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Classification of irreducible representations of the Poincaré group
In mathematics and theoretical physics, Wigner's classification is a classification of the nonnegative ( E ≥ 0 ) {\displaystyle ~(~E\geq 0~)~}
Wigner's_classification
Hungarian-American physicist and mathematician (1902–1995)
Wigner energy Wigner lattice Wigner quasiprobability distribution Wigner's classification Wigner's disease Wigner's friend Wigner's theorem Wigner–Eckart theorem
Eugene_Wigner
Theoretical massless elementary particle
Eugene Wigner in 1939. Historically, a compatible theory that could describe this elementary particle was unknown; however, 75 years after Wigner's classification
Continuous_spin_particle
Representation theory of the symmetries of non-relativistic quantum space
given of the existence of mass and spin (normally explained in Wigner's classification of relativistic mechanics) in terms of the representation theory
Representation theory of the Galilean group
Representation_theory_of_the_Galilean_group
Representation theory of an important group in physics
unitary. For a discussion of such unitary representations, see Wigner's classification. In quantum mechanics, the state of the system is determined by
Representation theory of the Poincaré group
Representation_theory_of_the_Poincaré_group
Group of flat spacetime symmetries
integer) and are associated with particles in quantum mechanics (see Wigner's classification). In accordance with the Erlangen program, the geometry of Minkowski
Poincaré_group
Describes the objects of a given type, up to some equivalence
general relativity Segre classification – Algebraic classification of rank two symmetric tensors Wigner's classification – Classification of irreducible representations
Classification_theorem
Projection of spin along the direction of momentum
object (specifically a baseball) exhibiting an analogous phenomenon Wigner's classification Pauli–Lubanski pseudovector Griffiths, David (2008). Introduction
Helicity_(particle_physics)
Theorem in the mathematical formulation of quantum mechanics
Wigner's theorem, proved by Eugene Wigner in 1931, is a cornerstone of the mathematical formulation of quantum mechanics. The theorem specifies how physical
Wigner's_theorem
Physics-mathematics connection
crucial case of the Poincaré group, Bargmann's theorem applies. (See Wigner's classification of the representations of the universal cover of the Poincaré group
Particle physics and representation theory
Particle_physics_and_representation_theory
Group representation
understood as giving a classification of the irreducible unitary representations of the Heisenberg group. Wigner's classification for representations of
Representation_of_a_Lie_group
Wigner–Inonu contraction Wigner–Seitz cell Wigner–Seitz radius Wigner–Weyl transform Wigner–Wilkins spectrum Wigner's classification Wigner quasi-probability
List of things named after Eugene Wigner
List_of_things_named_after_Eugene_Wigner
Mathematical invariance under transformations
conserved current, in Noether's original language); and also, Wigner's classification, which says that the symmetries of the laws of physics determine
Symmetry
Boson with spin 1
the photon, for reasons beyond the scope of this article. See Wigner's classification.) The space of spin states therefore is a discrete degree of freedom
Vector_boson
Primitive cell of crystal lattices with Voronoi decomposition applied
their sides. This classification of the 24 types of voronoi polyhedra for Bravais lattices was first laid out by Boris Delaunay. The Wigner–Seitz cell around
Wigner–Seitz_cell
Group homomorphism into the general linear group over a vector space
general results called Mackey theory, which is a generalization of Wigner's classification methods. Representation theory also depends heavily on the type
Group_representation
Map from algebra to geometric transforms
rise to projective representations of the Poincaré group, as in Wigner's classification. Passing to the cover is essential, in order to include the fractional
Projective_representation
Theoretical framework in physics
mechanics Ward–Takahashi identity Wheeler–Feynman absorber theory Wigner's classification Wigner's theorem Peskin, M.; Schroeder, D. (1995). An Introduction to
Quantum_field_theory
Representation of the symmetry group of spacetime in special relativity
