International Journal of Modern Physics A

We exhibit a class of quantum field theories where particles interact with pair potentials and for which the time evolution exists in the Heisenberg representation. The essential condition for existence is stability in the thermodynamic sense and this is achieved by having the interaction fall off with the relative momenta of the particles. This can be done in a Galilei-invariant manner. We show that these systems have some mixing properties which one postulates in ergodic theory but which are difficult to prove for classical systems.

The covariant (in the σ-model sense) background field method for calculating the anomalies of the heterotic string propagating on the background of its massless modes is developed in a curved superspace of the two-dimensional (1, 0) supergravity. As the massless background fields, we use a metric, an antisymmetric tensor, a dilaton and gauge bosons. Explicit calculation of the anomalies up to five loops is performed and the results are found to be in agreement with the known facts about the heterotic string low-energy effective action. The dilaton-dependent corrections to the anomalies at the two- and three-loop levels are shown to be absent.

Extended super-Riemann surfaces are studied and their underlying superconformal properties are derived as solutions of an operator equation. Superconformal tensors and differential forms are discussed in detail and are shown to be classified by means of a triplet of integers or half-integers. The integration on super-Riemann surfaces is developed. Finally, we derive the solution of the N=4 anomaly compatible with the non-locality feature and discuss the necessary conditions for its vanishing. A heuristic geometrical interpretation of these conditions is also given.

The linked-pair approximation to the hierarchy of cumulant correlation functions is tested in the central rapidity domain, where approximate translation invariance is appropriate. The bin-averaged factorial moments up to the fifth order are well described in terms of the second-order experimental moment for final states created in hadronic collisions. Given the two-particle correlation function, the only constants appearing in the higher moments are very close to those-appropriate to the negative binomial distribution, as pointed out recently by De Wolf. The close correspondence of the linked-pair decomposition to the same structure occurring in galaxy correlations (with slightly different coefficients) is noted, as is the apparently negative binomial character of the number distribution of galaxies in clusters. Preliminary results are discussed for the rapidity distributions arising in proton-nucleus and nucleus-nucleus collisions. We present a variety of fits to correlation functions and also discuss bin-bin correlations deriving from our model.

We study here the Berry phase from the point of view of stochastic quantization. The relativistic generalization of Nelson’s stochastic quantization procedure can be achieved when the Brownian motion process is taken into account in the internal space (apart from that in the external space). This effectively considers the particle as one that is stochastically extended, and nonrelativistic quantum mechanics is obtained in the sharp point limit. This can be formulated in terms of a gauge-field-theoretical extension of the particle. This inherent gauge field gives rise to the holonomy in a Hermitian line bundle, which appears as an extra phase factor in the adiabatic limit for a parameter-dependent Hamiltonian, and determines a unique connection. When the Hamiltonian is degenerate, the holonomy is defined in a complex vector bundle. In the case of a fermion, this Berry connection is found to be related to the Wess-Zumino term and can be considered to be of topological origin.

We examine the properties of the quantum Lorentz group SO_q(3, 1) using the matrix given in Ref. 14. We show that this matrix together with the q-deformed metric C provide a representation of a BWM algebra. Using the projection operators which decompose the matrix into irreducible components, we give the general definition of the corresponding quantum space, i.e. the q-deformed Minkowski space and the q-deformed Clifford algebra. We also construct the q analog of Dirac matrices and show that they form a matrix representation of the q-deformed Clifford algebra.

A class of metrics providing the complete separation of variables in the Klein-Gordon equation is considered. The general exact solution to the vacuum Einstein equation for such metrics is obtained by the variable separation method. It is shown that all these solutions correspond to curvilinear coordinate systems in the Minkowskian space-time. Several limit cases of such systems are investigated. Moreover, some other separating systems are constructed and it is shown that they make it possible to obtain partial exact solutions to nonlinear scalar field equations.