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First-class constraint

In physics, a first-class constraint is a dynamical quantity in a constrained Hamiltonian system whose Poisson bracket with all the other constraints vanishes on the constraint surface in phase space (the surface implicitly defined by the simultaneous vanishing of all the constraints). To calculate the first-class constraint, one assumes that there are…

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Overview

Poisson brackets

Geometric theory

Intuitive meaning

Constrained Hamiltonian dynamics from a Lagrangian gauge theory

Examples

Second-class constraints

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First-class constraint

Nodes98
Edges97
Triples5
Avg. degree1.98
Density0.020408
Components1

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First-class constraint

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First-class constraint → dynamical quantity in a constrained Hamiltonian system whose Poisson bracket with all the other constraints vanishes on the constraint surface in phase space

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Important terminology

hamiltonian constraints constraint constrained poisson subspace bracket space smooth second-class displaystyle one bundle action dirac note symplectic first-class brackets gauge

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
First-class constraintis adynamical quantity in a constrained Hamiltonian system whose Poisson bracket with all the other constraints vanishes on the constraint surface in phase space0.90text
gauge theories where the symplectic form is degenerate.The terminology of first-instance ofas a way of quantizing mechanical systems0.80text
second-class constraints is confusingly similar to that of primaryinstance ofas a way of quantizing mechanical systems0.80text
secondary constraintsinstance ofas a way of quantizing mechanical systems0.80text
reflecting the manner in which these are generatedinstance ofas a way of quantizing mechanical systems0.80text

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