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Search Results: 1 - 10 of 297257 matches for " D. V. Vassilevich "
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The Faddeev-Popov trick in the presence of boundaries
D. V. Vassilevich
Physics , 1997, DOI: 10.1016/S0370-2693(98)00008-2
Abstract: We formulate criteria of applicability of the Faddeev-Popov trick to gauge theories on manifolds with boundaries. With the example of Euclidean Maxwell theory we demonstrate that the path integral is indeed gauge independent when these criteria are satisfied, and depends on a gauge choice whenever these criteria are violated. In the latter case gauge dependent boundary conditions are required for a self-consistent formulation of the path intgral.
Quantum corrections to the mass of the supersymmetric vortex
D. V. Vassilevich
Physics , 2003, DOI: 10.1103/PhysRevD.68.045005
Abstract: We calculate quantum corrections to the mass of the vortex in N=2 supersymmetric abelian Higgs model in (2+1) dimensions. We put the system in a box and apply the zeta function regularization. The boundary conditions inevitably violate a part of the supersymmetries. Remaining supersymmetry is however enough to ensure isospectrality of relevant operators in bosonic and fermionic sectors. A non-zero correction to the mass of the vortex comes from finite renormalization of couplings.
Diffeomorphism covariant star products and noncommutative gravity
D. V. Vassilevich
Physics , 2009, DOI: 10.1088/0264-9381/26/14/145010
Abstract: The use of a diffeomorphism covariant star product enables us to construct diffeomorphism invariant gravities on noncommutative symplectic manifolds without twisting the symmetries. As an example, we construct noncommutative deformations of all two-dimensional dilaton gravity models thus overcoming some difficulties of earlier approaches. One of such models appears to be integrable. We find all classical solutions of this model and discuss their properties.
Tensor calculus on noncommutative spaces
D. V. Vassilevich
Physics , 2010, DOI: 10.1088/0264-9381/27/9/095020
Abstract: It is well known that for a given Poisson structure one has infinitely many star products related through the Kontsevich gauge transformations. These gauge transformations have an infinite functional dimension (i.e., correspond to an infinite number of degrees of freedom per point of the base manifold). We show that on a symplectic manifold this freedom may be almost completely eliminated if one extends the star product to all tensor fields in a covariant way and impose some natural conditions on the tensor algebra. The remaining ambiguity either correspond to constant renormalizations to the symplectic structure, or to maps between classically equivalent field theory actions. We also discuss how one can introduce the Riemannian metric in this approach and the consequences of our results for noncommutative gravity theories.
Non-commutative heat kernel
D. V. Vassilevich
Physics , 2003, DOI: 10.1023/B:MATH.0000035037.50663.b1
Abstract: We consider a natural generalisation of the Laplace type operators for the case of non-commutative (Moyal star) product. We demonstrate existence of a power law asymptotic expansion for the heat kernel of such operators on T^n. First four coefficients of this expansion are calculated explicitly. We also find an analog of the UV/IR mixing phenomenon when analysing the localised heat kernel.
Quantum noncommutative gravity in two dimensions
D. V. Vassilevich
Physics , 2004, DOI: 10.1016/j.nuclphysb.2005.02.003
Abstract: We study quantisation of noncommutative gravity theories in two dimensions (with noncommutativity defined by the Moyal star product). We show that in the case of noncommutative Jackiw-Teitelboim gravity the path integral over gravitational degrees of freedom can be performed exactly even in the presence of a matter field. In the matter sector, we study possible choices of the operators describing quantum fluctuations and define their basic properties (e.g., the Lichnerowicz formula). Then we evaluate two leading terms in the heat kernel expansion, calculate the conformal anomaly and the Polyakov action (as an expansion in the conformal field).
Holographic duals to Poisson sigma models and noncommutative quantum mechanics
D. V. Vassilevich
Physics , 2013, DOI: 10.1103/PhysRevD.87.104011
Abstract: Poisson sigma models are a very rich class of two-dimensional theories that includes, in particular, all 2D dilaton gravities. By using the Hamiltonian reduction method, we show that a Poisson sigma model (with a sufficiently well-behaving Poisson tensor) on a finite cylinder is equivalent to a noncommutative quantum mechanics for the boundary data.
Spectral branes
D. V. Vassilevich
Physics , 2001, DOI: 10.1088/1126-6708/2001/03/023
Abstract: We study the objects (called spectral branes or S-branes) which are obtained by imposing non-local spectral boundary conditions at the boundary of the world sheet of the bosonic string. They possess many nice properties which make them an ideal test ground for the string theory methods. Depending on a particular choice of the boundary operator S-branes may be commutative or non-commutative. We demonstrate that projection of the B-field on the brane directions (i.e. on the components which actually influence the boundary conditions) is done with the help of the chirality operator. We show that the T-duality transformation maps an S-brane to another S-brane. At the expense of introducing non-local interactions in the bulk we construct also a duality transformation between S-branes and D-branes or open strings.
Heat kernel expansion: user's manual
D. V. Vassilevich
Physics , 2003, DOI: 10.1016/j.physrep.2003.09.002
Abstract: 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 scattered in mathematical and physical literature. We present explicit expressions for these coefficients on manifolds with and without boundaries, subject to local and non-local boundary conditions, in the presence of various types of singularities (e.g., domain walls). In each case the heat kernel coefficients are given in terms of several geometric invariants. These invariants are derived for scalar and spinor theories with various interactions, Yang-Mills fields, gravity, and open bosonic strings. We discuss the relations between the heat kernel coefficients and quantum anomalies, corresponding anomalous actions, and covariant perturbation expansions of the effective action (both "low-" and "high-energy" ones).
Constraints, gauge symmetries, and noncommutative gravity in two dimensions
D. V. Vassilevich
Mathematics , 2005, DOI: 10.1007/s11232-006-0089-2
Abstract: After an introduction into the subject we show how one constructs a canonical formalism in space-time noncommutative theories which allows to define the notion of first-class constraints and to analyse gauge symmetries. We use this formalism to perform a noncommutative deformation of two-dimensional string gravity (also known as Witten black hole).
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