Related papers: Plugging the Gauge Fixing into the Lagrangian
Causal fermion systems incorporate local gauge symmetry in the sense that the Lagrangian and all inherent structures are invariant under local phase transformations of the physical wave functions. In the present paper it is explained and…
The SU(2) gauge invariant Dirac-Yang-Mills mechanics of spatially homogeneous isospinor and gauge fields is considered in the framework of the generalized Hamiltonian approach. The unconstrained Hamiltonian system equivalent to the model is…
We give an explicit formalism connecting softly broken supersymmetric gauge theories (with QCD as one limit) to $N=2$ and $N=1$ supersymmetric theories possessing exact solutions, using spurion fields to embed these models in an enlarged…
The properties of Lagrangians affine in velocities are analyzed in a geometric way. These systems are necessarily singular and exhibit, in general, gauge invariance. The analysis of constraint functions and gauge symmetry leads us to a…
This paper presents (in its Lagrangian version) a very general "historical" formalism for dynamical systems, including time-dynamics and field theories. It is based on the universal notion of history. Its condensed and universal formulation…
Gauge symmetries lead to first-class constraints. This assertion is of course true only for non trivial gauge symmetries, i.e., gauge symmetries that act non trivially on-shell on the dynamical variables. We illustrate this well-appreciated…
Phenomena in gauge theory are often described in the physics literature via a specific choice of gauge. In foundational and philosophical discussions this is often criticized as introducing gauge dependence, and contrasted against (often…
Variational calculus on a vector bundle E equipped with a structure of a general algebroid is developed, together with the corresponding analogs of Euler-Lagrange equations. Constrained systems are introduced in the variational and in the…
Starting from a generic Lagrangian, we discuss the number of propagating degrees of freedom in the framework of generalised non-linear electrodynamics when a photon-background split is applied. We start by stating results obtained in a…
We study several problems related to the construction and the use of effective Lagrangians by considering an extension of the standard model that includes a heavy scalar singlet coupled to the leptonic doublet. Starting from the full…
Hamiltonian systems with functionally dependent constraints (irregular systems), for which the standard Dirac procedure is not directly applicable, are discussed. They are classified according to their behavior in the vicinity of the…
We derive both Lagrangian and Hamiltonian mechanics as gauge theories of Newtonian mechanics. Systematic development of the distinct symmetries of dynamics and measurement suggest that gauge theory may be motivated as a reconciliation of…
One of the central concepts in modern theoretical physics, gauge symmetry, is typically realised by lifting a finite-dimensional global symmetry group of a given functional to an infinite-dimensional local one by extending the functional to…
A modification of the canonical quantization procedure for systems with time-dependent second-class constraints is discussed and applied to the quantization of the relativistic particle in a plane wave. The time dependence of constraints…
It is possible to introduce external time dependent back ground fields in the formulation of a system as fields whose dynamics can not be deduced from Euler Lagrange equations of motion. This method leads to singular Lagrangians for real…
It is shown that the Dirac approach to Hamiltonization of singular theories can be slightly modified in such a way that primary Dirac constraints do not appear in the process. According to the modified scheme, Hamiltonian formulation of…
An extension of the Legendre transform to non-convex functions with vanishing Hessian as a mix of envelope and general solutions of the Clairaut equation is proposed. Applying this to systems with constraints, the procedure of finding a…
Chiral perturbation theory is extended to nonrelativistic systems with spontaneously broken symmetry. In the effective Lagrangian, order parameters associated with the generators of the group manifest themselves as effective coupling…
The Lagrangian formulation of classical mechanics is widely applicable in solving a vast array of physics problems encountered in the undergraduate and graduate physics curriculum. Unfortunately, many treatments of the topic lack…
An equation is obtained to find the Lagrangian for a one-dimensional autonomous system. The continuity of the first derivative of its constant of motion is assumed. This equation is solved for a generic nonconservative autonomous system…