Related papers: New interpretation of variational principles for g…
A new derivation of the Bernoulli equation for water waves in three-dimensional rotating and translating coordinate systems is given. An alternative view on the Bateman-Luke variational principle is presented. The variational principle…
This thesis consists of two parts, connected by one central theme: the dynamics of the "shape of space". The first part of the thesis concerns the construction of a theory of gravity dynamically equivalent to general relativity (GR) in 3+1…
The Einstein theory of general relativity provides a peculiar example of classical field theory ruled by non-linear partial differential equations. A number of supplementary conditions (more frequently called gauge conditions) have also…
We introduce a general approximation scheme in order to calculate gauge invariant observables in the canonical formulation of general relativity. Using this scheme we will show how the observables and the dynamics of field theories on a…
The Dirac-Bergmann algorithm for the Hamiltonian analysis of constrained systems is a nice and powerful tool, widely used for quantization and non-perturbative counting of degrees of freedom. However, certain aspects of its application to…
The third post-Newtonian approximation to the general relativistic dynamics of two point-mass systems has been recently derived by two independent groups, using different approaches, and different coordinate systems. By explicitly…
Geometric properties of operators of quantum Dirac constraints and physical observables are studied in semiclassical theory of generic constrained systems. The invariance transformations of the classical theory -- contact canonical…
Variational methods are employed in situations where exact Bayesian inference becomes intractable due to the difficulty in performing certain integrals. Typically, variational methods postulate a tractable posterior and formulate a lower…
Gauge fields frequently used as an independent construction additional to so-called wave fields of matter. This artificial separation is of course useful in some applications (like Berry's interactions between the "heavy" and "light"…
Field theories with extra dimensions live in a limbo. While their classical solutions have been the subject of considerable study, their quantum aspects are difficult to control. A special class of such theories are anisotropic gauge…
Gauge invariance, a core principle in electrodynamics, has two separate meanings. One concept treats the photon as the gauge particle for electrodynamics. It is based on symmetries of the Lagrangian, and requires no mention of electric or…
Gauge theory underpins the quantum field theories of the standard model, and in a previous paper was shown via a geometric approach to describe classical electromagnetism in a form which approximates QED. Here we formalize and generalize…
We consider extra dimensional gauge theories on an interval. We first review the derivation of the consistent boundary conditions (BC's) from the action principle. These BC's include choices that give rise to breaking of the gauge…
Some conceptual issues concerning general invariant theories, with special emphasis on general relativity, are analyzed. The common assertion that observables must be required to be gauge invariant is examined in the light of the role…
We investigate the possibility of reducing the number of degrees of freedom (d.o.f.) starting from generic metric theories of gravity by introducing multiple auxiliary constraints (ACs), under the restriction of retaining spatial covariance…
Gauge invariance in discrete dynamical systems and its connection with quantization are considered. For a complete description of gauge symmetries of a system we construct explicitly a class of groups unifying in a natural way the space and…
The finite-volume QED$_{1+1}$ is formulated in terms of Dirac variables by an explicit solution of the Gauss constraint with possible nontrivial boundary conditions taken into account. The intrinsic nontrivial topology of the gauge group is…
We study the variational principle and derivation of the field equations for different classes of teleparallel gravity theories, using both their metric-affine and covariant tetrad formulations. These theories have in common that in…
It is shown that when in a higher order variational principle one fixes fields at the boundary leaving the field derivatives unconstrained, then the variational principle (in particular the solution space) is not invariant with respect to…
We use a canonical parametrization of twisted geometries describing the classical phase space of loop quantum gravity on a fixed graph, and establish its explicit correspondence with the associated frame bases and spinorial descriptions.…