## 66 Citations

### Revisiting the gauge principle: enforcing constants of motion as constraints

- Physics
- 2010

In this paper we examine an alternative formulation of the gauge principle in which the emphasis is shifted from the symmetry transformations to their generators. We show that the gauge principle can…

### Revisiting observables in generally covariant theories in the light of gauge fixing methods

- Physics, Mathematics
- 2009

We derive for generally covariant theories the generic dependency of observables on the original fields, corresponding to coordinate-dependent gauge fixings. This gauge choice is equivalent to a…

### Singular Lagrangians, Constrained Hamiltonian Systems and Gauge Invariance: An Example of the Dirac–Bergmann Algorithm

- PhysicsUniverse
- 2022

The Dirac–Bergmann algorithm is a recipe for converting a theory with a singular Lagrangian into a constrained Hamiltonian system. Constrained Hamiltonian systems include gauge theories—general…

### 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…

### A brief introduction to gauge-invariant dynamical systems

- PhysicsEuropean Journal of Physics
- 2020

We describe gauge symmetry at the elementary level aiming at undergraduate and first-year graduate theoretical physics students. The formal definition of gauge invariance as a local symmetry of the…

### Generalized duality, Hamiltonian formalism and new brackets

- Physics
- 2010

It is shown that any singular Lagrangian theory: 1) can be formulated without the use of constraints by introducing a Clairaut-type version of the Hamiltonian formalism; 2) leads to a special kind of…

### Canonical analysis of field theories in the presence of boundaries: Maxwell + Pontryagin

- PhysicsClassical and Quantum Gravity
- 2020

We study the canonical Hamiltonian analysis of gauge theories in the presence of boundaries. While the implementation of Dirac’s programme in the presence of boundaries, as put forward by Regge and…

### Change in Hamiltonian General Relativity with Spinors

- PhysicsFoundations of Physics
- 2021

In General Relativity in Hamiltonian form, change has seemed to be missing, defined only asymptotically, or otherwise obscured at best, because the Hamiltonian is a sum of first-class constraints and…

### How to Choose a Gauge? The Case of Hamiltonian Electromagnetism

- PhysicsErkenntnis
- 2022

We develop some ideas about gauge symmetry in the context of Maxwell’s theory of electromagnetism in the Hamiltonian formalism. One great benefit of this formalism is that it pairs momentum and…

### Léon Rosenfeld’s general theory of constrained Hamiltonian dynamics

- Physics
- 2016

Abstract
This commentary reflects on the 1930 general theory of Léon Rosenfeld dealing with phase-space constraints. We start with a short biography of Rosenfeld and his motivation for this article…

## References

SHOWING 1-10 OF 67 REFERENCES

### On Dirac＇s Conjecture

- Mathematics
- 2005

The extended canonical Noether identities and canonical first Noether theorem derived from an extended action in phase space for a system with a singular Lagrangian are formulated. Using these…

### Dynamics of gauge systems and Dirac's conjecture.

- Mathematics, PhysicsPhysical review. D, Particles and fields
- 1985

For systems possessing only first-class constraints, we rigorously prove that the secondary constraints act as independent generators of gauge transformations (Dirac's conjecture). The proof…

### 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…

### Reduced phase space: quotienting procedure for gauge theories

- Physics
- 1999

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…

### On Dirac's conjecture for Hamiltonian systems with first- and second-class constraints.

- MathematicsPhysical review. D, Particles and fields
- 1990

It is shown for a wide class of systems in the framework of the total Hamiltonian procedure that all first-class constraints generate canonical transformations connecting physically equivalent…

### Gauge group and reality conditions in Ashtekar's complex formulation of canonical gravity

- Mathematics
- 2000

We discuss reality conditions and the relation between spacetime diffeomorphisms and gauge transformations in Ashtekar’s complex formulation of general relativity. We produce a general theoretical…

### 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…