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

Based on our previous work on the differential geometry for the closed string double field theory, we construct a Yang-Mills action which is covariant under O(D,D) T-duality rotation and invariant under three-types of gauge transformations:…

We conjecture that the renormalized perturbative $S$-matrix of quantum field theory coincides with the evolution operator of the standard functional differential Schrodinger equation whose right hand side (quantum local Hamiltonian) is…

The N=(2,2) extended super Yang-Mills theory in 2 dimensions is formulated on the lattice as a dimensional reduction of a 4 dimensional lattice gauge theory. We use the plaquette action for a bosonic sector and the Wilson- or the…

We use the Yang-Mills gradient flow on the space of connections over a closed Riemann surface to construct a Morse-Bott chain complex. The chain groups are generated by Yang-Mills connections. The boundary operator is defined by counting…

We propose a reformulation of Yang-Mills theory as a perturbative deformation of a novel topological (quantum) field theory. We prove that this reformulation of the four-dimensional QCD leads to quark confinement in the sense of area law of…

The purpose of this work is to present a Non--Commutative Geometrical version of the Yang--Mills Theory and the Yang--Mills Scalar Matter Theory by constructing a concrete example using M. Durdevich's theory of quantum principal bundles.

We report on our non-perturbative investigations of supersymmetric Yang-Mills quantum mechanics with 4 supercharges. We employ two independent numerical methods. First of them is the cut Fock space method whose numerical implementation was…

The hamiltonian formulation of Supersymmetric Yang-Mills quantum mechanics (SYMQM) is discussed. We focus on the Fock space formulation of the models since it is convenient for the numerical analysis, however some novel analytical results…

We show that the principal part of the Dirac Hamiltonian in 3+1 dimensions emerges in a semi-classical approximation from a construction which encodes the kinematics of quantum gravity. The construction is a spectral triple over a…

The quantized free Dirac field is considered on Minkowski spacetime (of general dimension). The Dirac field is coupled to an external scalar potential whose support is finite in time and which acts by a Moyal-deformed multiplication with…

Using analyticity of the vacuum wave-functional under complex scalings, the vacuum of a quantum field theory may be reconstructed from a derivative expansion valid for slowly varying fields. This enables the eigenvalue problem for the…

The recently obtained solutions of Dirac equation in the confining SU(3)-Yang-Mills field in Minkowski spacetime are applied to describe the energy spectra of quarkonia (charmonium and bottomonium). The nonrelativistic limit is considered…

As a first step towards a strong coupling expansion of Yang-Mills theory, the SU(2) Yang-Mills quantum mechanics of spatially constant gauge fields is investigated in the symmetric gauge, with the six physical fields represented in terms of…

We employ the light-cone formalism to construct in the (super) Yang-Mills theories in the multi-color limit the one-loop dilatation operator acting on single trace products of chiral superfields separated by light-like distances. In the N=4…

We study the effective action associated to the Dirac operator in two dimensional non-commutative Field Theory. Starting from the axial anomaly, we compute the determinant of the Dirac operator and we find that even in the U(1) theory, a…

We construct the algebra of operators acting on the Hilbert spaces of Quantum Mechanics for systems of $N$ identical particles from the field operators acting in the Fock space of Quantum Field Theory by providing the explicit relation…

This paper is devoted to mathematical and physical properties of the Dirac operator and spectral geometry. Spin-structures in Lorentzian and Riemannian manifolds, and the global theory of the Dirac operator, are first analyzed. Elliptic…

We identify a diffeomorphism Lie algebra in the self-dual sector of Yang-Mills theory, and show that it determines the kinematic numerators of tree-level MHV amplitudes in the full theory. These amplitudes can be computed off-shell from…

This paper develops a chiral adelic operator framework in which the functional--equation symmetry of global $L$--functions is realized directly in the spectrum of a Dirac--type Hamiltonian. Working on the id\`ele class space, we place a…

We show how the well-known classical field equations as Einstein and Yang-Mills ones, which arise as the conformal invariance conditions of certain two-dimensional theories, expanded up to the second order in the formal parameter, can be…