Related papers: Fundamental theorem on gauge fixing at the action …

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…

We propose a new point of view to gauge theories based on taking the action of symmetry transformations directly on the coordinates of space. Via this approach the gauge fields are not introduced at the first step, and they can be…

We develop a complete Hamiltonian approach to the theory of perturbations around any spatially homogeneous spacetime. We employ the Dirac method for constrained systems which is well-suited to cosmological perturbations. We refine the…

We analyze the dynamics of gauge theories and constrained systems in general under small perturbations around a classical solution (background) in both Lagrangian and Hamiltonian formalisms. We prove that a fluctuations theory, described by…

The Landau gauge fixing algorithm in the new definition of gauge fields is presented. In this algorithm a new solver of the Poisson equations based on the Green's function method is used. Its numerical performance of the gauge fixing…

A solution for the Weinstein's Problem in the general framework of generalized Lie algebroids is the target of this paper. We present the mechanical systems called by use, mechanical (?; ?)-systems, Lagrange mechanical (?; ?)-systems or…

Perturbation theory in geometric theories of gravitation is a gauge theory of symmetric tensors defined on a Lorentzian manifold (the background spacetime). The gauge freedom makes uniqueness problems in perturbation theory particularly…

In the restricted four-body problem consisting of the Earth, the Moon and the Sun as the primaries and a spacecraft as the planetoid, we take into account the solar perturbation in the description of the motion of a spacecraft in the…

The gauge symmetry is said unfree if the gauge transformation leaves the action functional unchanged provided for the gauge parameters are constrained by the system of partial differential equations. The best known example of this…

Alternative theories of gravity have been recently studied in connection with their cosmological applications, both in the Palatini and in the metric formalism. The aim of this paper is to propose a theoretical framework (in the Palatini…

This work contains an exposition of foundations of the variational calculus in fibered manifolds. The emphasis is laid on the geometric aspects of the theory. Especially functionals defined by real functions (Lagrange functions) or…

In a recent publication a procedure was developed which can be used to derive completely gauge invariant models from general Lagrangian densities with $N$ order of derivatives and $M$ rank of tensor potential. This procedure was then used…

The Lagrangian and equations of the gauge model of the fifth fundamental interaction are constructed and the corresponding corrections to the Newtonian potential are obtained.

Some of the basic issues related to the regularization and anomalies in gauge theory are reviewed, with particular emphasis on the recent development in lattice gauge theory. The generalized Pauli-Villars regularization is discussed from a…

Higher Derivative (HD) Field Theories can be transformed into second order equivalent theories with a direct particle interpretation. In a simple model involving abelian gauge symmetries we examine the fate of the possible gauge fixings…

In the framework of Lagrangian formulation, some q-deformed physical systems are considered. The q-deformed Legendre transformation is obtained for the free motion of a non-relativistic particle on a quantum line. This is subsequently…

Equations of motion for a general relativistic post-Newtonian Lagrangian approach mainly refer to acceleration equations, i.e. differential equations of velocities. They are directly from the Euler-Lagrangian equations, and usually have…

When graviton loops are taken into account, the background metric obtained as a solution to the one-loop corrected Einstein equations turns out to be gauge fixing dependent. Therefore it is of no physical relevance. Instead we consider a…

We consider the free boundary problem for the Euler--Fourier system that describes the motion of compressible, inviscid and heat-conducting fluids. The effect of surface tension is neglected and there is no heat flux across the free…

Reparametrization invariance being treated as a gauge symmetry shows some specific peculiarities. We study these peculiarities both from a general point of view and on concrete examples. We consider the canonical treatment of…