic chemistry in France. Pierre-Auguste Renoir’s later paintings relied heavily on alizarin crimson. He also employed cobalt blue or a mixture of ultramarine and cobalt blue, a synthetic pigme... | Synthetic dye | 0.783023 |
85,181 | Synthetic colorants gained popularity as quickly with artists as with industry. The painters of the impressionist school in particular were famous early adopters. Critical reviews of Impressionists’ blues made comparisons to laundresses’ tubs, in particular the practice of laundry bluing, and to chemical waste dumped i... | Synthetic dye | 0.783023 |
85,182 | The algebra necessary for this example is easily carried out by a web service that computes normal form coordinate transforms of systems of differential equations, autonomous or non-autonomous, deterministic or stochastic.Consider the 2D system in variables u = ( y , z ) {\displaystyle u=(y,z)} evolving according to th... | Linearization theorem | 0.783017 |
85,183 | In mathematics, Kuiper's theorem (after Nicolaas Kuiper) is a result on the topology of operators on an infinite-dimensional, complex Hilbert space H. It states that the space GL(H) of invertible bounded endomorphisms of H is such that all maps from any finite complex Y to GL(H) are homotopic to a constant, for the nor... | Contractibility of unit sphere in Hilbert space | 0.783017 |
85,184 | For instance, the first idea “Angel” is broken down into “Inferior deities or demi-gods in polytheistic religion,” “the philosophical consideration of pure intelligences, spiritual substances, supra-human persons” and seven other subtopics. After this is the references section (for instance, “inferior deities or demi-g... | A Syntopicon | 0.783016 |
85,185 | The dynamical symmetry group of the n dimensional quantum harmonic oscillator is the special unitary group SU(n). As an example, the number of infinitesimal generators of the corresponding Lie algebras of SU(2) and SU(3) are three and eight respectively. This leads to exactly three and eight independent conserved quant... | Symmetry in quantum mechanics | 0.783016 |
85,186 | The representations of the group then describe the ways that the group G (or its Lie algebra) can act on a vector space. (The vector space might be, for example, the space of eigenvectors for a Hamiltonian having G as its symmetry group.) We denote the representations using a capital D. One can then differentiate D to ... | Symmetry in quantum mechanics | 0.783016 |
85,187 | The generators (whether matrices or differential operators) satisfy the commutation relations: where fabc are the (basis dependent) structure constants of the group. This makes, together with the vector space property, the set of all generators of a group a Lie algebra. Due to the antisymmetry of the bracket, the struc... | Symmetry in quantum mechanics | 0.783016 |
85,188 | (See the discussion below of the commutator.) One aspect of generators in theoretical physics is they can be constructed themselves as operators corresponding to symmetries, which may be written as matrices, or as differential operators. In quantum theory, for unitary representations of the group, the generators requir... | Symmetry in quantum mechanics | 0.783016 |
85,189 | the group elements, g, in G are functions of the parameters: and all parameters set to zero returns the identity element of the group: Group elements are often matrices which act on vectors, or transformations acting on functions. The generators of the group are the partial derivatives of the group elements with respec... | Symmetry in quantum mechanics | 0.783016 |
85,190 | These symmetries, which are represented by Lie superalgebras, have not been confirmed experimentally. It is now believed that they are broken symmetries, if they exist. But it has been speculated that dark matter is constitutes gravitinos, a spin 3/2 particle with mass, its supersymmetric partner being the graviton. | Symmetry in quantum mechanics | 0.783016 |
85,191 | A Lie superalgebra is an algebra in which (suitable) basis elements either have a commutation relation or have an anticommutation relation. Symmetries have been proposed to the effect that all fermionic particles have bosonic analogues, and vice versa. These symmetry have theoretical appeal in that no extra assumptions... | Symmetry in quantum mechanics | 0.783016 |
85,192 | Fermions therefore obey different statistics (called Fermi–Dirac statistics) than bosons (which obey Bose–Einstein statistics). One of the consequences of Fermi–Dirac statistics is the exclusion principle for fermions—no two identical fermions can share the same quantum state (in other words, the wave function of two i... | Symmetry in quantum mechanics | 0.783016 |
85,193 | Semi-integer spin particles change the sign of their wave function upon a 360 degree rotation (see more in spin–statistics theorem). Particles for which the wave function does not change sign upon exchange are called bosons, or particles with a symmetric wave function. The particles for which the wave function of the s... | Symmetry in quantum mechanics | 0.783016 |
85,194 | The concept of exchange symmetry or permutation symmetry is derived from a fundamental postulate of quantum statistics, which states that no observable physical quantity should change after exchanging two identical particles. It states that because all observables are proportional to | ψ | 2 {\displaystyle \left|\psi \... | Symmetry in quantum mechanics | 0.783016 |
85,195 | Symmetries in quantum mechanics describe features of spacetime and particles which are unchanged under some transformation, in the context of quantum mechanics, relativistic quantum mechanics and quantum field theory, and with applications in the mathematical formulation of the standard model and condensed matter physi... | Symmetry in quantum mechanics | 0.783016 |
85,196 | These equations are an expression of the fundamental properties of space and time as far as they are known today. They have a classical counterpart where the commutators are replaced by Poisson brackets. To describe spin in relativistic quantum mechanics, the Pauli–Lubanski pseudovector a Casimir operator, is the const... | Symmetry in quantum mechanics | 0.783016 |
85,197 | In special relativity, space and time can be collected into a four-position vector X = (ct, −r), and in parallel so can energy and momentum which combine into a four-momentum vector P = (E/c, −p). With relativistic quantum mechanics in mind, the time duration and spatial displacement parameters (four in total, one for ... | Symmetry in quantum mechanics | 0.783016 |
85,198 | The general form of an element of a U(2) element is parametrized by two complex numbers a and b: and for SU(2), the determinant is restricted to 1: In group theoretic language, the Pauli matrices are the generators of the special unitary group in two dimensions, denoted SU(2). Their commutation relation is the same as ... | Symmetry in quantum mechanics | 0.783016 |
85,199 | In the introduction, Weinberg explains his views on writing about physics for the nonspecialist: “When a lawyer writes for the public, he assumes that they do not know Law French or the Rule Against Perpetuities, but he does not think the worse of them for that, and he does not condescend to them… I picture the reader ... | The First Three Minutes | 0.783016 |
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