Geometric Constraints and Covariant Phase Space: A Hamiltonian Approach to de Sitter Relativity

Mous, Finn (2025) Geometric Constraints and Covariant Phase Space: A Hamiltonian Approach to de Sitter Relativity. Bachelor's Thesis, Physics.

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Abstract

This thesis unifies two extensions of the Hamiltonian formalism: the extended phase space, treating time as a dynamical variable, and Dirac’s theory of constrained systems. We first analyze the extended phase space, showing that the Poincare group forms a subgroup of the canonical group in Minkowski ´ spacetime and that the extended Hamiltonian is Lorentz-invariant. Next, Dirac’s formalism is applied to phase space on curved surfaces, revealing an elegant relation between the hypersurface metric and the Poisson structure via the Dirac bracket. Combining these, we develop a consistent phase space description for relativistic systems on curved spacetimes. This framework is tested on de Sitter spacetime, which models our expanding universe’s asymptotic structure. We derive a Poisson structure respecting curvature and time for a free massive particle, from which we demonstrate that the equations of motion reproduce geodesics and that de Sitter’s isometry group is a subgroup of its canonical group. This work illustrates how the extended Dirac formalism provides, to a certain degree, a consistent Hamiltonian framework for particles in curved spacetimes.

Item Type:	Thesis (Bachelor's Thesis)
Supervisor name:	Boer, D.
Degree programme:	Physics
Thesis type:	Bachelor's Thesis
Language:	English
Date Deposited:	17 Jul 2025 10:32
Last Modified:	17 Jul 2025 10:32
URI:	https://fse.studenttheses.ub.rug.nl/id/eprint/36341

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