physicist E. P. Wigner and mathematician Valentine Bargmann with their Bargmann–Wigner program, one conclusion of which is, roughly, a classification of all unitary
Representation theory of the Lorentz group
Representation_theory_of_the_Lorentz_group
Axiomatization of quantum field theory
particles by E. P. Wigner in his famous paper of 1939; see Wigner's classification. Wigner postulated the transition probability between states to be the same
Wightman_axioms
State space for internal degrees of freedom of a subatomic particle
in terms of the representation theory of the groups above. See Wigner's classification. These groups all appear in the theory of the Standard model. For
Multiplet
Branch of mathematics that studies abstract algebraic structures
Mackey theory, which is a generalization of the methods used in Wigner's classification of representations of the Poincaré group. A Lie algebra over a
Representation_theory
(representation theory) Cartan's theorem Spinor Wigner's classification, Representation theory of the Poincaré group Wigner–Eckart theorem Stone–von Neumann theorem
List of representation theory topics
List_of_representation_theory_topics
Type of dressed particle
At first sight, this might appear to be in contradiction with Wigner's classification, which implies that the whole one-particle Hilbert space lies in
Infraparticle
Operator in quantum field theory
right-helicity anti-neutrinos each must have non-zero mass. Wigner's classification – Classification of irreducible representations of the Poincaré group Angular
Pauli–Lubanski_pseudovector
Dirac sea Spin foam Poincaré group gamma matrices Dirac adjoint Wigner's classification anyon Copenhagen interpretation locality principle Bell's theorem
List of mathematical topics in quantum theory
List_of_mathematical_topics_in_quantum_theory
matrices Gell-Mann matrices Poisson bracket Noether's theorem Wigner's classification Gauge theory Grand Unified Theory Supergroup Lie superalgebra Twistor
List_of_Lie_groups_topics
Random matrix with gaussian entries
take any real positive value. The gaussian ensembles are also called the Wigner ensembles, or the Hermite ensembles. There are many conventions for defining
Gaussian_ensemble
Wigner's classification Wigner's friend Wigner's theorem Wigner 3-j symbols Wigner crystal Wigner effect Wigner quasiprobability distribution Wigner–Eckart
Index_of_physics_articles_(W)
Israeli scientist
award of the Israel Prize to Emile Habibi), the Albert Einstein Award, the Wigner Medal, and the EMET Prize for Arts, Sciences and Culture. Yuval Ne'eman
Yuval_Ne'eman
Special state of wave and quantum systems in physics
continuum. Bound states in the continuum were first predicted in 1929 by Eugene Wigner and John von Neumann. Two potentials were described, in which BICs appear
Bound_state_in_the_continuum
Hungarian-American physicist and inventor (1898–1964)
James Franck and Max von Laue. He also met fellow Hungarian students Eugene Wigner, John von Neumann and Dennis Gabor. Szilard's doctoral dissertation on thermodynamics
Leo_Szilard
Special class of quantum states
are equivalent to its one-point and two-point correlation functions. The Wigner quasiprobability distribution of a bosonic Gaussian state is always a classical
Gaussian_state
Computer programming for quantum computers
measurement simulation, entanglement monotones, partial trace/transpose, discrete Wigner transforms, stabilizer methods, and tensor-network utilities—as well as
Quantum_programming
Chemical element with atomic number 6 (C)
applications where graphite is used as a neutron moderator, accumulation of Wigner energy followed by a sudden, spontaneous release may occur. Annealing to
Carbon
temperature and pressure, present properties of both a solid and liquid. Wigner crystal: a crystalline phase of low-density electrons. Hexatic state, a
List_of_states_of_matter
International new religious movement
(Physiology or Medicine 1963, who chaired the 1976 conference), as well as Eugene Wigner (Physics 1963). The relationship between the Unification Movement and science
Unification_Church
Elementary particle with negative charge
equation treats the electron as a point charge, but the equivalent Newton–Wigner form does not. In quantum field theory mathematical treatments of self-energy
Electron
Wigner in 1932 in the context of quantum mechanics and, later, reformulated as a general TFR by Ville in 1948 to form what is now known as the Wigner–Ville
Time–frequency_representation
Emissions from unstable atomic nuclei
