Hamiltonian Quantization of Chern-Simons theory with SL(2,C) Group

We analyze the hamiltonian quantization of Chern-Simons theory associated to the universal covering of the Lorentz group SO(3,1). The algebra of observables is generated by finite dimensional spin networks drawn on a punctured topological surface. Our main result is a construction of a unitary representation of this algebra. For this purpose, we use the formalism of combinatorial quantization of Chern-Simons theory, i.e we quantize the algebra of polynomial functions on the space of flat SL(2,C)-connections on a topological surface with punctures. This algebra admits a unitary representation acting on an Hilbert space which consists in wave packets of spin-networks associated to principal unitary representations of the quantum Lorentz group. This representation is constructed using only Clebsch-Gordan decomposition of a tensor product of a finite dimensional representation with a principal unitary representation. The proof of unitarity of this representation is non trivial and is a consequence of properties of intertwiners which are studied in depth. We analyze the relationship between the insertion of a puncture colored with a principal representation and the presence of a world-line of a massive spinning particle in de Sitter space.Comment: 78 pages. Packages include

2D Conformal Field Theories and Holography

It is known that the chiral part of any 2d conformal field theory defines a 3d topological quantum field theory: quantum states of this TQFT are the CFT conformal blocks. The main aim of this paper is to show that a similar CFT/TQFT relation exists also for the full CFT. The 3d topological theory that arises is a certain ``square'' of the chiral TQFT. Such topological theories were studied by Turaev and Viro; they are related to 3d gravity. We establish an operator/state correspondence in which operators in the chiral TQFT correspond to states in the Turaev-Viro theory. We use this correspondence to interpret CFT correlation functions as particular quantum states of the Turaev-Viro theory. We compute the components of these states in the basis in the Turaev-Viro Hilbert space given by colored 3-valent graphs. The formula we obtain is a generalization of the Verlinde formula. The later is obtained from our expression for a zero colored graph. Our results give an interesting ``holographic'' perspective on conformal field theories in 2 dimensions.Comment: 29+1 pages, many figure

New Test of Supernova Electron Neutrino Emission using Sudbury Neutrino Observatory Sensitivity to the Diffuse Supernova Neutrino Background

Supernovae are rare nearby, but they are not rare in the Universe, and all past core-collapse supernovae contributed to the Diffuse Supernova Neutrino Background (DSNB), for which the near-term detection prospects are very good. The Super-Kamiokande limit on the DSNB electron {\it antineutrino} flux, $\phi(E_\nu > 19.3 {\rm MeV}) < 1.2$ cm$^{-2}$ s$^{-1}$, is just above the range of recent theoretical predictions based on the measured star formation rate history. We show that the Sudbury Neutrino Observatory should be able to test the corresponding DSNB electron {\it neutrino} flux with a sensitivity as low as $\phi(22.5 < E_\nu < 32.5 {\rm MeV}) \simeq 6$ cm$^{-2}$ s$^{-1}$, improving the existing Mont Blanc limit by about three orders of magnitude. While conventional supernova models predict comparable electron neutrino and antineutrino fluxes, it is often considered that the first (and forward-directed) SN 1987A event in the Kamiokande-II detector should be attributed to electron-neutrino scattering with an electron, which would require a substantially enhanced electron neutrino flux. We show that with the required enhancements in either the burst or thermal phase $\nu_e$ fluxes, the DSNB electron neutrino flux would generally be detectable in the Sudbury Neutrino Observatory. A direct experimental test could then resolve one of the enduring mysteries of SN 1987A: whether the first Kamiokande-II event reveals a serious misunderstanding of supernova physics, or was simply an unlikely statistical fluctuation. Thus the electron neutrino sensitivity of the Sudbury Neutrino Observatory is an important complement to the electron antineutrino sensitivity of Super-Kamiokande in the quest to understand the DSNB.Comment: 10 pages, 3 figure

The 1/N-expansion, quantum-classical correspondence and nonclassical states generation in dissipative higher-order anharmonic oscillators

