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Constrained Hamiltonian Systems: the Dirac–Bergmann Formalism
Constrained Hamiltonian Systems: the Dirac–Bergmann Formalism
foundations +1 more results +6 more equations 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) 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 26.1: Weak and strong equality 26.1 Weak and strong… definition 26.3: Singular Lagrangian 26.3 Singular Lagrang… definition 26.8: Total Hamiltonian 26.8 Total Hamiltonian definition 26.9: Consistency conditions 26.9 Consistency cond… definition 26.11: The final constraint set 26.11 The final constr… definition 26.12: First and second class 26.12 First and second… definition 26.16: Extended Hamiltonian 26.16 Extended Hamilto… definition 26.20: Dirac bracket 26.20 Dirac bracket definition 26.23: Gauge conditions 26.23 Gauge conditions notation 26.28: Field systems 26.28 Field systems notation 26.36: Gauge fields and their SI dimensions 26.36 Gauge fields and… definition 26.40: The 3+1 decomposition 26.40 The 3+1 decompos… postulate 26.47: Dirac quantization 26.47 Dirac quantizati… proposition 26.5: Primary constraints 26.5 Primary constrai… proposition 26.6: The canonical Hamiltonian is defined on the constraint
surface 26.6 The canonical Ha… proposition 26.10: The four outcomes 26.10 The four outcomes proposition 26.13: The first-class functions close 26.13 The first-class… theorem 26.14: First-class constraints generate gauge transformations 26.14 First-class cons… theorem 26.17: Counting the physical degrees of freedom 26.17 Counting the phy… proposition 26.19: Second-class constraints come in pairs 26.19 Second-class con… theorem 26.21: Properties of the Dirac bracket 26.21 Properties of th… proposition 26.24: The Faddeev–Popov determinant 26.24 The Faddeev–Popo… proposition 26.25: The Liouville measure of a second-class surface 26.25 The Liouville me… proposition 26.29: Reparametrization invariance and the mass-shell
constraint 26.29 Reparametrizatio… proposition 26.32: Constraint structure of the free Maxwell field 26.32 Constraint struc… proposition 26.34: Proca constraints are second class 26.34 Proca constraint… equation 26.2: eq:cd-primary eq. (26.2) equation 26.4: eq:cd-canonical-hamiltonian eq. (26.4) equation 26.7: eq:cd-evolution eq. (26.7) equation 26.16: eq:cd-first-class-algebra eq. (26.16) equation 26.24: eq:cd-c-matrix eq. (26.24) equation 26.42: eq:cd-reduced-projector eq. (26.42) equation 26.78: eq:cd-adm-metric eq. (26.78) equation 26.79: eq:cd-adm-extrinsic eq. (26.79) equation 26.82: eq:cd-adm-momentum eq. (26.82) equation 26.84: eq:cd-adm-hamiltonian-constraint eq. (26.84) equation 26.85: eq:cd-adm-momentum-constraint eq. (26.85) equation 26.97: eq:cd-brst-charge eq. (26.97) equation 26.98: eq:cd-brst-nilpotent eq. (26.98) The chain of Constrained Hamiltonian Systems: the Dirac–Bergmann Formalism: 39 of 46 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.