Related papers: Spectral functions and their applications
We present an analysis of four sum rules, each based on chiral symmetry and containing the difference $\rho_{\rm V}(s) - \rho_{\rm A}(s)$ of isovector vector and axialvector spectral functions. Experimental data from tau lepton decay and…
The finite temperature Casimir effect for a charged, massive scalar field confined between very large, perfectly conducting parallel plates is studied using the zeta function regularization technique. The scalar field satisfies Dirichlet…
Riemann zeta function is an important object of number theory. It was also used for description of disordered systems in statistical mechanics. We show that Riemann zeta function is also useful for the description of integrable model. We…
We use a spectral theory perspective to reconsider properties of the Riemann zeta function. In particular, new integral representations are derived and used to present its value at odd positive integers.
The in-medium modifications of hadron properties such as masses and decay widths have been a major focus of the scientific work of Gerry Brown and the insights gained by him and his collaborators made them major drivers of this field for…
In this paper we analyze the spectral zeta function associated with a Laplace operator acting on scalar functions on an N-dimensional Euclidean space in the presence of a spherically symmetric background potential. The obtained analytic…
An analysis of the zeta and gamma function is presented, using elementary functions like [] and {}, a general formula for the angle of zeta(1/2 + i*n) is found and the same for the gamma function.
We investigate the analytic structure of thermal spectral function of holographic CFTs, synthesizing recent developments into a set of observations about its asymptotics. Specifically, for a class of scalar primaries with integral…
We rewrite the exact expression for the finite temperature two-point correlation function for the magnetization as a partition function of some field theory. This removes singularities and provides a convenient form to develop a virial…
Equilibrium finite temperature observables of a CFT can be described by a local effective action for background fields -- a "thermal effective action." This effective action determines the asymptotic density of states of a CFT as a detailed…
In this paper some techniques useful to perform quantum field theory computations in a covariant manner are reviewed. In particular the background field gauge, the zeta function regularization and the heat kernel approach are highlighted.…
In this paper, we firstly establish weighted heat kernel comparison theorems for the weighted heat equation on complete manifolds with radial curvatures bounded, and then by mainly using this conclusion, we can obtain two eigenvalue…
A quantum field-theoretical model which describes spatially non-homogeneous one-dimensional non-relativistic repulsive Bose gas in an external harmonic potential is considered. We calculate the two-point thermal correlation function of the…
Asymptotic relations between zeta functions (such as, $\zeta(s),\,\beta(s)$, and other Dirichlet $L$-functions) and interpolation differences of functions like $\vert y\vert^s$ and their interpolating entire functions of exponential type…
Based on the Mehler heat kernel of the Schroedinger operator for a free electron in a constant magnetic field an estimate for the kernel of E_A is derived, where E_A represents the kinetic energy of a Dirac electron within the…
In this paper we study spectral zeta functions associated to finite and infinite graphs. First we establish a meromorphic continuation of these functions under some general conditions. Then we study special values in the case of standard…
The computation and inversion of the binomial and negative binomial cumulative distribution functions play a key role in many applications. In this paper, we explain how methods used for the central beta distribution function (described in…
Chiral theories of constituent quarks interacting with bosons and photons at high temperatures are studied. In the expected chirally symmetric phase effective electromagnetic anomalous couplings for e.g. $\pi \sigma \to \gamma \gamma, ~…
We consider two-component fermions with a zero-range interaction both in two and three dimensions and study their spectral functions of bulk and shear viscosities for an arbitrary scattering length. Here the Kubo formulas are systematically…
In quantum field theories at finite temperature spectral functions describe how particle systems behave in the presence of a thermal medium. Although data from lattice simulations can in principle be used to determine spectral function…