Related papers: Soliton Fermionic number from the heat kernel expa…
The scattering of Dirac fermions in the background fields of topological solitons of the $(2+1)$-dimensional $\mathbb{CP}^{N-1}$ model is studied using analytical and numerical methods. It is shown that the exact solutions for fermionic…
We calculate the partition function of a harmonic oscillator with quasi-periodic boundary conditions using the zeta-function method. This work generalizes a previous one by Gibbons and contains the usual bosonic and fermionic oscillators as…
The heat kernel expansion is a very convenient tool for studying one-loop divergences, anomalies and various asymptotics of the effective action. The aim of this report is to collect useful information on the heat kernel coefficients…
It is argued that the derivative expansion is a suitable method to deal with finite temperature field theory, if it is restricted to spatial derivatives only. Using this method, a simple and direct calculation is presented for the…
We compute the full asymptotic expansion of the heat kernel Trace$(\exp(-tD^2))$ where $D$ is, assuming RH, the self-adjoint operator whose spectrum is formed of the imaginary parts of non-trivial zeros of the Riemann zeta function. The…
We study fermionic excitations in a hot and dense strongly interacting medium consisting of quarks and (pseudo-)scalar mesons. In particular, we use the two-flavor quark-meson model in combination with the Functional Renormalization Group…
By using ideas and strong results borrowed from the classical moment problem, we show how -under very general conditions- a discrete number of values of the spectral zeta function (associated generically with a non-decreasing sequence of…
We give a prescription for calculating the high-temperature expansion of the thermal sunset integral to arbitrary order. We derive all terms odd in $T$, and rederive previous results up to $\mathcal{O}(T^0) $ for both bosonic and fermionic…
We study again the phenomenon of charge fractionalization at finite temperature. Our calculations are done in a framework in which the connection between the induced fermion number and the chiral anomaly is manifest. We find that the…
Stellar cores may be considered as a nuclear reactor that play important role in injecting new synthesized elements in the interstellar medium Helium burning is an important stage that contribute to the synthesis of key elements such as…
We perform an unitary transformation for the symmetric phonon mode of the Holstein molecular crystal hamiltonian. We show how to compute the electronic spectral functions by exact numerical diagonalisation of an effective hamiltonian fully…
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…
The heat kernel associated with an elliptic second-order partial differential operator of Laplace type acting on smooth sections of a vector bundle over a Riemannian manifold, is studied. A general manifestly covariant method for…
Using the Hamiltonian formulation of Composite Fermions developed recently, the temperature dependence of the spin polarization is computed for the translationally invariant fractional quantum Hall states at $\nu=1/3$ and $\nu=2/5$ in two…
The scattering of fermions in the background field of a topological soliton of the modified $(2 + 1)$-dimensional $\mathbb{CP}^{1}$ model is studied here both analytically and numerically. Unlike the original $\mathbb{CP}^{1}$ model, the…
These notes focus on the applications of the stochastic Taylor expansion of solutions of stochastic differential equations to the study of heat kernels in small times. As an illustration of these methods we provide a new heat kernel proof…
In a previous paper we have presented a general formalism for computing Feynman diagrams for scalar fields in curved spacetime at any loop order using heat kernel methods. The main technique used is the expansion of the fully off-diagonal…
Hermite polynomials, which are associated to a Gaussian weight and solve the Laplace equation with a drift term of linear growth, are classical in analysis and well-understood via ODE techniques. Our main contribution is to give explicit…
A functorial derivation is presented of a heat-kernel expansion coefficient on a manifold with a singular fixed point set of codimension two. The existence of an extrinsic curvature term is pointed out.
We present analytical methods to calculate the magnetic response of non-interacting electrons constrained to a domain with boundaries and submitted to a uniform magnetic field. Two different methods of calculation are considered - one…