In quantum mechanics, the Wigner–Weyl transform or Weyl–Wigner transform (after Hermann Weyl and Eugene Wigner) is the invertible mapping between functions...
15 KB (2,271 words) - 01:06, 27 August 2024
Hermann Weyl in 1927, in a context related to representation theory in mathematics (see Weyl quantization). In effect, it is the Wigner–Weyl transform of the...
38 KB (5,299 words) - 06:00, 31 August 2024
also Wigner–Weyl transform, for another definition of the Weyl transform. In theoretical physics, the Weyl transformation, named after Hermann Weyl, is...
3 KB (697 words) - 10:21, 17 October 2023
distribution Thomas–Wigner rotation Wigner–Eckart theorem Wigner–Inonu contraction Wigner–Seitz cell Wigner–Seitz radius Wigner–Weyl transform Wigner–Wilkins spectrum...
50 KB (5,212 words) - 09:16, 13 September 2024
using the Fourier transform to a class of integrable functions larger than the polynomial functions), see Wigner–Weyl transform. Weyl algebras and Clifford...
25 KB (3,592 words) - 04:03, 9 September 2024
arise in the phase space formulation of quantum mechanics through the Wigner transform of Heisenberg operators of canonical coordinates and momenta. These...
26 KB (3,908 words) - 12:52, 20 November 2023
Donder–Weyl theory Hodge−Weyl decomposition Majorana–Weyl spinor Peter–Weyl theorem Schur–Weyl duality Weyl–Berry conjecture Weyl–Groenewold product Wigner–Weyl...
4 KB (272 words) - 12:27, 22 March 2023
theorem Wigner–Inonu contraction Wigner–Seitz cell Wigner–Seitz radius Wigner–Weyl transform Wigner–Wilkins spectrum Wigner's classification Wigner quasi-probability...
3 KB (220 words) - 18:45, 21 March 2022
Canonical commutation relation (section Weyl relations)
finally elucidated the consistent correspondence mechanism, the Wigner–Weyl transform, that underlies an alternate equivalent mathematical representation...
20 KB (2,992 words) - 08:16, 12 July 2024
Stone–von Neumann theorem (redirect from Weyl representation)
representation Wigner–Weyl transform CCR and CAR algebras (for bosons and fermions respectively) Segal–Bargmann space Moyal product Weyl algebra Stone's...
27 KB (3,687 words) - 16:58, 25 May 2024
Neumann theorem#Relation to the Fourier transform for details. Canonical commutation relations Wigner–Weyl transform Stone–von Neumann theorem Projective...
32 KB (5,894 words) - 17:23, 16 April 2024
quantum field theory, the Weyl equation is a relativistic wave equation for describing massless spin-1/2 particles called Weyl fermions. The equation is...
28 KB (4,772 words) - 20:55, 20 June 2024
Wigner's theorem, proved by Eugene Wigner in 1931, is a cornerstone of the mathematical formulation of quantum mechanics. The theorem specifies how physical...
31 KB (4,715 words) - 22:01, 2 May 2024
Mathematics Cotangent bundle Dynamic system Symplectic manifold Wigner–Weyl transform Physics Classical mechanics Hamiltonian mechanics Lagrangian mechanics...
18 KB (2,130 words) - 14:12, 13 June 2024
f_{2}]=\Phi [f_{1}]\Phi [f_{2}].\,} where Φ {\displaystyle \Phi } is the Wigner–Weyl transform. The star product is not commutative in general, but goes over to...
7 KB (1,067 words) - 13:11, 20 August 2024
quantum observables, the most famous of these schemes being the Wigner–Weyl transform. It underlies Moyal’s dynamical equation, an equivalent formulation...
11 KB (1,359 words) - 19:13, 23 January 2024
Moyal product (redirect from Weyl–Groenewold product)
two-dimensional euclidean phase space) is given in the article on the Wigner–Weyl transform: two Gaussians compose with this ★-product according to a hyperbolic...
11 KB (1,622 words) - 07:00, 25 August 2024
Royal Statistical Society B, 11, (1949), 150–210. Moyal bracket Wigner–Weyl transform Wigner quasiprobability distribution Gani, J. (1998). "Obituary: José...
6 KB (491 words) - 12:37, 6 August 2024
and Wigner–Weyl transform). This more algebraic approach not only permits ultimately extending probability distributions in phase space to Wigner quasi-probability...
52 KB (9,273 words) - 03:43, 13 September 2024
Moyal product Noncommutative geometry Noncommutative standard model Wigner–Weyl transform It is possible to have a noncommuting time coordinate as in the...
8 KB (1,084 words) - 07:27, 25 July 2024
not semisimple and it does not satisfy Weyl's theorem on complete reducibility.) It was introduced by Eugene Wigner, to classify particles and fields in...
10 KB (1,422 words) - 21:11, 24 September 2023
Quantum chaos Quantum decoherence Quantum limit Semiclassical physics Wigner–Weyl transform WKB approximation Bohm, D. (1989). Quantum Theory. Dover Publications...
12 KB (1,507 words) - 23:47, 23 May 2024
phase space as A(x, p) through the Wigner transform. Conversely, this operator may be recovered by the Weyl transform. The expectation value of the observable...
27 KB (3,591 words) - 00:31, 29 August 2024
was the first to achieve full understanding of the Wigner–Weyl transform as an invertible transform, rather than as an unsatisfactory quantization rule...
7 KB (624 words) - 11:10, 17 April 2023
fermion is transformed into the Newton–Wigner representation. The powerful machinery of the Foldy–Wouthuysen transform originally developed for the Dirac...
27 KB (3,113 words) - 21:29, 15 August 2024
Dirac equation (section Weyl theory)
Moreover, in the limit of zero mass, the Dirac equation reduces to the Weyl equation. In the context of quantum field theory, the Dirac equation is reinterpreted...
78 KB (12,978 words) - 16:52, 6 September 2024
Thomas–Wigner rotation or Wigner rotation. If a sequence of non-collinear boosts returns an object to its initial velocity, then the sequence of Wigner rotations...
44 KB (6,411 words) - 06:51, 14 September 2024
3-j symbol (redirect from Wigner 3-j symbol)
In quantum mechanics, the Wigner 3-j symbols, also called 3-jm symbols, are an alternative to Clebsch–Gordan coefficients for the purpose of adding angular...
33 KB (5,972 words) - 13:26, 20 August 2024
Linear canonical transformation (redirect from Linear canonical transform)
transform Ray transfer matrix analysis de Bruijn, N. G. (1973). "A theory of generalized functions, with applications to Wigner distribution and Weyl...
21 KB (3,124 words) - 14:00, 28 May 2024
Segal–Bargmann space (redirect from Bargmann transform)
the Wigner function by smearing with a Gaussian. This connection will be made more precise below, after we introduce the Segal–Bargmann transform. One...
13 KB (2,004 words) - 18:53, 26 January 2024