Related papers: Dirac Operators on Configuration Spaces and Yang-M…

In this paper we study the foundations of the algebraic treatment of classical and quantum field theories for Dirac fermions under external backgrounds following the initial contributions made by several collegues. The treatment is…

We study a series of problems in classical Yang-Mills theories using lattice methods. We first investigate SU(N) self-dual configurations on the torus with twisted boundary conditions. We also study the zero modes of the Dirac equation in…

In the framework of algebraic quantum field theory we analyze the anomalous statistics exhibited by a class of automorphisms of the observable algebra of the two-dimensional free massive Dirac field, constructed by fermionic gauge group…

Proofs of two statements are provided in this paper. First, the authors prove that the formalism of the pseudo-Hermitian quantum mechanics allows describing the Dirac particles motion in arbitrary stationary gravitational fields. Second, it…

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…

We present a brief review of the cohomological solutions of self-coupling interactions of the fields in the free Yang-Mills theory. All consistent interactions among the fields have been obtained using the antifield formalism through…

We consider SU(2)-equivariant dimensional reduction of Yang-Mills-Dirac theory on manifolds of the form M x CP(1), with emphasis on the effects of non-trivial magnetic flux on CP(1). The reduction of Yang-Mills fields gives a chain of…

Operator fields in the bundle of Dirac spinors and their conversion to spatial fields are considered. Some commutator equations are studied with the use of the conversion technique.

The issue of general covariance of spinors and related objects is reconsidered. Given an oriented manifold $M$, to each spin structure $\sigma$ and Riemannian metric $g$ there is associated a space $S_{\sigma, g}$ of spinor fields on $M$…

The main issues of the spectral theory of Dirac operators are presented, namely: transformation operators, asymptotics of eigenvalues and eigenfunctions, description of symmetric and self-adjoint operators in Hilbert space, expansion in…

We examine an extension of the ideas of quantum cosmology and, in particular, the proposal of Hartle and Hawking for the boundary conditions of the Universe, to models which incorporate Yang-Mills fields. Inhomogeneous perturbations about a…

We construct quantum flux operators with respect to the Poincar\'e symmetry in the massless Dirac theory at future null infinity. An anomalous helicity flux operator emerges from the commutator of the superrotation generators. The helicity…

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 study the Dirac-Yang-Mills equations on closed spin manifolds with a focus on uncoupled solutions, i.e. solutions for which the connection form satisfies the Yang-Mills equation. Such solutions require the Dirac current, a quadratic form…

This seminal paper marks the beginning of our investigation into on the spectral theory based on $S$-spectrum applied to the Dirac operator on manifolds. Specifically, we examine in detail the cases of the Dirac operator $\mathcal{D}_H$ on…

The Dirac Hamiltonian formalism is applied to a system in $(2+1)$-dimensions consisting of a Dirac field $\psi$ minimally coupled to Chern-Simons $U(1)$ and $SO(2,1)$ connections, $A$ and $\omega$, respectively. This theory is connected to…

A geometrization of the Yang-Mills field, by which an SU(2) gauge theory becomes equivalent to a 3-space geometry - or optical system - is examined. In a first step, ambient space remains Euclidean and current problems on flat space can be…

Quantum mechanics in the presence of $\delta$-function potentials is known to be plagued by UV divergencies which result from the singular nature of the potentials in question. The standard method for dealing with these divergencies is by…

We show that the Yang-Mills quantum field theory with momentum and spacetime cutoffs in four Euclidean dimensions is equivalent, term by term in an appropriately resummed perturbation theory, to a Fermionic theory with nonlocal interaction…

The task of calculating operator dimensions in the planar limit of N=4 super Yang-Mills theory can be vastly simplified by mapping the dilatation generator to the Hamiltonian of an integrable spin chain. The Bethe ansatz has been used in…