39 research outputs found
Cosmological Daemon
Classical versions of the Big Bang cosmological models of the universe
contain a singularity at the start of time, hence the time variable in the
field equations should run over a half-line. Nonlocal string field theory
equations with infinite number of derivatives are considered and an important
difference between nonlocal operators on the whole real line and on a half-line
is pointed out.
We use the heat equation method and show that on the half-line in addition to
the usual initial data a new arbitrary function (external source) occurs that
we call the daemon function. The daemon function governs the evolution of the
universe similar to Maxwell`s demon in thermodynamics. The universe and
multiverse are open systems interacting with the daemon environment. In the
simplest case the nonlocal scalar field reduces to the usual local scalar field
coupled with an external source which is discussed in the stochastic approach
to inflation. The daemon source can help to get the chaotic inflation scenario
with a small scalar field.Comment: LATEX, 31 pages, Sect. "Inflation and External Sources" and refs. are
adde
Note on the Unruh Effect
It was suggested by Unruh that a uniformly accelerated detector in vacuum
would perceive a noise with a thermal distribution. We obtain a representation
of solutions of the wave equation in two dimensions suitable for the Rindler
regions. The representation includes the dependence on a parameter. The Unruh
field corresponds to a singular limit of the representation.Comment: 5 pages, Late
Anisotropic Asymptotics and High Energy Scattering
Recently E.Verlinde and H.Verlinde have suggested an effective
two-dimensional theory describing the high-energy scattering in QCD. In this
report we attempt to clarify some issues of this suggestion. We consider {\it
anisotropic asymptotics} of correlation functions for scalar and gauge theories
in four dimensions. Anisotropic asymptotics describe behaviour of correlation
functions when some components of coordinates are large as compare with others
components. It is occurred that (2+2) anisotropic asymptotics for 4-points
functions are related with the well known Regge regime of scattering
amplitudes. We study an expansion of correlation functions with respect to the
rescaling parameter over a part of variables (anisotropic
-expansion). An effective theory describing the anisotropic limit of
free scalar field contains two 2 dim conformal theories. One of them is a
conformal theory in configuration space and another one is a conformal theory
in momentum space. In some special cases ,in particular for the Wilson line
correlators in gauge theories, the leading term of the anisotropic expansion
involves only one of the conformal theories and it can be described by an
effective theory with an action being a dimensional reduction of the original
action.Comment: 16 pages, LATEX, 3 figures, Invited talk at the Conference Quarks 94,
Vladimir, May, 199
On the Breaking of Conformal Symmetry in the AdS/CFT Correspondence
The renormalization of the boundary action in the AdS/CFT correspondence is
considered and the breaking of conformal symmetry is discussed.Comment: 10 pages, Latex, references adde
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.Comment: 7 pages, Latex, Talk presented at the Birthday Conference dedicated
to A.Arvilski, February, 1998; one ref. adde
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.Comment: 19 pages, 3 figures. Invited lecture given by I.V. Volovich at the
Madeira workshop on Noncommutative Infinite Dimensional Analysis, July 1999;
typos correcte
The Master Field for QCD and -Deformed Quantum Field Theory
The master fields for the large limit of matrix models and gauge theory
are constructed. The master fields satisfy to standard equations of
relativistic field theory but fields are quantized according to a new rule. To
define the master field we use the Yang-Feldman equation with a free field
quantized in the Boltzmannian Fock space. The master field for gauge theory
does not take values in a finite-dimensional Lie algebra however there is a
non-Abelian gauge symmetry. For the construction of the master field it is
essential to work in Minkowski space-time and to use the Wightman correlation
functions. The BRST quantization of the master field for gauge theory and a
loop equation are considered.Comment: More comments about a new gauge theory and more references are added,
14 pages, late
On Large N Conformal Theories, Field Theories in Anti-De Sitter Space and Singletons
It was proposed by Maldacena that the large 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.Comment: 12 pages, Latex, discussion of the singular behavior of the classical
action is added, typos corrected, refs adde
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.Comment: 30 pages, 9 figure
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.Comment: 21 pages, 3 figures, To be published in the Special Issue of Proc. of
the Steklov Mathematical Institute dedicated to the 90th birth day of
N.N.Bogoliubo