In quantum mechanics, the Wigner–Weyl transform or Weyl–Wigner transform (after Hermann Weyl and Eugene Wigner) is the invertible mapping between functions...

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...

also Wigner–Weyl transform, for another definition of the Weyl transform. In theoretical physics, the Weyl transformation, named after Hermann Weyl, is...

distribution Thomas–Wigner rotation Wigner–Eckart theorem Wigner–Inonu contraction Wigner–Seitz cell Wigner–Seitz radius Wigner–Weyl transform Wigner–Wilkins spectrum...

Donder–Weyl theory Hodge−Weyl decomposition Majorana–Weyl spinor Peter–Weyl theorem Schur–Weyl duality Weyl–Berry conjecture Weyl–Groenewold product Wigner–Weyl...

arise in the phase space formulation of quantum mechanics through the Wigner transform of Heisenberg operators of canonical coordinates and momenta. These...

theorem Wigner–Inonu contraction Wigner–Seitz cell Wigner–Seitz radius Wigner–Weyl transform Wigner–Wilkins spectrum Wigner's classification Wigner quasi-probability...

using the Fourier transform to a class of integrable functions larger than the polynomial functions), see Wigner–Weyl transform. Weyl algebras and Clifford...

Wigner's theorem, proved by Eugene Wigner in 1931, is a cornerstone of the mathematical formulation of quantum mechanics. The theorem specifies how physical...

Neumann theorem#Relation to the Fourier transform for details. Canonical commutation relations Wigner–Weyl transform Stone–von Neumann theorem Projective...

representation Wigner–Weyl transform CCR and CAR algebras (for bosons and fermions respectively) Segal–Bargmann space Moyal product Weyl algebra Stone's...

quantum field theory, the Weyl equation is a relativistic wave equation for describing massless spin-1/2 particles called Weyl fermions. The equation is...

Mathematics Cotangent bundle Dynamic system Symplectic manifold Wigner–Weyl transform Physics Classical mechanics Hamiltonian mechanics Lagrangian mechanics...

finally elucidated the consistent correspondence mechanism, the Wigner–Weyl transform, that underlies an alternate equivalent mathematical representation...

quantum observables, the most famous of these schemes being the Wigner–Weyl transform. It underlies Moyal’s dynamical equation, an equivalent formulation...

and Wigner–Weyl transform). This more algebraic approach not only permits ultimately extending probability distributions in phase space to Wigner quasi-probability...

Moyal product Noncommutative geometry Noncommutative standard model Wigner–Weyl transform It is possible to have a noncommuting time coordinate as in the...

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...

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...

Royal Statistical Society B, 11, (1949), 150–210. Moyal bracket Wigner–Weyl transform Wigner quasiprobability distribution Gani, J. (1998). "Obituary: José...

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...

Quantum chaos Quantum decoherence Quantum limit Semiclassical physics Wigner–Weyl transform WKB approximation Bohm, D. (1989). Quantum Theory. Dover Publications...

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...

was the first to achieve full understanding of the Wigner–Weyl transform as an invertible transform, rather than as an unsatisfactory quantization rule...

fermion is transformed into the Newton–Wigner representation. The powerful machinery of the Foldy–Wouthuysen transform originally developed for the Dirac...

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...

the Wigner function by smearing with a Gaussian. This connection will be made more precise below, after we introduce the Segal–Bargmann transform. One...

equation for the time evolution of the Wigner function, known as Moyal equation, is then the Wigner-transform of the above von Neumann equation, ∂ W (...

fields, but this was phenomenological. Weyl found a relativistic equation in terms of the Pauli matrices; the Weyl equation, for massless spin-⁠1/2⁠ fermions...

transform Ray transfer matrix analysis de Bruijn, N. G. (1973). "A theory of generalized functions, with applications to Wigner distribution and Weyl...