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The Poisson Algebra and the Canonical Bridge to Quantum Mechanics
The Poisson Algebra and the Canonical Bridge to Quantum Mechanics
foundations results +13 more equations +1 more depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) notation 25.1: not:pq-notation 25.1 notation definition 25.2: Poisson algebra 25.2 Poisson algebra definition 25.6: Infinitesimal canonical transformation 25.6 Infinitesimal ca… definition 25.11: Generators of the Galilei transformations 25.11 Generators of th… definition 25.18: Phase-space action 25.18 Phase-space acti… definition 25.21: First-order action in general coordinates 25.21 First-order acti… postulate 25.27: Dirac's correspondence rule 25.27 Dirac's correspo… definition 25.42: Ordering rule 25.42 Ordering rule definition 25.44: Weyl and normal ordering 25.44 Weyl and normal… definition 25.50: Star product and Moyal bracket 25.50 Star product and… definition 25.52: Wigner function 25.52 Wigner function theorem 25.3: The bracket is a Lie bracket 25.3 The bracket is a… proposition 25.4: Leibniz rule and derivations 25.4 Leibniz rule and… proposition 25.7: Generating function of an infinitesimal transformation 25.7 Generating funct… proposition 25.8: The Hamiltonian generates time translation 25.8 The Hamiltonian… theorem 25.9: Noether, bracket form 25.9 Noether, bracket… proposition 25.12: The algebra of generators closes 25.12 The algebra of g… proposition 25.14: The Galilei cocycle is not a coboundary 25.14 The Galilei cocy… theorem 25.19: Hamilton's equations from the first-order action 25.19 Hamilton's equat… theorem 25.22: Faddeev–Jackiw equations and brackets 25.22 Faddeev–Jackiw e… proposition 25.25: Noncommuting coordinates and the Landau degeneracy 25.25 Noncommuting coo… proposition 25.29: Canonical commutation relations 25.29 Canonical commut… corollary 25.30: The relation cannot be realized by matrices 25.30 The relation can… proposition 25.31: The Heisenberg equation is the evolution equation 25.31 The Heisenberg e… equation 25.5: eq:pq-infinitesimal-ct eq. (25.5) equation 25.15: eq:pq-galilei-central eq. (25.15) equation 25.20: eq:pq-phase-space-action eq. (25.20) equation 25.25: eq:pq-fj-bracket eq. (25.25) equation 25.28: eq:pq-landau-bracket eq. (25.28) equation 25.31: eq:pq-dirac-rule eq. (25.31) equation 25.33: eq:pq-ccr eq. (25.33) equation 25.34: eq:pq-heisenberg eq. (25.34) equation 25.40: eq:pq-forced-quadratic eq. (25.40) equation 25.51: eq:pq-star eq. (25.51) equation 25.53: eq:pq-wigner eq. (25.53) equation 25.54: eq:pq-wigner-marginal-x eq. (25.54) equation 25.56: eq:pq-wigner-overlap eq. (25.56) The chain of The Poisson Algebra and the Canonical Bridge to Quantum Mechanics: 37 of 51 objects, read left to right from what the chapter assumes to what tests it. Solid lines are declared logical edges, dashed ones were inferred from the structure of the source. Click any node to open its own chain.