Searcharxiv⌕ Search

arXiv subjects

I. Ya. Aref'eva

Publications and source records attributed to I. Ya. Aref'eva.

At least 73 records · Page 4Linked to original sources
arXiv1999

High Energy Scattering in the Brane-World and Black Hole Production

Black hole production in the collision of ultra-relativistic particles in the brane-world approach is considered. In particular, stability of the brane under collision with ultra-relativistic particles is discussed. As a toy model we consider the 3 dimensional version of the Randall and Sundrum solution and show that stability of the brane depends on a choice of continuation of the solution across the horizon. In the unstable case black holes can be produced in the collision of a particle with the brane.

hep-th↗
arXiv1999

The Large Time Behaviour in Quantum Field Theory and Quantum Chaos

An exact general formula for the matrix elements of the evolution operator in quantum theory is established. The formul ("ABC-formula") has the form =exp(At+B+C(t)). The constants A and B and the decreasing function C(t) are computed in perturbation theory. The ABC-formula is valid for a general class of Hamiltonians used in statistical physics and quantum field theory. The formula includes the higher order corrections to the well known Weisskopf-Wigner approximation and to the stochastic (van Hove) limit which are widely used in considerations of problems of radiation, decay, quantum decoherence, derivation of master and kinetic equations etc. The function C(t) admits an interpretation as an analogue of the autocorrelation function describing quantum chaos for the quantum baker's map.

quant-ph↗
arXiv1999

Noncommutative Gauge Fields on Poisson Manifolds

It is shown by Connes, Douglas and Schwarz that gauge theory on noncommutative torus describes compactifications of M-theory to tori with constant background three-form field. This indicates that noncommutative gauge theories on more general manifolds also can be useful in string theory. We discuss a framework to noncommutative quantum gauge theory on Poisson manifolds by using the deformation quantization. The Kontsevich formula for the star product was given originally in terms of the perturbation expansion and it leads to a non-renormalizable quantum field theory. We discuss the nonperturbative path integral formulation of Cattaneo and Felder as a possible approach to construction of noncommutative quantum gauge theory on Poisson manifolds. Some other aspects of classical and quantum noncommutative field theory are also discussed.

hep-th↗
arXiv1999

Quantum Decoherence and Higher Order Corrections to the Large Time Exponential Behaviour

There exists the well known approximate expression describing the large time behaviour of matrix elements of the evolution operator in quantum theory: =exp(at)+... This expression plays the crucial role in considerations of problems of quantum decoherence, radiation, decay, scattering theory, stochastic limit, derivation of master and kinetic equations etc. This expression was obtained in the Weisskopf-Wigner approximation and in the van Hove (stochastic) limit. We derive the exact general formula which includes the higher order corrections to the above approximate expression: =exp(At+B+C(t)). The constants A and B and the oscillating function C(t) are computed in perturbation theory. The method of perturbation of spectra and renormalized wave operators is used. The formula is valid for a general class of Hamiltonians used in statistical physics and quantum field theory.

quant-ph↗
arXiv1999

Non-Equilibrium Quantum Field Theory and Entangled Commutation Relations

Non-equilibrium quantum field theory studies time dependence of processes which are not available for the S-matrix description. One of the new methods of investigation in non-equilibrium quantum theory is the stochastic limit method. This method is an extension of the works by Bogoliubov, van Hove and Prigogine and it permits to study not only the system but also the reservoir degrees of freedom. We consider the stochastic limit of translation invariant Hamiltonians in quantum field theory and show that the master field satisfies a new type of commutation relations, the so called entangled (or interacting) commutation relations. These relations extend the interacting Fock relations established earlier in non-relativistic QED and the free (or Boltzmann) commutation relations which have been found in the large N limit of QCD. As an application of the stochastic limit method we consider the photon splitting cascades in magnetic field and show that photons in cascades form entangled states ("triphons") and they obey not Bose but a new type of statistics corresponding to the entangled commutation relations.

hep-th↗
arXiv1999

On the Holographic S-matrix

The recent proposal by Polchinski and Susskind for the holographic flat space S-matrix is discussed. By using Feynman diagrams we argue that in principle all the information about the S-matrix in the interacting field theory in the bulk of the anti-de Sitter space is encoded into the data on the timelike boundary. The problem of locality of interpolating field is discussed and it is suggested that the interpolating field lives in a quantum Boltzmannian Hilbert space.

hep-th↗
arXiv1998

Chaos-Order Transition in Matrix Theory

Classical dynamics in SU(2) Matrix theory is investigated. A classical chaos-order transition is found. For the angular momentum small enough (even for small coupling constant) the system exhibits a chaotic behavior, for angular momentum large enough the system is regular.

hep-th↗
arXiv1998

Matrix Theory in Curved Space

According to the Matrix theory proposal of Banks, Fischler, Shenker and Susskind M-theory in the infinite momentum frame is the large N limit of super Yang-Mills theory in a flat background. To address some physical issues of classical gravity such as gravitational collapse and cosmological expansion we consider an extension of the BFSS proposal by defining M-theory in curved space as the large N limit of super Yang-Mills theory in a curved background. Motivations and possible implications of this extension are discussed.

