Related papers: Local momentum space and the vector field
I discuss the trace of a heat kernel Tr[e^(-tA)] for compact fuzzy spaces. In continuum theory its asymptotic expansion for t -> +0 provides geometric quantities, and therefore may be used to extract effective geometric quantities for fuzzy…
We develop a new method of computing radiation reaction for a point particle interacting with massless scalar and vector fields in curved space-time. It is based on the analysis of field Green's functions with both points lying on the…
We consider certain results for the heat kernel of nonminimal operators. The general expressions provided by Gusynin and Kornyak resulting from symbolic computation programmes for n dimensions are evaluated for 4 dimensions which are…
The heat kernel method is extended to the case of finite temperature. Special emphasis is given to the study of gauge theories. Due to the compactness of space in the Euclidean time direction (inverse temperature) the field strength cannot…
The low energy effective action of gravity in any even dimension generally acquires non-local terms associated with the trace anomaly, generated by the quantum fluctuations of massless fields. The local auxiliary field description of this…
We build a systematic calculational method for the covariant expansion of the two-point heat kernel $\hat K(\tau|x,x')$ for generic minimal and non-minimal differential operators of any order. This is the expansion in powers of dimensional…
In these notes we construct the momentum-space potentials from configuration-space using for the Fourier-transformation the Gaussian-Expansion-Method (GEM). This has the advantage that the Fourier-Bessel integrals can be performed…
Using the heat kernel method and the analytic continuation of the zeta function, we calculate the canonical and improved vacuum stress tensors, ${T_{\mu \nu}(\vec{x})}$ and ${\Theta_{\mu \nu}(\vec{x})}$, associated with a massless scalar…
For a large class of scalar-tensor-like modified gravity whose action contains nonminimal couplings between a scalar field $\phi(x^\alpha)$ and generic curvature invariants $\mathcal{R}$ beyond the Ricci scalar $R=R^\alpha_{\;\;\alpha}$, we…
Asymptotic expansions of Green functions and spectral densities associated with partial differential operators are widely applied in quantum field theory and elsewhere. The mathematical properties of these expansions can be clarified and…
The basis of this work is the first full application of the Poisson-Wiseman-Anderson method of `matched expansions' to compute the self-force acting on a point particle moving in a curved spacetime. The method employs two expansions for the…
After establishing the positivity constraint and spin content of the theory for gravitons interacting with a necessarily, and \textit{a priori}, \textit{non}-conserved external energy-momentum tensor, the expectation value formalism of the…
We show that an high temperature expansion at fixed order parameter can be derived for the quantum Ising model. The basic point is to consider a statistical generating functional associated to the local spin state. The probability at…
The question of thermodynamic consistence and $\Phi$-derivability of the asymptotic limit of high spatial dimensions for quantum itinerant models is addressed. It is shown that although the irreducible $n$-particle Green functions are…
A new formalism is presented for high-energy analysis of the Green function for Fokker-Planck and Schr\"odinger equations in one dimension. Formulas for the asymptotic expansion in powers of the inverse wave number are derived, and…
We derive an action for scalar quantum field theory with cubic interaction in the context of relative locality. Beginning with the generating functional for standard $\varphi^3$--theory and the corresponding Feynman rules we modify them to…
In this article, we consider the problem of estimating the heat kernel on measure-metric spaces equipped with a resistance form. Such spaces admit a corresponding resistance metric that reflects the conductivity properties of the set. In…
The implications of conformal invariance, as relevant in quantum field theories at a renormalisation group fixed point, are analysed with particular reference to results for correlation functions involving conserved currents and the energy…
In this paper we analyze the small-t asymptotic expansion of the trace of the heat kernel associated with a Laplace operator endowed with a spherically symmetric polynomially confining potential on the unbounded, d-dimensional Euclidean…
We analyze the space-time structure of local gauge string with a phenomenological energy momentum tensor, as prescribed by Vilenkin in an arbitrary number of space-time dimensions with a non-zero cosmological constant >. A set of solutions…