Related papers: Quantization of a particle in a background Yang-Mi…
We present a simple geometric construction linking geometric to deformation quantization. Both theories depend on some apparently arbitrary parameters, most importantly a polarization and a symplectic connection, and for real polarizations…
A perturbative formulation of algebraic field theory is presented, both for the classical and for the quantum case, and it is shown that the relation between them may be understood in terms of deformation quantization.
In the present paper we propose a new approach to quantum fields in terms of category algebras and states on categories. We define quantum fields and their states as category algebras and states on causal categories with partial involution…
The paper is devoted to a description of quantum group structures in the geometric quantization of a self-interacting string field, which appear under a transition from a tree-level of the theory to the account of loop effects in…
This paper is concerned with theories describing spinning particles that are formulated in terms of actions possessing either local world-line supersymmetry or local fermionic {\it kappa} invariance. These classical actions are obtained by…
An explicit canonical transformation is constructed to relate the physical subspace of Yang-Mills theory to the phase space of the ADM variables of general relativity. This maps 3+1 dimensional Yang-Mills theory to local evolution of…
The kinematics of SL(2,R) Yang-Mills theory on a circle is considered, for reasons that are spelled out. The gauge transformations exhibit hyperbolic fixed points, and this results in a physical configuration space with a non-Hausdorff…
We construct the gauge-invariant electric and magnetic charges in Yang-Mills theory coupled to cosmological General Relativity (or any other geometric gravity), extending the flat spacetime construction of Abbott and Deser. For…
We calculate the effective action in Yang-Mills and scalar \phi^4 quantum field theory with quantized scale invariant metric treated non-perturbatively in d=4 dimensions. There is no charge renormalization in the one-loop order for matter…
The quantization of Yang-Mills field theories requires the introduction of a gauge fixing which leads to a violation of the Local Gauss Law described by the so-called Gauss operator. We discuss the local quantizations of Yang-Mills theories…
We discuss relation between lattice phenomenology of confining fields in the vacuum state of Yang-Mills theories (mostly SU(2) case) and continuum theories. In the continuum, understanding of the confinement is most straightforward in the…
The system of two relativistic particles with einbein fields is quantized as a constrained system.A method of the introduction of the Newton--Wigner collective coordinate is discussed in presence of different gauge fixing conditions. Some…
We study quantized Yang-Mills theory with massive vector fields in the framework of causal perturbation theory. The most general form of the interaction which is invariant under operator gauge transformations is pointed out. The generator…
Quantum Yang-Mills theory, Classical Statistical Field Theory (for Hamiltonians which are non-polynomial in the fields, e.g. General relativistic statistical mechanics) and Quantum Gravity all suffer from severe mathematical inconsistencies…
The paper is devoted to quantization of polynomial momentum observables in the cotangent bundle of a smooth manifold. A quantization procedure is proposed allowing to quantize a wide class of functions which are polynomials of any order in…
In double field theory, the equation of motion for a point particle in the background field is considered. We find that the motion is described by a geodesic flow in the doubled geometry. Inspired by the analysis on the particle motion, we…
We consider theories with degenerate kinetic terms such as those that arise at strong coupling in $N=2$ super Yang-Mills theory. We compute the components of generalized $N=1,2$ supersymmetric sigma model actions in two dimensions. The…
I articulate and discuss a geometrical interpretation of Yang-Mills theory. Analogies and disanalogies between Yang-Mills theory and general relativity are also considered.
Geometric quantization is an attempt at using the differential-geometric ingredients of classical phase spaces regarded as symplectic manifolds in order to define a corresponding quantum theory. Generally, the process of geometric…
The self-duality equations for gauge fields in pseudoeuclidean spaces of eight and seven dimensions are considered. Some new classes of solutions of the equations are found.