of death or serious injury One of several dangerous goods transport classification signs for radioactive materials Actinides in the environment Background
Radioactive_decay
Generalized function whose value is zero everywhere except at zero
}{2}},\\0,&{\text{otherwise}}.\end{cases}}} Another example is with the Wigner semicircle distribution η ε ( x ) = { 2 π ε 2 ε 2 − x 2 , − ε < x < ε ,
Dirac_delta_function
Archimedean solid with 14 faces
as the Wigner–Seitz cell of a sodium. The background for this discovery dates back to Eugene Wigner and Frederick Seitz's proposal on the Wigner–Seitz
Truncated_octahedron
Hadron (subatomic particle) that is composed of three quarks
similar to spin. This unknown excitation was later dubbed isospin by Eugene Wigner in 1937. This belief lasted until Murray Gell-Mann proposed the quark model
Baryon
Meitner Oliphant Oppenheimer Proca Purcell Rabi Rutherford Soddy Strassmann Świątecki Szilárd Teller Thomson Walton Wigner Physics portal Category v t e
Interacting_boson_model
Type of quantum state
the Wigner quasi-probability distribution. The intensity of the light wave, its coherent excitation, is given by the displacement of the Wigner distribution
Squeezed_coherent_state
Interplay between observation, experiment, and theory in science
2420250407. ISSN 0046-2772. Wigner, Eugene Paul (1967). Symmetries and reflections. Indiana University Press. p. 15. : Wigner also differentiates between
Scientific_method
Algebraic structure used in analysis
theorem). This correspondence allows one to study the structure and classification of Lie groups in terms of Lie algebras, which are simpler objects of
Lie_algebra
Type of plane partition
rise to many familiar tessellations. The corresponding cells are known as Wigner–Seitz cells. A 2D lattice gives an irregular honeycomb tessellation, with
Voronoi_diagram
Number of heavy particles in the atomic nucleus
Meitner Oliphant Oppenheimer Proca Purcell Rabi Rutherford Soddy Strassmann Świątecki Szilárd Teller Thomson Walton Wigner Physics portal Category v t e
Mass_number
Atomic nucleus of three bound components with no paired binding
Meitner Oliphant Oppenheimer Proca Purcell Rabi Rutherford Soddy Strassmann Świątecki Szilárd Teller Thomson Walton Wigner Physics portal Category v t e
Borromean_nucleus
Meitner Oliphant Oppenheimer Proca Purcell Rabi Rutherford Soddy Strassmann Świątecki Szilárd Teller Thomson Walton Wigner Physics portal Category v t e
Ab initio methods (nuclear physics)
Ab_initio_methods_(nuclear_physics)
Ability to automatically recognize targets
continue to be developed that allow for more accuracy and speed in classification. ATR can be used to identify man-made objects such as ground and air
Automatic_target_recognition
Energy needed to remove a specified particle from an atom's nucleus
Meitner Oliphant Oppenheimer Proca Purcell Rabi Rutherford Soddy Strassmann Świątecki Szilárd Teller Thomson Walton Wigner Physics portal Category v t e
Separation_energy
theories for condensed matter, especially liquid helium." 1963 Eugene Paul Wigner United States "For his contributions to the theory of the atomic nucleus
List of Nobel laureates in Physics
List_of_Nobel_laureates_in_Physics
Guide, CG-HR-3, U.S. Department of Energy, Appendix B" (PDF). Office of Classification and Information Control, DoE. October 2005. "nh4_1.gif". Archived from
List of military nuclear accidents
List_of_military_nuclear_accidents
Type of radioactive decay
Meitner Oliphant Oppenheimer Proca Purcell Rabi Rutherford Soddy Strassmann Świątecki Szilárd Teller Thomson Walton Wigner Physics portal Category v t e
Positron_emission
Prediction in nuclear physics
Meitner Oliphant Oppenheimer Proca Purcell Rabi Rutherford Soddy Strassmann Świątecki Szilárd Teller Thomson Walton Wigner Physics portal Category v t e
Island_of_stability
Chemical element with atomic number 90 (Th)
this issue, the Chicago team discussed reactor design solutions. Eugene Wigner proposed to use the 240Pu-contaminated plutonium to drive the conversion
Thorium
Mode of radioactive decay
Meitner Oliphant Oppenheimer Proca Purcell Rabi Rutherford Soddy Strassmann Świątecki Szilárd Teller Thomson Walton Wigner Physics portal Category v t e
Double_electron_capture
Reaction that combines atomic nuclei
Meitner Oliphant Oppenheimer Proca Purcell Rabi Rutherford Soddy Strassmann Świątecki Szilárd Teller Thomson Walton Wigner Physics portal Category v t e
Nuclear_fusion
Non-associative algebras with positive-definite quadratic form
