Related papers: Dirac operator on the quantum fuzzy four-sphere $ …
Lattice studies of QCD at temperatures above the chiral restoration and QCD with truncated low modes of the Dirac operator indicate approximate and explicit $SU(4)$ degeneracies in hadron spectra, respectively. At the same time, the QCD…
We consider the direct and inverse spectral problems for Dirac operators that are generated by the differential expressions $$ \mathfrak t_q:=\frac{1}{i}[I&0 0&-I]\frac{d}{dx}+[0&q q^*&0] $$ and some separated boundary conditions. Here $q$…
The fractional q-calculus is the q-extension of the ordinary fractional calculus and dates back to early 20-th century. The theory of q-calculus operators are used in various areas of science such as ordinary fractional calculus, optimal…
We consider the quantum theory of a two-form gauge field on a space-time which is a direct product of time and a spatial manifold, taken to be a compact five-manifold with no torsion in its cohomology. We show that the Hilbert space of this…
We discuss a generalized representation of the Dirac delta function in $d$ dimensions in terms of $q$-exponential functions. We apply this new representation to the study of the so-called $q$-Fourier transform, proving its invertibility for…
The system of gravity coupled to the non-rotational dust field is studied at both classical and quantum levels. The scalar constraint of the system can be written in the form of a true physical Hamiltonian with respect to the dust time. In…
We report on an ongoing project to parametrize the Fixed-Point Dirac operator for massless quarks, using a very general construction which has arbitrarily many fermion offsets and gauge paths, the complete Clifford algebra and satisfies all…
The coupling of spin 0 and spin 1 external fields to Dirac fermions defines a theory which displays gauge chiral symmetry. Quantum mechanically, functional integration of the fermions yields the determinant of the Dirac operator, known as…
The intersection of the 10-dimensional fuzzy conifold $Y_F^{10}$ with $S^5_F \times S^5_F$ is the compact 8-dimensional fuzzy space $X_F^8$. We show that $X_F^8$ is (the analogue of) a principal $U(1)\times U(1)$ bundle over fuzzy…
In this paper we construct a non-commutative geometry over a configuration space of gauge connections and show that it gives rise to a candidate for an interacting, non-perturbative quantum gauge theory coupled to a fermionic field on a…
We compute the low-lying spectrum of the staggered Dirac operator above and below the finite temperature phase transition in both quenched QCD and in dynamical four flavor QCD. In both cases we find, in the high temperature phase, a density…
Starting with the first-order singular Lagrangian describing the dynamical system with 2nd-class constraints, the noncommutative quantum mechanics on a curved space is investigated by the constraint star-product quantization formalism of…
We construct a parametrization of a Fixed Point (FP) Dirac operator and apply it in quenched lattice QCD. The symmetry requirements for a general lattice Dirac operator are discussed and an efficient way to make a practical construction of…
Operators, refered to as k-fermion operators, that interpolate between boson and fermion operators are introduced through the consideration of two noncommuting quon algebras. The deformation parameters for these quon algebras are roots of…
Consider a formally self-adjoint first order linear differential operator acting on pairs (2-columns) of complex-valued scalar fields over a 4-manifold without boundary. We examine the geometric content of such an operator and show that it…
A new approach to a unified theory of quantum gravity based on noncommutative geometry and canonical quantum gravity is presented. The approach is built around a *-algebra generated by local holonomy-diffeomorphisms on a 3-manifold and a…
In this paper, we give two Lichnerowicz type formulas for Dirac operators and signature operators twisted by a vector bundle with a non-unitary connection. We also prove two Kastler-Kalau-Walze type theorems for twisted Dirac operators and…
We explore a new simple N=2 SQM model describing the motion over complex manifolds in external gauge fields. The nilpotent supercharge Q of the model can be interpreted as a (twisted) exterior holomorphic derivative, such that the model…
In this paper we discuss a connection between Dirac operators on configuration spaces and Yang-Mills quantum field theory. We first show that the Hamilton operators of the self-dual and anti-self-dual sectors of a Yang-Mills quantum field…
We study the spectrum of the QCD Dirac operator near zero virtuality for $N_c =2$. According to a universality argument, it can be described by a random matrix theory with the chiral structure of QCD, but with $real$ matrix elements. Using…