Related papers: Spectral functions and their applications
Conformal Field Theories (CFTs) are special classes of quantum field theories that find applications ranging from critical phenomena to theories of quantum gravity via holography. Understanding thermal effects in CFTs is crucial:…
It is well known that short-time expansions of heat kernels correlate to formal high-frequency expansions of spectral densities. It is also well known that the latter expansions are generally not literally true beyond the first term.…
We use a Harnack-type inequality on exit times and spectral bounds to characterize upper bounds of the heat kernel associated with any regular Dirichlet form without killing part, where the scale function may vary with position. We further…
Lecture notes for one of the courses at the OPSFA Summerschool 6, July 11-15, 2016. All the results in these notes have appeared in the literature. Many special functions are eigenfunctions to explicit operators, such as difference and…
This is a mini-review of the heat kernel expansion for generalized Laplacians on various noncommutative spaces. Applications to the spectral action principle, renormalization of noncommutative theories and anomalies are also considered.
Working within the framework of the covariant perturbation theory, we obtain the coincidence limit of the heat kernel of an elliptic second order differential operator that is applicable to a large class of quantum field theories. The basis…
The fermionic dispersion relation in the presence of a background magnetic field and a high temperature QED plasma is calculated exactly in the external field, using the Hard Thermal Loop effective action. As the field strength increases…
This is a short review on the thermal, spectral representation in the real-time version of the finite temperature quantum field theory. After presenting a clear derivation of the spectral representation, we discuss the properties of its…
We obtain two-sided estimates for the heat kernel (or the fundamental function) associated with the following fractional Schr\"odinger operator with negative Hardy potential $$\Delta^{\alpha/2} -\lambda |x|^{-\alpha}$$ on $\RR^d$, where…
A diagramatic heat kernel expansion technique is presented. The method is especially well suited to the small-derivative expansion of the heat kernel, but it can also be used to reproduce the results obtained by the approach known as…
By using gauge/gravity duality, we calculate the spectral function of the heavy vector mesons with the presence of an intense magnetic field in a hot and dense medium. The results show that, a general conclusion, as the increases of…
We analyze the spectra of general non-minimal second-order operators. To do this, we derive the local part of the trace of the second Seeley-DeWitt heat kernel coefficient for such operators in a completely model-independent way.…
We show how the Binomial Theorem can be used to continue the Riemann Zeta Function to the left hand half-plane. This method yields the explicit values of the function at non-positive integers in terms of the Bernoulli numbers.
In this paper we continue the analysis of spectral problems in the setting of complete manifolds with fibred boundary metrics, also referred to as $\phi$-metrics, as initiated in our previous work. We consider the Hodge Laplacian for a…
The spectral function of the scalar-isoscalar channel of the O(N) symmetric linear $\sigma$ model is studied in the broken symmetry phase. The investigation is based on the leading order evaluation of the self-energy in the limit of large…
In this paper, we introduce and investigate a new extension of the beta function by means of an integral operator involving a product of Bessel-Struve kernel functions. We also define a new extension of the well-known beta distribution, the…
The zeta function regularization technique is used to study the finite temperature Casimir effect for a charged and massless scalar field confined between parallel plates and satisfying Dirichlet boundary conditions at the plates. A…
We introduce a method of constructing a general Laakso space while calculating the spectrum and multiplicities of the Laplacian operator on it. Using this information, we found the leading term of the trace of the heat kernel of a Laakso…
We generalize earlier studies on the Laplacian for a bounded open domain $\Omega\in \real^2$ with connected complement and piecewise smooth boundary. We compare it with the quantum mechanical scattering operator for the exterior of this…
We present a brief overview of several approaches for calculating the local asymptotic expansion of the heat kernel for Laplace-type operators. The different methods developed in the papers of both authors some time ago are described in…