hep-th↗
arXiv1998

On Large N Conformal Theories, Field Theories in Anti-De Sitter Space and Singletons

It was proposed by Maldacena that the large $N$ limit of certain conformal field theories can be described in terms of supergravity on anti-De Sitter spaces (AdS). Recently, Gubser, Klebanov and Polyakov and Witten have conjectured that the generating functional for certain correlation functions in conformal field theory is given by the classical supergravity action on AdS. It was shown that the spectra of states of the two theories are matched and the two-point correlation function was studied. We discuss the interacting case and compare the three- and four-point correlation functions computed from a classical action on AdS with the large N limit of conformal theory. We discuss also the large N limit for the Wilson loop and suggest that singletons which according to Flato and Fronsdal are constituents of composite fields in spacetime should obey the quantum Boltzmann statistics.

hep-th↗
arXiv1998

Non-extremal Localised Branes and Vacuum Solutions in M-Theory

Non-extremal overlapping p-brane supergravity solutions localised in their relative transverse coordinates are constructed. The construction uses an algebraic method of solving the bosonic equations of motion. It is shown that these non-extremal solutions can be obtained from the extremal solutions by means of the superposition of two deformation functions defined by vacuum solutions of M-theory. Vacuum solutions of M-theory including irrational powers of harmonic functions are discussed.

hep-th↗
arXiv1997

Chaos in M(atrix) Theory

We consider the classical and quantum dynamics in M(atrix) theory. Using a simple ansatz we show that a classical trajectory exhibits a chaotic motion. We argue that the holographic feature of M(atrix) theory is related with the repulsive feature of energy eigenvalues in quantum chaotic system. Chaotic dynamics in N=2 supersymmetric Yang-Mills theory is also discussed. We demonstrate that after the separation of "slow" and "fast" modes there is a singular contribution from the "slow" modes to the Hamiltonian of the "fast" modes.

hep-th↗
arXiv1997

Photon splitting cascades and a new statistics

Photon splitting cascades in a magnetic field are considered. It is shown, in the stochastic limit approximation, that photons in cascades might form entangled states (``triphons'') and that they obey not Bose but a new type of statistics, the so called infinite or quantum Boltzmann statistics. These states belong to an interacting Fock space which is a generalization of the ordinary Fock space. The new photon statistics in principle can be detected in future astrophysical experiments such as the planned Integral mission and also in nonlinear quantum optics.

hep-ph↗
arXiv1997

Classical and Quantum Composite p-branes

We discuss classical composite p-brane solutions and their quantization using the conjecture that their fluctuations may be described via degrees of freedom of Dirichlet strings ended on these p-branes. We work with Dirichlet (super)strings in framework of string field theory for open (super)strings. To elaborate in this scheme the eleventh dimension modes we take just a collection of Dirichlet strings which in their middle points have jumps in eleventh dimension. This theory can be seen as string field theory in infinite momentum frame of an eleven dimensional object.

hep-th↗
arXiv1997

Properties of Intersecting p-branes in Various Dimensions

General properties of intersecting extremal p-brane solutions of gravity coupled with dilatons and several different d-form fields in arbitrary space-time dimensions are considered. It is show that heuristically expected properties of the intersecting p-branes follow from the explicit formulae for solutions. In particular, harmonic superposition and S-duality hold for all p-brane solutions. Generalized T-duality takes place under additional restrictions on the initial theory parameters .

hep-th↗
arXiv1997

Non-extremal Intersecting p-branes in Various Dimensions

Non-extremal intersecting p-brane solutions of gravity coupled with several antisymmetric fields and dilatons in various space-time dimensions are constructed. The construction uses the same algebraic method of finding solutions as in the extremal case and a modified "no-force" conditions. We justify the "deformation" prescription. It is shown that the non-extremal intersecting p-brane solutions satisfy harmonic superposition rule and the intersections of non-extremal p-branes are specified by the same characteristic equations for the incidence matrices as for the extremal p-branes. We show that S-duality holds for non-extremal p-brane solutions. Generalized T-duality takes place under additional restrictions to the parameters of the theory which are the same as in the extremal case.

hep-th↗
arXiv1996

Incidence Matrix Description of Intersecting p-brane Solutions

An algebraic method for a general construction of intersecting p-brane solutions in diverse spacetime dimensions is discussed. An incidence matrix describing configurations of electric and magnetic fields is introduced. Intersecting p-branes are specified by solutions of a system of characteristic algebraic equations for the incidence matrix. This set of characteristic equations generalizes a single characteristic equation found before for a special "flower" ansatz. The characteristic equations admit solutions only for quantized values of scalar coupling parameters. A wide list of examples including solutions with regular horizons and non-zero entropy in D=11 and D=10 theories is presented.

hep-th↗
arXiv1996

Planar Approximation as Two-Field Boltzmann Theory

A modified interaction representation for the master field describing connected $SU(N)$-invariant Wightman's functions in the large $N$ limit of matrix fields is constructed. This construction is based on the representation of the master field in terms of Boltzmannian field theory found before. In the modified interaction representation we deal with two scalar Boltzmann fields ({\it up} and {\it down} fields). For up and down fields only half-planar diagrams contribute and this could help to write down a recursive set of non-linear integral-differential equations summing up planar diagrams.

hep-th↗