Related papers: The problem of gauge invariance in Dirac field the…
We are taught that gauge transformations in classical and quantum mechanics do not change the physics of the problem. Nevertheless here we discuss three broad scenarios where under gauge transformations: (i) conservation laws are not…
Over the past five years, there has been significant progress on the problem of quantization of diffeomorphism covariant field theories with {\it local} degrees of freedom. The absence of a background space-time metric in these theories…
In standard quantum field theory, the one-particle states are classified by the unitary representations of the Poincar\'e group, whereas the causal fields' classification employs the finite-dimensional (non-unitary) representations of the…
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…
An unstable field theory is what we obtain when we linearise the equations of an interacting field theory near an unstable state. Theories of this kind are adopted to model the onset of spontaneous symmetry breakings, when the fields are…
This talk reports on work aimed at improving our understanding of charged states in gauge theories.Emphasis is placed on different ways of implementingthe gauge invariance of physical states. QED perturbative calculations are used to stress…
Gravitation theory is formulated as gauge theory on natural bundles with spontaneous symmetry breaking where gauge symmetries are general covariant transformations, gauge fields are general linear connections, and Higgs fields are…
The quantisation of gauge invariant systems usually proceeds through some gauge fixing procedure of one type or another. Typically for most cases, such gauge fixings are plagued by Gribov ambiguities, while it is only for an admissible…
The hypothesis is suggested that the equation for the Dirac free wave field is, in fact, a group-theoretical relation describing propagation of specific microscopic deviations of space geometry from the euclidean one (closed topological…
Quantum theory of the gravitation in the causal approach is studied up to the second order of perturbation theory. We prove gauge invariance and renormalizability in the second order of perturbation theory for the pure gravity system…
A quantum physical projector is proposed for generally covariant theories which are derivable from a Lagrangian. The projector is the quantum analogue of the integral over the generators of finite one-parameter subgroups of the gauge…
Along the general framework of the gauge invariant perturbation theory developed in the papers [K. Nakamura, Prog. Theor. Phys. {\bf 110} (2003), 723; {\it ibid}, {\bf 113} (2005), 481.], we formulate the second order gauge invariant…
In this paper we put forward a systematic and unifying approach to construct gauge invariant composite fields out of connections. It relies on the existence in the theory of a group valued field with a prescribed gauge transformation. As an…
The question of general covariance in quantum gravity is considered in the first post-Newtonian approximation. Transformation properties of observable quantities under deformations of a reference frame, induced by variations of the gauge…
We develop a gauge theory of the combined gravitational-electromagnetic field by expanding the Poincar\'e group to include clock synchronization transformations. We show that the electromagnetic field can be interpreted as a local gauge…
The theory of cosmological perturbations is a well elaborated field. To deal with the diffeomorphism invariance of general relativity one generally introduces combinations of the metric and matter perturbations which are gauge invariant up…
The gauge field theories are usually quantized by fixing gauge. In this paper, we propose a new formalism that quantizes gauge fields without gauge fixing but naturally follows canonical formalism. New physical implications will follow.
The following two loosely connected sets of topics are reviewed in these lecture notes: 1) Gauge invariance, its treatment in field theories and its implications for internal symmetries and edge states such as those in the quantum Hall…
The theory of gauge fields in Theoretical Physics poses several mathematical problems of interest in Differential Geometry and in Field Theory. Below we tackle one of these problems: The existence of a finite system of generators of…
We present in detail a four-dimensional unified quantum theory. In this theory, we identify three class of parameters, coordinate-momentum, spin and gauge, as all and as the only fundamental parameters to describe quantum fields. The…