Related papers: A Geometric Representation for the Proca Model
An $\alpha$-parameter representation is derived for gauge field theories.It involves, relative to a scalar field theory, only constants and derivatives with respect to the $\alpha$-parameters. Simple rules are given to obtain the…
We show how to systematically derive the exact form of local symmetries for the abelian Proca and CS models, which are converted into first class constrained systems by the BFT formalism, in the Lagrangian formalism. As results, without…
The Lagrangian formalism is used to derive covariant equations that are suitable for use in continuously distributed matter in curved spacetime. Special attention is given to theoretical representation, in which the Lagrangian and its…
Abelian Gauge Theories are quantized in a geometric representation that generalizes the Loop Representation and treates electric and magnetic operators on the same footing. The usual canonical algebra is turned into a topological algebra of…
These lectures present an elementary introduction to quantum gauge fields. The first aim is to show how, in the tree approximation, gauge invariance follows from covariance and unitarity. This leads to the standard construction of the…
Higher-spin theories are most commonly modelled on the example of spin 2. While this is appropriate for the description of free irreducible spin-s particles, alternative options could be equally interesting. In particular Maxwell's…
Important characteristics of the loop approach to quantum gravity are a specific choice of the algebra A of observables and of a representation of A on a measure space over the space of generalized connections. This representation is…
Geometrical interpretation on U(1) gage theory of Dirac monopole, introduced here from the line integral\cite{Brandt} form of vector potentials, shows the gauge representation be multi-valued. In this paper, we construct Euclidean form of…
For the quadratic Poincar\'e gauge theory of gravity (PG) we consider the FLRW cosmologies using an isotropic Bianchi representation. Here the considered cosmologies are for the general case: all the even and odd parity terms of the…
A set of differential operators acting by continuous deformations on path dependent functionals of open and closed curves is introduced. Geometrically, these path operators are interpreted as infinitesimal generators of curves in the base…
In this paper we discuss how the gauge principle can be applied to classical-mechanics models with finite degrees of freedom. The local invariance of a model is understood as its invariance under the action of a matrix Lie group of…
In this paper, we show that the propagator of the dual of a general Proca-like theory, derived from the gauging iterative Noether Dualization Method, can be written by means of a simple relation between known propagators. This result is…
Starting with a Hilbert space endowed with a representation of a unitary Lie algebra and an action of a generalized Dirac operator, we develop a mathematical concept towards gauge field theories. This concept shares common features with the…
We convert the second class Proca model into a first class theory by using the generalised prescription of Batalin, Fradkin and Tyutin. We then show how a basic set of gauge invariant fields in the embedded model can be identified with the…
A recently proposed pregeometric auxiliary vector mediated gauge theory is studied in its canonical domain, by performing the Legendre transform on a curved background and by considering its covariant phase space, with further application…
Metric independent $\sigma$ models are constructed. These are field theories which generalise the membrane idea to situations where the target space has fewer dimensions than the base manifold. Instead of reparametrisation invariance of the…
There is considered an extension of gauge theories according to the assumption of a generalized uncertainty principle which implies a minimal length scale. A modification of the usual uncertainty principle implies an extended shape of…
We give here a covariant definition of the path integral formalism for the Lagrangian, which leaves a freedom to choose anyone of many possible quantum systems that correspond to the same classical limit without adding new potential terms…
To date, different alternative theories of gravity, although related, involving Proca fields have been proposed. Unfortunately, the procedure to obtain the relevant terms in some formulations has not been systematic enough or exhaustive,…
We construct the most general physically admissible positive-definite inner product on the space of Proca fields. Up to a trivial scaling this defines a five-parameter family of Lorentz invariant inner products that we use to construct a…