homotopy groups of the classical groups and in quantum mechanics to the classification of simple Jordan algebras. A Hurwitz algebra or composition algebra
Hurwitz's theorem (composition algebras)
Hurwitz's_theorem_(composition_algebras)
Penetrating form of electromagnetic radiation
Meitner Oliphant Oppenheimer Proca Purcell Rabi Rutherford Soddy Strassmann Świątecki Szilárd Teller Thomson Walton Wigner Physics portal Category v t e
Gamma_ray
Open convex self-dual cones
for the trace form. The classification of simple Euclidean Jordan algebras was accomplished by Jordan, von Neumann & Wigner (1934), with details of the
Symmetric_cone
Partial differential equation describing physical fields
spin-0 particles the Dirac equation for spin-1/2 particles the Bargmann–Wigner equations for particles of any spin In quantum field equations, it is common
Field_equation
Type of radioactive decay
drop Nuclear shell model Interacting boson model Ab initio Nuclides' classification Isotopes – equal Z Isobars – equal A Isotones – equal N Isodiaphers
Alpha_decay
Hungarian and American mathematician and physicist (1903–1957)
Neumann entered the Lutheran Fasori Evangélikus Gimnázium in 1914. Eugene Wigner was a year ahead of von Neumann at the school and soon became his friend
John_von_Neumann
Indian electrical engineer (born 1979)
Analysis Techniques and their Applications (CRC Press, 2023). "Wigner-Specific Research". Wigner Initiative. Retrieved 27 January 2025. "Neural Dynamics of
Ram_Bilas_Pachori
Ratio of neutrons to protons in an atomic nucleus
Meitner Oliphant Oppenheimer Proca Purcell Rabi Rutherford Soddy Strassmann Świątecki Szilárd Teller Thomson Walton Wigner Physics portal Category v t e
Neutron–proton_ratio
Manifold with inversion symmetry
complete classification of irreducible spaces, with four classical series, studied by Cartan, and two exceptional cases; the classification can be deduced
Hermitian_symmetric_space
Nuclear physics classification method
Meitner Oliphant Oppenheimer Proca Purcell Rabi Rutherford Soddy Strassmann Świątecki Szilárd Teller Thomson Walton Wigner Physics portal Category v t e
Even_and_odd_atomic_nuclei
Atomic species
Meitner Oliphant Oppenheimer Proca Purcell Rabi Rutherford Soddy Strassmann Świątecki Szilárd Teller Thomson Walton Wigner Physics portal Category v t e
Nuclide
City in Tennessee, United States
photographer in Oak Ridge during the Manhattan Project Richard White, actor Eugene Wigner, Nobel Prize-winning physicist, founding Director of the Oak Ridge National
Oak_Ridge,_Tennessee
Range of physical processes in physics
2024-08-06 at the Wayback Machine Scattering and diffraction Optics Classification and Indexing Scheme (OCIS), Optical Society of America, 1997 Lectures
Scattering
Meitner Oliphant Oppenheimer Proca Purcell Rabi Rutherford Soddy Strassmann Świątecki Szilárd Teller Thomson Walton Wigner Physics portal Category v t e
Nucleon pair breaking in fission
Nucleon_pair_breaking_in_fission
Russian mathematician
France, both in 1981, and a Guggenheim Fellowship in 1986. He received the Wigner Medal (1996) "in recognition of work on affine Lie algebras that has had
Victor_Kac
Physical theory with fields invariant under the action of local "gauge" Lie groups
work to show that the differentiable classification of smooth 4-manifolds is very different from their classification up to homeomorphism. Michael Freedman
Gauge_theory
Transformation of a nuclide to another
Meitner Oliphant Oppenheimer Proca Purcell Rabi Rutherford Soddy Strassmann Świątecki Szilárd Teller Thomson Walton Wigner Physics portal Category v t e
Nuclear_reaction
Disorder of consciousness
Laureys Stuart Hameroff Wolf Singer Others Annaka Harris David Bohm Eugene Wigner Erwin Schrödinger Marvin Minsky Max Planck Roger Penrose Susan Blackmore
Minimally_conscious_state
Different nuclides with the same neutron number
Meitner Oliphant Oppenheimer Proca Purcell Rabi Rutherford Soddy Strassmann Świątecki Szilárd Teller Thomson Walton Wigner Physics portal Category v t e
Isotone
Generalization of the one-dimensional normal distribution to higher dimensions
Power function Raised cosine Reciprocal Triangular U-quadratic Uniform Wigner semicircle supported on a semi-infinite interval Benini Benktander 1st kind
Multivariate normal distribution
Multivariate_normal_distribution
Intersection of nuclear physics and high-energy physics
