Dirac bracket and time dependent constraints
Nuno Barros e S\'a
TL;DR
This paper derives the Dirac bracket and equations of motion for systems with time-dependent second-class constraints, emphasizing the importance of time-dependent gauge-fixing through examples and geometric interpretation.
Contribution
It presents a unified derivation of the Dirac bracket and equations of motion for time-dependent constraints, highlighting the role of gauge-fixing.
Findings
Time-dependent gauge-fixing conditions are necessary for constrained systems.
The derivation is illustrated with parameterized mechanics.
Geometric interpretation clarifies the role of constraints.
Abstract
We provide a simultaneous derivation of the Dirac bracket and of the equations of motion for second-class constrained systems when the constraints are time-dependent. The necessity of time-dependent gauge-fixing conditions is shown in the example of parameterized mechanics and is illustrated geometrically.
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Taxonomy
TopicsRelativity and Gravitational Theory · Algebraic and Geometric Analysis · Noncommutative and Quantum Gravity Theories