Related papers: Path integral calculation of heat kernel traces wi…
This paper reviews the grading technique developed by Getzler to prove the local index theorem and shows how to adapt it to compute the leading terms of asymptotic expansions of traces of heat kernels in two other situations.
We solve numerically exactly a simple toy model to quantum general relativity or more properly to path integral on a curved space. We consider the thermal equilibrium of a quantum many body problem on the sphere, the surface of constant…
We propose a path integral formulation for scale invariant quantum field theories. We do it by modifying the functional integration measure in such a way that the partition function is always exactly scale invariant, at the cost of having…
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…
This paper introduces a novel, non-deterministic method for embedding data in low-dimensional Euclidean space based on computing realizations of a Gaussian process depending on the geometry of the data. This type of embedding first appeared…
We develop a heat kernel method to compute the one-loop effective action for a general class of nonlinear electrodynamic (NLED) theories in four dimensional Minkowski spacetime. Working in the background field formalism, we extract the…
The first objective of this article is to show that the black hole partition function can be placed on a firm logical foundation by enclosing the black hole in a spatially finite "box" or boundary. The presence of the box has the effect of…
Feynman's path integral approach is studied in the framework of the Wigner-Dunkl deformation of quantum mechanics. We start with reviewing some basics from Dunkl theory and investigate the time evolution of a Gaussian wave packet, which…
We present a formalism for computing arbitrary multi-loop Feynman graphs in curved spacetime using the heat kernel approach. To this end, we compute the off-diagonal components of the heat kernel in Riemann normal coordinates up to second…
The conformal powers of the Laplacian of a Riemannian metric which are known as the GJMS-operators admit a combinatorial description in terms of the Taylor coefficients of a natural second-order one-parameter family $\H(r;g)$ of…
A method for calculation of the DWSG coefficients for operators in spaces with metric incompatible with connection is suggested based on a generalization of the pseudodifferential operators technique. By using the proposed method, the…
The prediction and subsequent discovery of topological semimetal phases of matter in solid state systems has instigated a surge of activity investigating the exotic properties of these unusual materials. Amongst these are transport…
We outline a proposal, based on the Heat-Kernel method, to compute 1PI effective action up to any loop order for quantum field theory with scalar and fermion fields. We algebraically extract the divergences associated with the composite…
The paper solves the problem of continuum limit in bosonic thermal coherent-state path integrals. For this purpose, exact discrete versions of the path integral are constructed for three different orderings of the Hamiltonian: normal,…
We discuss the path integral representation for the fermionic particles and strings and concentrate at the problems arising when some target-space dimensions are compact. An example of partition function for fermionic particle at finite…
We consider a class of fourth order uniformly elliptic operators in planar Euclidean domains and study the associated heat kernel. For operators with $L^{\infty}$ coefficients we obtain Gaussian estimates with best constants, while for…
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.…
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 kernel polynomial method allows to sample overall spectral properties of a quantum system, while sparse diagonalization provides accurate information about a few important states. We present a method combining these two approaches…
We apply the method of spectral sequences to study classical problems in analysis. We illustrate the method by finding polynomial vector fields that commute with a given polynomial vector field and finding integrals of polynomial…