111 research outputs found

### On Classical and Quantum Cryptography

Lectures on classical and quantum cryptography. Contents: Private key
cryptosystems. Elements of number theory. Public key cryptography and RSA
cryptosystem. Shannon`s entropy and mutual information. Entropic uncertainty
relations. The no cloning theorem. The BB84 quantum cryptographic protocol.
Security proofs. Bell`s theorem. The EPRBE quantum cryptographic protocol.Comment: 27 page

### On Holographic Thermalization and Dethermalization of Quark-Gluon Plasma

We estimate the ratio of the thermalization time over the freeze-out time
using a holographic AdS-Vaidya model for quark-gluon plasma formed in the heavy
ion collisions. In the model the process of thermalization is described as
formation of the black hole in AdS space while dethermalization process,
related with the freeze-out, as the black hole evaporation due to the Hawking
radiation that is modeled by the Vaidya metric with a negative mass. In this
model the thermalization takes place only at small scales and absent in the
infrared region. At small scales the system tends towards a state of the
thermal equilibrium only for the short time after which the processes of
dethermalization starts. In this simple model the dethermalization time has a
low bound about 7 fm/c which is consistent with experimental data.Comment: 15 pages, 5 figure

### 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

### 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

### 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 $\lambda$ over a part of variables (anisotropic
$\lambda$-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

### Knots and Matrix Models

We consider a matrix model with d matrices NxN and show that in the limit of
large N and d=0 the model describes the knot diagrams. The same limit in matrix
string theory is also discussed. We speculate that a prototypical M(atrix)
without matrix theory exists in void.Comment: 9 pages, LaTex, 6 figure

### The Master Field for QCD and $q$-Deformed Quantum Field Theory

The master fields for the large $N$ 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

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