Related papers: New interpretation of variational principles for g…
"Physical theories of fundamental significance tend to be gauge theories. These are theories in which the physical system being dealt with is described by more variables than there are physically independent degree of freedom. The…
Variational principles for field theories where variations of fields are restricted along a parametrization are considered. In particular, gauge-natural parametrized variational problems are defined as those in which both the Lagrangian and…
Using the extended ADM-phase space formulation in the canonical framework we analyze the relationship between various gauge choices made in cosmological perturbation theory and the choice of geometrical clocks in the relational formalism.…
Physical systems may couple to other systems through variables that are not gauge invariant. When we split a gauge system into two subsystems, the gauge-invariant variables of the two subsystems have less information than the gauge…
Laws of motion given in terms of differential equations can not always be derived from an action principle, at least not without introducing auxiliary variables. By allowing auxiliary variables, e.g. in the form of Lagrange multipliers, an…
It is shown that gauge theories are most naturally studied via a polar decomposition of the field variable. Gauge transformations may be viewed as those that leave the density invariant but change the phase variable by additive amounts. The…
The standard techniques of variational calculus are geometrically stated in the ambient of fiber bundles endowed with a (pre)multisymplectic structure. Then, for the corresponding variational equations, conserved quantities (or, what is…
Gauge theory is a well-established concept in quantum physics, electrodynamics, and cosmology. This theory has recently proliferated into new areas, such as mechanics and astrodynamics. In this paper, we discuss a few applications of gauge…
The aim of the present article is to give physical meaning to the ingredients of standard gauge field theory in the framework of the scale relativity theory. Owing to the principle of the relativity of scales, the scale-space is not…
The usual treatment of a (first order) classical field theory such as electromagnetism has a little drawback: It has a primary constraint submanifold that arise from the fact that the dynamics is governed by the antisymmetric part of the…
Dirac's approach to gauge symmetries is discussed. We follow closely the steps that led him from his conjecture concerning the generators of gauge transformations {\it at a given time} --to be contrasted with the common view of gauge…
Gauge symmetry breaking by boundary conditions is studied in a general warped geometry in five dimensions. It has been suggested that a wider class of boundary conditions is allowed by requiring only vanishing surface terms when deriving…
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…
A new form of the dynamical equations of vacuum general relativity is proposed. This form involves the canonical Hamiltonian structure but non canonical variables. The new field variables are the electric field $E^{a}{}_{i}$ and the…
We apply the covariant analytic mechanics with the differential forms to the Dirac field and the gravity with the Dirac field. The covariant analytic mechanics treats space and time on an equal footing regarding the differential forms as…
Basic notions of Dirac theory of constrained systems have their analogs in differential geometry. Combination of the two approaches gives more clear understanding of both classical and quantum mechanics, when we deal with a model with…
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 choice of intrinsically defined coordinates…
Applications of variational methods are typically restricted to conservative systems. Some extensions to dissipative systems have been reported too but require ad hoc techniques such as the artificial doubling of the dynamical variables.…
The concept of gauge invariance is one of the most subtle and useful concepts in modern theoretical physics. It is one of the Standard Model cornerstones. The main benefit due to the gauge invariance is that it can permit the comprehension…
Assuming that the natural gauge group of gravity is given by the group of isometries of a given space, for a maximally symmetric space we derive a model in which gravity is essentially a gauge theory of translations. Starting from first…