Generalized q-deformed Correlation Functions as Spectral Functions of Hyperbolic Geometry

We analyse the role of vertex operator algebra and 2d amplitudes from the point of view of the representation theory of infinite dimensional Lie algebras, MacMahon and Ruelle functions. A p-dimensional MacMahon function is the generating function of p-dimensional partitions of integers. These functions can be represented as amplitudes of a two-dimensional c=1 CFT. In this paper we show that p-dimensional MacMahon functions can be rewritten in terms of Ruelle spectral functions, whose spectrum is encoded in the Patterson-Selberg function of three dimensional hyperbolic geometry.Comment: 12 pages, no figure

Operator Product on Locally Symmetric Spaces of Rank One and the Multiplicative Anomaly

The global multiplicative properties of Laplace type operators acting on irreducible rank one symmetric spaces are considered. The explicit form of the multiplicative anomaly is derived and its corresponding value is calculated exactly, for important classes of locally symmetric spaces and different dimensions.Comment: Int. Journal of Modern Physics A, vol. 18 (2003), 2179-218

Euclidean thermal spinor Green's function in the spacetime of a straight cosmic string

Within the framework of the quantum field theory at finite temperature on a conical space, we determine the Euclidean thermal spinor Green's function for a massless spinor field. We then calculate the thermal average of the energy-momentum tensor of a thermal bath of massless fermions. In the high-temperature limit, we find that the straight cosmic string does not perturb the thermal bathComment: 11 pages, latex, no figure

Quantum Effects in the Spacetime of a Magnetic Flux Cosmic String

In this work we compute the vacuum expectation values of the energy-momentum tensor and the average value of a massive, charged scalar field in the presence of a magnetic flux cosmic string for both zero- and finite-temperature cases.Comment: To appear in the Int. Journal of Modern Phys. A (special issue). Proceedings of the Second International Londrina Winter School on Mathematical Methods in Physics, Londrina, Brazil, August 200

Massive scalar field near a cosmic string

The $\zeta$ function of a massive scalar field near a cosmic string is computed and then employed to find the vacuum fluctuation of the field. The vacuum expectation value of the energy-momentum tensor is also computed using a point-splitting approach. The obtained results could be useful also for the case of self-interacting scalar fields and for the finite-temperature Rindler space theory.Comment: 15 pages, standard LaTeX, no figures. Reference [14] correcte