Related papers: Quantization of a particle in a background Yang-Mi…
We argue that, ideally, the ways to measure magnitudes in non-quantum theories of physics (spacetime, field theory), limit drastically their possible mathematical models. In particular, gauge invariance in the Yang-Mills framework, is a…
A suitable deformation of the Hopf algebra of the creation and annihilation operators for a complex scalar field, initially quantized in Minkowski space--time, induces the canonical quantization of the same field in a generic gravitational…
In order to have a new perspective on the long-standing problem of the mass gap in Yang-Mills theory, we study the quantum Yang-Mills theory in the presence of topologically nontrivial backgrounds in this paper. The topologically stable…
The compactification on a torus in $SU(\infty)$ Yang-Mills theory is considered. A special form of the configuration of a gauge field on a torus is examined. The vacuum energy and free energy in the presence of fermions coupled with this…
A formalism for describing charged particles interaction in both a finite volume and a uniform magnetic field is presented. In the case of short-range interaction between charged particles, we show that the factorization between short-range…
Witten's observables of topological Yang-Mills theory, defined as classes of an equivariant cohomology, are reobtained as the BRST cohomology classes of a superspace version of the theory.
The third quantization formalism of quantum cosmology adds simplicity and conceptual insight into the quantum description of the multiverse. Within such a formalism, the existence of squeezed and entangled states raises the question of…
I review some recent work on applications of category theory to questions concerning theoretical structure and theoretical equivalence of classical field theories, including Newtonian gravitation, general relativity, and Yang-Mills…
After a short introduction on the theory of homogeneous algebras we describe the application of this theory to the analysis of the cubic Yang-Mills algebra, the quadratic self-duality algebras, their "super" versions as well as to some…
By means of simple models in a flat spacetime manifold we examine some of the issues that arise when quantizing interacting quantum fields in multi-metric backgrounds. In particular we investigate the maintenance of a causal structure in…
We study the quantization of a free scalar field when the background metric satisfies Einstein's equations and develops gravitational shock waves.
We introduce a special class of bimetric theories of quantized fields with preserved classical energy conditions. More precisely, we describe the missing anti-particles in our visible universe as being trapped in a spacetime patch with…
Using tangent bundle geometry we construct an equivalent reformulation of classical field theory on flat spacetimes which simultaneously encodes the perspectives of multiple observers. Its generalization to curved spacetimes realizes a new…
We consider two-dimensional Yang-Mills theories on arbitrary Riemann surfaces. We introduce a generalized Yang-Mills action, which coincides with the ordinary one on flat surfaces but differs from it in its coupling to two-dimensional…
This paper is a survey of author's mathematical and logical study of the problem of quantization of fields.
These are six papers joined by the same title. The main topics are: 1. algebraic nature of quantization of relativistic fields, 2. constructive definition of space of states of quantum electromagnetic field, 3. structure of space of states…
In certain scenarios of deformed relativistic symmetries relevant for non-commutative field theories particles exhibit a momentum space described by a non-abelian group manifold. Starting with a formulation of phase space for such particles…
We study a method to obtain invariants under area-preserving diffeomorphisms associated to closed curves in the plane from classical Yang-Mills theory in two dimensions. Taking as starting point the Yang-Mills field coupled to non dynamical…
We describe a $q$-deformed dynamical system corresponding to the quantum free particle moving along the circle. The algebra of observables is constructed and discussed. We construct and classify irreducible representations of the system.
We demonstrate how one can see quantization of geometry, and quantum algebraic structure in supersymmetric gauge theory.