相关论文: Nonperturbative heat kernel and nonlocal effective…
We work out the general features of perturbative field theory on noncommutative manifolds defined by isospectral deformation. These (in general curved) `quantum spaces', generalizing Moyal planes and noncommutative tori, are constructed…
We compute the gravitational effective action by integrating out quantum matter fields in a weak gravitational field, using the Schwinger-Keldysh (in-in) formalism. We pay particular attention to the role of the initial quantum state in the…
We review the status of covariant methods in quantum field theory and quantum gravity, in particular, some recent progress in the calculation of the effective action via the heat kernel method. We study the heat kernel associated with an…
We discuss a variety of developments in the study of large time behavior of the positive minimal heat kernel of a time independent (not necessarily symmetric) second-order parabolic operator defined on a domain M in $R^d$, or more…
In this paper we review some recent results on nonlocal interaction problems. The focus is on interaction kernels that are anisotropic variants of the classical Coulomb kernel. In other words, while preserving the same singularity at zero…
We apply a recently suggested technique of the Neumann-Dirichlet reduction to a toy model of brane-induced gravity for the calculation of its quantum one-loop effective action. This model is represented by a massive scalar field in the…
We study the large-time asymptotic behavior of solutions to the discrete-time heat equation, i.e., caloric functions, on affine buildings, including those without transitive group actions. For each $p \in [1, \infty]$, we introduce a notion…
We consider the non-local energy-momentum tensor of quantum scalar and spinor fields in $2 w$-dimensional curved spaces. Working to lowest order in the curvature we show that, while the non-local terms proportional to $\Box {\cal R}$, $\Box…
We rederive non-perturbatively the Coleman-Weinberg expression for the effective potential for massless scalar QED. Our result is not restricted to small values of the coupling constants. This shows that the Coleman- Weinberg result can be…
The evaluation of effective potentials is critical for a range of phenomenological applications, including inflation, vacuum stability, and phase transitions. A drawback arises from the gauge-dependence of the effective potential.…
We study the heat kernel for a Laplace type partial differential operator acting on smooth sections of a complex vector bundle with the structure group $G\times U(1)$ over a Riemannian manifold $M$ without boundary. The total connection on…
Among the available perturbative approaches in quantum field theory, heat kernel techniques provide a powerful and geometrically transparent framework for computing effective actions in nontrivial backgrounds. In this work, resummation…
A short informal overview about recent progress in the calculation of the effective action in quantum gravity is given. I describe briefly the standard heat kernel approach to the calculation of the effective action and discuss the…
Casimir energy is a nonlocal effect; its magnitude cannot be deduced from heat kernel expansions, even those including the integrated boundary terms. On the other hand, it is known that the divergent terms in the regularized (but not yet…
In this paper, we study the heat kernel associated to the intrinsic sublaplacian on a quaternionic contact manifold considered as a subriemannian manifold. More precisely, we explicitly compute the first two coefficients $c_0$ and $c_1$…
We review an approach developed in the last few years by our group in which GR is modified in the infrared, at an effective level, by nonlocal terms associated to a mass scale. We begin by recalling the notion of quantum effective action…
We explicitly construct a heat kernel as a Neumann series for certain function spaces, such as $L^{1}$, $L^{2}$, and Hilbert spaces, associated to a locally compact Hausdorff space $\mathfrak{X}$ with Borel $\sigma$-algebra $\mathcal{B}$,…
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.
We use our recently proposed algebraic approach for calculating the heat kernel associated with the Laplace operator to calculate the one-loop effective action in the non-Abelian gauge theory. We consider the most general case of arbitrary…
The paper is devoted to a local heat kernel, which is a special part of the standard heat kernel. Locality means that all considerations are produced in an open convex set of a smooth Riemannian manifold. We study such properties and…