DeWitt-Schwinger expansion for projective and Grassmann spaces

We propose a method of calculating the heat kernel expansion of coset spaces. The five first coefficients of this expansion on symmetric spaces of dimension d8 are obtained.     

Heat Kernel and Number Theory on NC-Torus

The heat trace asymptotics on the noncommutative torus, where generalized Laplacians are made out of left and right regular representations, is fully determined. It turns out that this question is very sensitive to the number-theoretical aspect of the deformation parameters. The central condition we use is of a Diophantine type. More generally, the importance of number theory is made explicit in a few examples. We apply the results to the spectral action computation and revisit the UV/IR mixing phenomenon for a scalar theory. Although we find non-local counterterms in the NC theory on , we show that this theory can be made renormalizable at least at one loop, and maybe even beyond.     

Constraints, gauge symmetries, and noncommutative gravity in two dimensions

After a short introduction, we show how the canonical formalism is constructed in space-time noncommutative theories such that it allows defining the notion of first-class constraints and analyzing gauge symmetries. We use this formalism to noncommutatively deform the two-dimensional string gravity (also known as the Witten black hole). Dedicated to Yu. V. Novozhilov on the occasion of his 80th birthday __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 148, No. 1, pp. 64–79, July, 2006.     

Virtual black holes in generalized dilaton theories

The virtual black hole phenomenon, which has been observed previously in specific models, is established for generic 2D dilaton gravity theories with scalar matter. The ensuing effective line element can become asymptotically flat only for two classes of models; among them spherically reduced theories and the string inspired dilaton black hole. We present simple expressions for the lowest order scalar field vertices of the effective theory which one obtains after integrating out geometry exactly. Treating the boundary in a natural and simple way, asymptotic states, tree-level vertices and the tree-level S-matrix are conformally invariant. Examples are provided pinpointing the physical consequences of virtual black holes on the (CPT-invariant) S-matrix for gravitational scattering of scalar particles. For minimally coupled scalars the evaluation of the S-matrix in closed form is straightforward. For a class of theories including the string inspired dilation black hole all tree-graph vertices vanish, which explains the particular simplicity of that model and at the same time shows yet another essential difference to the Schwarzschild case.Received: 7 August 2002, Revised: 2 June 2003, Published online: 11 July 2003D.V. Vassilevich: On leave from V. Fock Institute of Physics, St. Petersburg University, 198904 St. Petersburg, Russia     

Spectral Action Beyond the Weak-Field Approximation

The spectral action for a non-compact commutative spectral triple is computed covariantly in a gauge perturbation up to order 2 in full generality. In the ultraviolet regime, p????, the action decays as 1/p ⁴ in any even dimension.     

Algebraic approach to Kaluza-Klein models

We propose a new method for the construction of injections into classical Lie algebras. This method is very useful for the analysis of vacuum solutions in Kaluza-Klein models. With the help of the proposed procedure, one can obtain all the known solutions as well as a new one explicitly constructed in this letter.     

Heat Trace Asymptotics Defined by Transfer Boundary Conditions

We compute the first five terms in the short-time heat trace asymptotics expansion for an operator of the Laplace type with transfer boundary conditions using the functorial properties of these invariants.     

Nearly associative deformation quantization

We study several classes of non-associative algebras as possible candidates for deformation quantization in the direction of a Poisson bracket that does not satisfy Jacobi identities. We show that in fact alternative deformation quantization algebras require the Jacobi identities on the Poisson bracket and, under very general assumptions, are associative. At the same time, flexible deformation quantization algebras exist for any Poisson bracket.