Gauge invariance of the action principle for gauge systems with noncanonical symplectic structures

2007/07/24 by Vladimir Cuesta, Merced Montesinos, J. David Vergara · 1 citation
Physics and Astronomy · Mathematics · #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #Cosmology and Gravitation Theories #Symplectic geometry #Hamiltonian lattice gauge theory #Mathematical physics #Gauge theory #Homogeneous space #Physics #Hamiltonian (control theory) #Moment map #Boundary value problem #Symplectomorphism #Introduction to gauge theory #Quantum gauge theory #Gauge fixing #Pure mathematics #Quantum mechanics #Mathematics #Gauge boson #Geometry

paper · doi:10.1103/physrevd.76.025025

openalex publication_date 2007/07/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The effect of the gauge transformation in the action principle for Hamiltonian gauge systems formulated in terms of noncanonical symplectic structures is studied and, particularly, the compatibility between gauge conditions and boundary conditions is analyzed. It is shown that the complete set of commuting observables at the time boundary is now fixed by the boundary term and the symplectic structure. The theory is applied to two nontrivial models having SL(2,ℝ) and SU(2) gauge symmetries, respectively, whose extended phase spaces are endowed with new interactions produced by noncanonical symplectic structures.

Citations

• Quantization of Gauge Systems
• SL(2,R)model with two Hamiltonian constraints
• Generalized Hamiltonian Dynamics
• BRST-BFV method for nonstationary systems

Cited by

• Noether's theorem [wikipedia]

Related

• Gauge systems with noncommutative phase space
• Embedding Second Class Systems via Symplectic Gauge-invariant Formalism
• Gauge invariance and dual equivalence of Abelian and non-Abelian actions via dual embedding formalism
• Restoring the gauge invariance in non-Abelian second-class theories
• Noncommutativity from Canonical and Noncanonical Structures