Meitner Oliphant Oppenheimer Proca Purcell Rabi Rutherford Soddy Strassmann Świątecki Szilárd Teller Thomson Walton Wigner Physics portal Category v t e
High-energy_nuclear_physics
Atoms of different elements with the same number of nucleons
Meitner Oliphant Oppenheimer Proca Purcell Rabi Rutherford Soddy Strassmann Świątecki Szilárd Teller Thomson Walton Wigner Physics portal Category v t e
Isobar_(nuclide)
Fourth standardized moment in statistics
raised cosine distribution, cyan curve, excess kurtosis = −0.593762... W: Wigner semicircle distribution, blue curve, excess kurtosis = −1 U: uniform distribution
Kurtosis
Metastable excited state of a nuclide
Meitner Oliphant Oppenheimer Proca Purcell Rabi Rutherford Soddy Strassmann Świątecki Szilárd Teller Thomson Walton Wigner Physics portal Category v t e
Nuclear_isomer
In the following years, with contributions from Wolfgang Pauli, Eugene Wigner, Pascual Jordan, Werner Heisenberg and an elegant formulation of quantum
History of electromagnetic theory
History_of_electromagnetic_theory
Scientific background leading to the discovery of subatomic particles
nuclei obey Bose statistics. However, a then unpublished result of Eugene Wigner showed that a composite system with an odd number of spin-1/2 particles
Discovery_of_the_neutron
Weinberg–Witten theorem (quantum field theory) Wick's theorem (physics) Wigner–Eckart theorem (Clebsch–Gordan coefficients) Bohr–van Leeuwen theorem (physics)
List_of_theorems
Type of radioactive decay
Meitner Oliphant Oppenheimer Proca Purcell Rabi Rutherford Soddy Strassmann Świątecki Szilárd Teller Thomson Walton Wigner Physics portal Category v t e
Neutron_emission
Field of knowledge
and their fields of application. The contemporary Mathematics Subject Classification lists more than sixty first-level areas of mathematics. Before the Renaissance
Mathematics
Ratio of two stable isotopes
Meitner Oliphant Oppenheimer Proca Purcell Rabi Rutherford Soddy Strassmann Świątecki Szilárd Teller Thomson Walton Wigner Physics portal Category v t e
Stable_isotope_ratio
Ordered arrangement of atoms, ions, or molecules in a crystalline material
small piece of a single crystal used to initiate growth of a larger crystal Wigner–Seitz cell – a primitive cell of a crystal lattice with Voronoi decomposition
Crystal_structure
Fission of a nucleus via absorption of a gamma ray
Meitner Oliphant Oppenheimer Proca Purcell Rabi Rutherford Soddy Strassmann Świątecki Szilárd Teller Thomson Walton Wigner Physics portal Category v t e
Photofission
Nuclides predating the Earth's formation (found on Earth)
Meitner Oliphant Oppenheimer Proca Purcell Rabi Rutherford Soddy Strassmann Świątecki Szilárd Teller Thomson Walton Wigner Physics portal Category v t e
Primordial_nuclide
Subatomic particle; made of equal numbers of quarks and antiquarks
decided that properties other than particle mass should control their classification. There were years of delays in the subatomic particle research during
Meson
Constructs with triply-connected vertices
... vertices is 1, 2, 5, 19, ... (sequence A002851 in the OEIS). A classification according to edge connectivity is made as follows: the 1-connected and
Table_of_simple_cubic_graphs
Atoms or particles produced by nuclear fission
Meitner Oliphant Oppenheimer Proca Purcell Rabi Rutherford Soddy Strassmann Świątecki Szilárd Teller Thomson Walton Wigner Physics portal Category v t e
Nuclear_fission_product
Energy change of a nucleus after radioactive decay
Meitner Oliphant Oppenheimer Proca Purcell Rabi Rutherford Soddy Strassmann Świątecki Szilárd Teller Thomson Walton Wigner Physics portal Category v t e
Decay_energy
Generalization of the Dirac equation
isomorphic to C 4 {\displaystyle \mathbb {C} ^{4}} as a vector space. In the classification of Lorentz group representations, the representation is labelled ( 1
Dirac equation in curved spacetime
Dirac_equation_in_curved_spacetime
Reaction that splits an atomic nucleus
reaction." On 25 January 1939, after learning of Hahn's discovery from Eugene Wigner, Szilard noted, "...if enough neutrons are emitted...then it should be,
Nuclear_fission
Processes in astrophysics
Meitner Oliphant Oppenheimer Proca Purcell Rabi Rutherford Soddy Strassmann Świątecki Szilárd Teller Thomson Walton Wigner Physics portal Category v t e
P-process
WIGNERS CLASSIFICATION
WIGNERS CLASSIFICATION
WIGNERS CLASSIFICATION
WIGNERS CLASSIFICATION
WIGNERS CLASSIFICATION
WIGNERS CLASSIFICATION
WIGNERS CLASSIFICATION
WIGNERS CLASSIFICATION
WIGNERS CLASSIFICATION