We develop a method for the determination of thecdynamics of dissipative quantum systems in the limit of large number of quanta N, based on the 1/N-expansion of Heidmann et al. [ Opt. Commun. 54, 189 (1985) ] and the quantum-classical correspondence. Using this method, we find analytically the dynamics of nonclassical states generation in the higher-order anharmonic dissipative oscillators for an arbitrary temperature of a reservoir. We show that the quantum correction to the classical motion increases with time quadratically up to some maximal value, which is dependent on the degree of nonlinearity and a damping constant, and then it decreases. Similarities and differences with the corresponding behavior of the quantum corrections to the classical motion in the Hamiltonian chaotic systems are discussed. We also compare our results obtained for some limiting cases with the results obtained by using other semiclassical tools and discuss the conditions for validity of our approach.Comment: 15 pages, RevTEX (EPSF-style), 3 figs. Replaced with final version (stylistic corrections

On solving Schwinger-Dyson equations for non-Abelian gauge theory

A method for solving Schwinger-Dyson equations for the Green function generating functional of non-Abelian gauge theory is proposed. The method is based on an approximation of Schwinger-Dyson equations by exactly soluble equations. For the SU(2) model the first step equations of the iteration scheme are solved which define a gauge field propagator. Apart from the usual perturbative solution, a non-perturbative solution is found which corresponds to the spontaneous symmetry breaking and obeys infrared finite behaviour of the propagator.Comment: 12 pages, Plain LaTeX, no figures, extended and revised version published in Journal of Physics

On interrelations between Sibgatullin's and Alekseev's approaches to the construction of exact solutions of the Einstein-Maxwell equations

The integral equations involved in Alekseev's "monodromy transform" technique are shown to be simple combinations of Sibgatullin's integral equations and normalizing conditions. An additional complex conjugation introduced by Alekseev in the integrands makes his scheme mathematically inconsistent; besides, in the electrovac case all Alekseev's principal value integrals contain an intrinsic error which has never been identified before. We also explain how operates a non-trivial double-step algorithm devised by Alekseev for rewriting, by purely algebraic manipulations and in a different (more complicated) parameter set, any particular specialization of the known analytically extended N-soliton electrovac solution obtained in 1995 with the aid of Sibgatullin's method.Comment: 7 pages, no figures, section II extende

Nonperturbative Contributions in an Analytic Running Coupling of QCD

In the framework of analytic approach to QCD the nonperturbative contributions in running coupling of strong interaction up to 4-loop order are obtained in an explicit form. For all $Q>\Lambda$ they are shown to be represented in the form of an expansion in inverse powers of Euclidean momentum squared. The expansion coefficients are calculated for different numbers of active quark flavors $n_f$ and for different number of loops taken into account. On basis of the stated expansion the effective method for precise calculation of the analytic running coupling can be developed.Comment: 9 pages, LaTeX, 1 table, 1 eps figur

Braided Cyclic Cocycles and Non-Associative Geometry

We use monoidal category methods to study the noncommutative geometry of nonassociative algebras obtained by a Drinfeld-type cochain twist. These are the so-called quasialgebras and include the octonions as braided-commutative but nonassociative coordinate rings, as well as quasialgebra versions \CC_{q}(G) of the standard q-deformation quantum groups. We introduce the notion of ribbon algebras in the category, which are algebras equipped with a suitable generalised automorphism $\sigma$, and obtain the required generalisation of cyclic cohomology. We show that this \emph{braided cyclic cocohomology} is invariant under a cochain twist. We also extend to our generalisation the relation between cyclic cohomology and differential calculus on the ribbon quasialgebra. The paper includes differential calculus and cyclic cocycles on the octonions as a finite nonassociative geometry, as well as the algebraic noncommutative torus as an associative example.Comment: 36 pages latex, 9 figure

Physical phase space of lattice Yang-Mills theory and the moduli space of flat connections on a Riemann surface

It is shown that the physical phase space of \g-deformed Hamiltonian lattice Yang-Mills theory, which was recently proposed in refs.[1,2], coincides as a Poisson manifold with the moduli space of flat connections on a Riemann surface with $(L-V+1)$ handles and therefore with the physical phase space of the corresponding $(2+1)$-dimensional Chern-Simons model, where $L$ and $V$ are correspondingly a total number of links and vertices of the lattice. The deformation parameter \g is identified with $\frac {2\pi}{k}$ and $k$ is an integer entering the Chern-Simons action.Comment: 12 pages, latex, no figure