Simplicial vs. Continuum String Theory and Loop Equations

We derive loop equations in a scalar matrix field theory. We discuss their solutions in terms of simplicial string theory -- the theory describing embeddings of two--dimensional simplicial complexes into the space--time of the matrix field theory. This relation between the loop equations and the simplicial string theory gives further arguments that favor one of the statements of the paper hep-th/0407018. The statement is that there is an equivalence between the partition function of the simplicial string theory and the functional integral in a continuum string theory -- the theory describing embeddings of smooth two--dimensional world--sheets into the space--time of the matrix field theory in question.Comment: 6 page

Towards the Theory of Non--Abelian Tensor Fields I

We present a triangulation--independent area--ordering prescription which naturally generalizes the well known path ordering one. For such a prescription it is natural that the two--form ``connection'' should carry three ``color'' indices rather than two as it is in the case of the ordinary one--form gauge connection. To define the prescription in question we have to define how to {\it exponentiate} a matrix with three indices. The definition uses the fusion rule structure constants.Comment: 22 pages, 18 figure

Oscillations of high energy neutrinos in matter: Precise formalism and parametric resonance

We present a formalism for precise description of oscillation phenomena in matter at high energies or high densities, V > \Delta m^2/2E, where V is the matter-induced potential of neutrinos. The accuracy of the approximation is determined by the quantity \sin^2 2\theta_m \Delta V/2\pi V, where \theta_m is the mixing angle in matter and \Delta V is a typical change of the potential over the oscillation length (l \sim 2\pi/V). We derive simple and physically transparent formulas for the oscillation probabilities, which are valid for arbitrary matter density profiles. They can be applied to oscillations of high energy (E > 10 GeV) accelerator, atmospheric and cosmic neutrinos in the matter of the Earth, substantially simplifying numerical calculations and providing an insight into the physics of neutrino oscillations in matter. The effect of parametric enhancement of the oscillations of high energy neutrinos is considered. Future high statistics experiments can provide an unambiguous evidence for this effect.Comment: LaTeX, 5 pages, 1 figure. Linestyles in the figure corrected to match their description in the caption; improved discussion of the accuracy of the results; references added. Results and conclusions unchange

Expansion in Feynman Graphs as Simplicial String Theory

We show that the series expansion of quantum field theory in the Feynman diagrams can be explicitly mapped on the partition function of the simplicial string theory -- the theory describing embeddings of the two--dimensional simplicial complexes into the space--time of the field theory. The summation over two--dimensional geometries in this theory is obtained from the summation over the Feynman diagrams and the integration over the Schwinger parameters of the propagators. We discuss the meaning of the obtained relation and derive the one--dimensional analog of the simplicial theory on the example of the free relativistic particle.Comment: Latex, 11pp, Minor mintakes are correcte

TOPOLOGICAL OBJECTS AND CONFINEMENT ON THE LATTICE

First we discuss various topological objects (monopoles, ``minopoles'' and ``hybrids'') which may be important for the confinement mechanism in various abelian projections. The second topic is the string between quark and antiquark. The standard quantum string with the Nambu-Goto action exists only in D=26. If we start from the field theory, in which the string excitations exist, and change the variables in the path integral to the string variables, then the Jacobian appears. This Jacobian generates the correction to the Nambu-Goto action. For this effective action the conformal anomaly cancels in D=4. Thus we get the quantum string theory in D=4.Comment: 9 pages, LaTeX, 2 uuencoded tar-compressed postscript figures, needs psfig.tex; talk given by Polikarpov M.I. at International RCNP Workshop on Color Confinement and Hadrons (Confinement 95), March 22--24, 1995, RCNP, Osaka, Japan. (Revision: problems in figures fixed

On the evolution of an entangled lepton-neutrino pair

The evolution of the entangled muon-neutrino system emerging from charged pion decay is explored both in vacuum and in matter. The study is based on a Weisskopf-Wigner type wave-packet description. Explicit formulae are derived displaying modulation and attenuation of the oscillations due to additional time scales characterising the production process. The case of neutrinos disentangled due to the detection of the muon is also considered

Beta decay and other processes in strong electromagnetic fields

We consider effects of the fields of strong electromagnetic waves on various characteristics of quantum processes. After a qualitative discussion of the effects of external fields on the energy spectra and angular distributions of the final-state particles as well as on the total probabilities of the processes (such as decay rates and total cross sections), we present a simple method of calculating the total probabilities of processes with production of non-relativistic charged particles. Using nuclear beta-decay as an example, we study the weak and strong field limits, as well as the field-induced beta-decay of nuclei stable in the absence of the external fields, both in the tunneling and multi-photon regimes. We also consider the possibility of accelerating forbidden nuclear beta-decays by lifting the forbiddeness due to the interaction of the parent or daughter nuclei with the field of a strong electromagnetic wave. It is shown that for currently attainable electromagnetic fields all effects on total beta-decay rates are unobservably small.Comment: LaTeX, 30 pages, 2 figures. Invited contribution to the special issue of Yadernaya Fizika dedicated to the centennial anniversary of birthday of A.B. Migdal. V2: references adde