The Becci-Rouet-Stora-Tyutin (BRST) operator quantization of a finitedimensional gauge system featuring two quadratic super Hamiltonian and m linear supermomentum constraints is studied as a model for quantizing generally covariant gauge theories. The proposed model “completely” mimics the constraint algebra of general relativity. The Dirac constraint operators are identified by realizing the B...

The expectation values of a Hermitian operator  in (2s + 1)2 specific coherent states of a spin are known to determine the operator unambiguously. As shown here, (almost) any other set of (2s + 1)2 coherent state projectors also provide a basis for self-adjoint operators. This is proved by considering the determinant of the Gram matrix associated with the coherent state projectors as a Hamilto...

For an invertible (bounded) linear operator Q acting in a Hilbert space H, we consider the consequences of the QT -symmetry of a non-Hermitian Hamiltonian H : H → H where T is the time-reversal operator. If H is symmetric in the sense that THT = H, then QT symmetry is equivalent toQ-weak-pseudo-Hermiticity. But in general this equivalence does not hold. We show this using some specific examples...

The problem of expanding a density operator p in forms that simplify the evaluation of important classes of quantum-mechanical expectation values is studied. The weight function P(n) of the P representation, the Wigner distribution W(o), and the function (n ~ p ~o), where ~n) is a coherent state, are discussed from a unified point of view. Each of these quasiprobability distributions is examine...

In the present paper, we study unitary orbit of a compact Hermitian diagonal operator with spectral multiplicity one under action group U K + C unitization operators ( H ) , or equivalently, quotient / D . We relate this and different subgroups to describe metric geodesics (using natural distance) which join end points. As consequence obtain local Hopf-Rinow theorem. also explore cases about un...

We investigate the index of the Neuberger’s Dirac operator in abelian gauge theories on finite lattices by numerically analyzing the spectrum of the hermitian Wilson-Dirac operator for a continuous family of gauge fields connecting different topological sectors. By clarifying the characteristic structure of the spectrum leading to the index theorem we show that the index coincides to the topolo...

We consider the Dolbeault operator √ 2(∂ + ∂ *) of K 1 2 – the square root of the canon-ical line bundle which determines the spin structure of a compact Hermitian spin surface (M, g, J). We prove that all cohomology groups H 1 2)) vanish if the scalar curvature of g is non-negative and non-identically zero. Moreover, we estimate the first eigenvalue of the Dolbeault operator when the conformal...

In this paper we consider the hermitian extension of the cross-ΨB-energy operator that we will denote by ΨH . In addition, cross energy terms are formalized through multivariate signals representation. We investigate the connection between the interaction energy function of ΨH and the cross-power spectral density (CPSD) of two complex valued signals. In particular, this link permits to use this...

We investigate the peculiar feature of non-Hermitian operators, namely, existence spectral branch points (also known as exceptional or level crossing points), at which two (or many) eigenmodes collapse onto a single eigenmode and thus loose their completeness. Such are generic produce non-analyticities in spectrum operator, which, turn, result finite convergence radius perturbative expansions b...

Recently, a non-Hermitian chiral random matrix model was proposed to describe the eigenvalues of the QCD Dirac operator at nonzero chemical potential. This matrix model can be constructed from QCD by mapping it to an equivalent matrix model which has the same symmetries as QCD with chemical potential. Its microscopic spectral correlations are conjectured to be identical to those of the QCD Dira...