Related papers: Antibracket, Antifields and Gauge-Theory Quantizat…
We analyze how gauge fixing, which is required by any practical continuum approach to gauge systems, can interfere with the physical symmetries of such systems. In principle, the gauge fixing procedure, which deals with the (unphysical)…
This extended write-up of a talk gives an introductory survey of mathematical problems of the quantization of gauge systems. Using the Schwinger model as an exactly tractable but nontrivial example which exhibits general features of gauge…
Gauge field theories may quite generally be defined as describing the coupling of a matter-field to an interaction-field, and they are suitably represented in the mathematical framework of fiber bundles. Their underlying principle is the…
A brief overview of the recent developments of operadic and higher categorical techniques in algebraic quantum field theory is given. The relevance of such mathematical structures for the description of gauge theories is discussed.
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…
The first part of this work deals with the development of a natural differential calculus on non-commutative manifolds. The second part extends the covariance and equivalence principle as well studies its kinematical consequences such as…
We explore a field theoretical approach to quantum computing and control. This book consists of three parts. The basics of systems theory and field theory are reviewed in Part I. In Part II, a gauge theory is reinterpreted from a systems…
The problems which arise for a relativistic quantum mechanics are reviewed and critically examined in connection with the foundations of quantum field theory. The conflict between the quantum mechanical Hilbert space structure, the locality…
It is well-known that principal bundles and associated bundles underlie the geometric structure of classical gauge field theories. In this paper, we explore the reformulation of gauge theories in terms of Lie algebroids and their associated…
We introduce the key ideas behind the group field theory approach to quantum gravity, and the basic elements of its formalism. We also briefly report on some recent results obtained in this approach, concerning both the mathematical…
Pure gravity and gauge theories in two dimensions are shown to be special cases of a much more general class of field theories each of which is characterized by a Poisson structure on a finite dimensional target space. A general scheme for…
I review the formalism for gauge-field perturbation theory in noncovariant gauges, particularly the temporal axial gauge. I show that, even at zero temperature, there are complications and it is not known whether a formalism exists for…
Synthesizing older ideas about the 1/N expansion in gauge theory, the quantum mechanics of black holes, and quantum field theory in Anti de Sitter space, a new correspondence between gauge theory and quantum gravity has illuminated both…
In this article we construct and discuss a new rigorous geometric formalism for gauge field theories. The basis of our work is the notion of the Tulczyjew triple, a geometric structure which successfully solved numerous problems in…
We propose how to incorporate the Leites-Shchepochkina-Konstein-Tyutin deformed antibracket into the quantum field-antifield formalism.
The antifield formalism adapted in the exact renormalization group is found to be useful for describing a system with some symmetry, especially the gauge symmetry. In the formalism, the vanishing of the quantum master operator implies the…
A review is given of the Peierls bracket formalism in field theory, and of a new, recent application of this concept to the analysis of dissipative systems.
In the generalized Schwinger model the vector and axial vector currents are linearly coupled, with arbitrary coefficients, to the gauge connection. Therefore it represents an interesting example of a theory where both gauge anomalies and…
We consider gaugeon formulations which discuss the quantum gauge freedom covariantly in the framework of generalized BRST transformation for the Yang-Mills theory as well as the BRST invariant Higgs model. We generalize the BRST symmetries…
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…