# Reduced phase space: quotienting procedure for gauge theories

@article{Pons1999ReducedPS, title={Reduced phase space: quotienting procedure for gauge theories}, author={Josep M. Pons and Donald C. Salisbury and Lawrence Charles Shepley}, journal={Journal of Physics A}, year={1999}, volume={32}, pages={419-430} }

We present a reduction procedure for gauge theories based on quotienting out the kernel of the presymplectic form in configuration-velocity space. Local expressions for a basis of this kernel are obtained using phase-space procedures; the obstructions to the formulation of the dynamics in the reduced phase space are identified and circumvented. We show that this reduction procedure is equivalent to the standard Dirac method as long as the Dirac conjecture holds: that the Dirac Hamiltonian…

## 8 Citations

RIGID AND GAUGE NOETHER SYMMETRIES FOR CONSTRAINED SYSTEMS

- Mathematics
- 1999

We develop the general theory of Noether symmetries for constrained systems, that is, systems that are described by singular Lagrangians. In our derivation, the Dirac bracket structure with respect…

Symplectic Reduction and the Problem of Time in Nonrelativistic Mechanics

- PhysicsThe British Journal for the Philosophy of Science
- 2012

The deep connection between the interpretation of theories invariant under local symmetry transformations (i.e. gauge theories) and the philosophy of space and time can be illustrated…

Constrained dynamics: generalized Lie symmetries, singular Lagrangians, and the passage to Hamiltonian mechanics

- Physics, MathematicsJournal of Physics Communications
- 2020

Guided by the symmetries of the Euler–Lagrange equations of motion, a study of the constrained dynamics of singular Lagrangians is presented. We find that these equations of motion admit a…

Gauge transformation in Einstein–Yang–Mills theories

- Physics
- 2000

We discuss the relation between space–time diffeomorphisms and gauge transformations in theories of the Yang–Mills type coupled with Einstein’s general relativity. We show that local symmetries of…

Symmetries and infinitesimal symmetries of singular differential equations

- Mathematics
- 2002

The aim of this paper is to study symmetries of linearly singular differential equations, namely, equations that cannot be written in normal form because the derivatives are multiplied by a singular…

INTEGRABILITY AND ACTION FUNCTION IN MULTI-HAMILTONIAN SYSTEMS

- Mathematics
- 2004

Multi-Hamiltonian systems are investigated by using the Hamilton–Jacobi method. Integration of a set of total differential equations which includes the equations of motion and the action integral…

Singular Lagrangians: some geometric structures along the Legendre map

- Physics, Mathematics
- 2001

New geometric structures that relate the Lagrangian and Hamiltonian formalisms defined upon a singular Lagrangian are presented. Several vector fields are constructed in velocity space that give new…

## References

SHOWING 1-10 OF 38 REFERENCES

Dirac bracket transformations in phase space

- Physics
- 1955

The purpose of this paper is twofold. One is to analyze the group-theoretical significance of the Dirac bracket and to examine, in particular, the apparent ambiguities in the presence of both…

FADDEEV-JACKIW APPROACH TO GAUGE THEORIES AND INEFFECTIVE CONSTRAINTS

- Physics
- 1998

The general conditions for the applicability of the Faddeev–Jackiw approach to gauge theories are studied. When the constraints are effective, a new proof in the Lagrangian framework of the…

Equivalence of Faddeev–Jackiw and Dirac Approaches for Gauge Theories

- Physics
- 1996

The equivalence between the Dirac method and Faddeev–Jackiw analysis for gauge theories is proven. In particular we trace out, in a stage-by-stage procedure, the standard classification of first and…

Gauge transformations in the Lagrangian and Hamiltonian formalisms of generally covariant theories

- Physics
- 1997

We study spacetime diffeomorphisms in the Hamiltonian and Lagrangian formalisms of generally covariant systems. We show that the gauge group for such a system is characterized by having generators…

Local symmetries and constraints

- Mathematics
- 1990

The general relationship between local symmetries occurring in a Lagrangian formulation of a field theory and the corresponding constraints present in a phase space formulation are studied. First, a…

Evolutionary laws, initial conditions and gauge fixing in constrained systems

- Mathematics
- 1995

We describe in detail how to eliminate nonphysical degrees of freedom in the Lagrangian and Hamiltonian formulations of a constrained system. Two important and distinct steps in our method are the…

Non-Linear Field Theories

- Mathematics
- 1949

This is the first paper in a program concerned with the quantization of field theories which are covariant with respect to general coordinate transformations, like the general theory of relativity.…

Origin of the Lagrangian constraints and their relation with the Hamiltonian formulation

- Physics
- 1988

The theory of presymplectic systems is used for the study of mechanical systems described by singular Lagrangians in order to clarify the geometric meaning of the Euler–Lagrange equations for such…

Presymplectic manifolds and the Dirac-Bergmann theory of constraints

- Mathematics
- 1978

We present an algorithm which enables us to state necessary and sufficient conditions for the solvability of generalized Hamilton‐type equations of the form ι (X) ω=α on a presymplectic manifold…

On the quantization of presymplectic dynamical systems via coisotropic imbeddings

- Mathematics
- 1981

We study certain aspects of the problem of quantizing a presymplectic dynamical system. Such a system is quantized by imbedding the presymplectic manifoldM under consideration into a symplectic…