Related papers: Fermionic observables in Numerical Stochastic Pert…
We derive the vector-like four dimensional overlap Dirac operator starting from a five dimensional Dirac action in the presence of a delta-function space-time defect. The effective operator is obtained by first integrating out all the…
We discuss possible definitions of discrete Dirac operators, and discuss their continuum limits. It is well-known in the lattice field theory that the straightforward discretization of the Dirac operator introduces unwanted spectral…
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 discuss the steps to construct Dirac operators which have arbitrary fermion offsets, gauge paths, a general structure in Dirac space and satisfy the basic symmetries (gauge symmetry, hermiticity condition, charge conjugation, hypercubic…
We present a construction of an integrable model as a projective type limit of spin Calogero-Sutherland model with $N$ fermionic particles, where $N$ tends to infinity. It is implemented in the multicomponent fermionic Fock space. Explicit…
The topological charge in the $\U(N)$ vector-like reduced model can be defined by using the overlap Dirac operator. We obtain its large $N$ limit for a fermion in a general gauge-group representation under a certain restriction of gauge…
In this paper we continue the development of a spectral triple-like construction on a configuration space of gauge connections. We have previously shown that key elements of bosonic and fermionic quantum field theory emerge from such a…
The simple method for the calculating of the anomalous dimensions of the composite operators up to 1/N^2 order is developed. We demonstrate the effectiveness of this approach by computing the critical exponents of the…
We give a functional analytic construction of the fermionic projector on a globally hyperbolic Lorentzian manifold of finite lifetime. The integral kernel of the fermionic projector is represented by a two-point distribution on the…
We develop the analytic bootstrap in several directions. First, we discuss the appearance of nonperturbative effects in the Lorentzian inversion formula, which are exponentially suppressed at large spin but important at finite spin. We show…
This paper studies geometric structures on noncommutative hypersurfaces within a module-theoretic approach to noncommutative Riemannian (spin) geometry. A construction to induce differential, Riemannian and spinorial structures from a…
In presence of string solitons, index theorems for the generalised Dirac operators have to be revisited. We show that in supersymmetric configurations the fermionic operators decouple, so that there are no mixing effects between different…
The mathematical methods that have been used to analyze the statistical properties of boson fields, and in particular the coherence of photons in quantum optics, have their counterparts for Fermi fields. The coherent states, the…
To simulate the quantum systems at classical or quantum computers, it is necessary to reduce continuous observables (e.g. coordinate and momentum or energy and time) to discrete ones. In this work we consider the continuous observables…
According to the necessary requirements for a chirally symmetric Dirac operator, we present a systematic construction of such operators. We formulate a criterion for the hermitian operator which enters the construction such that the doubled…
Concerning Numerical Stochastic Perturbation Theory, we discuss the convergence of the stochastic process (idea of the proof, features of the limit distribution, rate of convergence to equilibrium). Then we also discuss the expected…
We investigate the effect of non-symmetric relatively bounded perturbations on the spectrum of self-adjoint operators. In particular, we establish stability theorems for one or infinitely many spectral gaps along with corresponding…
We study the Dirac equation in the Reissner-Nordstr\"om geometry in horizon-penetrating coordinates up to the Cauchy horizon. A mass decomposition theorem is proved, which gives a covariant representation of the spacetime inner product that…
The inverse nodal problem for Dirac type integro-differential operator with the spectral parameter in the boundary conditions is studied. We prove that dense subset of the nodal points determines the coefficients of differential part of…
We are focused on the idea that observables in quantum physics are a bit more than just hermitian operators and that this is, in general, a "tricky business". The origin of this idea comes from the fact that there is a subtle difference…