RESEARCH
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Dirac Brackets and Time-Dependent Constraints

N. Barros e Sá

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.

Keywords
constrained systems / analytical mechanics / Quantum Mechanics / General Relativity and Quantum Cosmology / Mathematical Physics / Quantum Physics

Universe
Volume 11, Number 233
2025 July

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Faculdade de Ciências da Universidade de Lisboa Universidade do Porto Faculdade de Ciências e Tecnologia da Universidade de Coimbra
Fundação para a Ciência e a Tecnologia COMPETE 2020 PORTUGAL 2020 União Europeia