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searching for Poisson bracket 13 found (89 total)

Quantization (physics) (1,513 words) [view diff] exact match in snippet view article

operators, then no quantization scheme can perfectly reproduce the Poisson bracket relations among the classical observables. There is a way to perform

Superintegrable Hamiltonian system (549 words) [view diff] exact match in snippet view article find links to article

s i j {\displaystyle s_{ij}} on N {\displaystyle N} such that the Poisson bracket of integrals of motion reads { F i , F j } = s i j ∘ F {\displaystyle

Batalin–Vilkovisky formalism (3,114 words) [view diff] exact match in snippet view article find links to article

for the Gerstenhaber bracket are Buttin bracket, antibracket, or odd Poisson bracket. The antibracket satisfies | ( a , b ) | = | a | + | b | − 1 {\displaystyle

Hamiltonian constraint of LQG (7,798 words) [view diff] exact match in snippet view article find links to article

will have vanishing Poisson bracket with the volume, so the only contribution will come from the connection. As the Poisson bracket is already proportional

Garnier integrable system (1,403 words) [view diff] exact match in snippet view article find links to article

N {\displaystyle r=1,\cdots ,N} on the phase space satisfying the Poisson bracket { X ( r ) a , X ( s ) b } = δ r s f c a b X ( r ) c . {\displaystyle

Poisson–Lie group (1,124 words) [view diff] exact match in snippet view article find links to article

Poisson–Lie group is a Lie group G {\displaystyle G} equipped with a Poisson bracket for which the group multiplication μ : G × G → G {\displaystyle \mu

Ashtekar variables (1,856 words) [view diff] exact match in snippet view article find links to article

A b k , {\displaystyle \ A_{b}^{k}\ ,} in that it satisfies the Poisson bracket relation { E ~ j a ( x ) , A b k ( y ) } = 8 π G N e w t

Symplectic group (3,109 words) [view diff] exact match in snippet view article find links to article

physics as the symmetries of canonical coordinates preserving the Poisson bracket. Consider a system of n particles, evolving under Hamilton's equations

Wigner–Weyl transform (2,271 words) [view diff] exact match in snippet view article find links to article

all quantization schemes, comes as close as possible to mapping the Poisson bracket on the classical side to the commutator on the quantum side. (An exact

Alexandre Mikhailovich Vinogradov (2,415 words) [view diff] exact match in snippet view article find links to article

ISSN 0373-0956. Cabras, A.; Vinogradov, A.M. (1992). "Extensions of the poisson bracket to differential forms and multi-vector fields". Journal of Geometry

Mori-Zwanzig formalism (1,733 words) [view diff] exact match in snippet view article find links to article

L={\frac {1}{\hbar }}[H,\cdot ]} in the quantum case and using the Poisson bracket L = − i { H , ⋅ } {\displaystyle L=-i\{H,\cdot \}} in the classical

Hamiltonian constraint (3,745 words) [view diff] exact match in snippet view article find links to article

V\}F_{ab}^{k}{\tilde {\epsilon }}^{abc}} upon using Thiemann's identity. This Poisson bracket is replaced by a commutator upon quantization. It turns out that a

Universal enveloping algebra (8,954 words) [view diff] exact match in snippet view article find links to article

(anti-)commutator of the superalgebra lifts to an (anti-)commuting Poisson bracket. Another possibility is to use something other than the tensor algebra