Trends in Mathematical Physics: (AMS/IP Studies in Advanced Mathematics)

This volume presents the proceedings of the conference on 'Trends in Mathematical Physics' held at the University of Tennessee. The conference drew international experts from mathematical and computational physics. The following topics were addressed: superstrings and quantum gravity, pattern formation, and crystallographic topology. The cutting-edge research reflected in the extensive surveys in the book are written for a diverse audience.

Table of Contents:
Berry's connection in a quantum relativistic description of the curved space analogue of development by R. R. Aldinger Heat-kernel asymptotics of the Gilkey-Smith boundary-value problem by I. G. Avramidi and G. Esposito On ellipticity and gauge invariance in Euclidean quantum gravity by I. G. Avramidi and G. Esposito Undercompressive waves in driven thin film flow: Theory, computation, and experiment by A. L. Bertozzi, A. Munch, and M. Shearer Internal time peculiarities as a cause of bifurcations arising in classical trajectory problem and quantum chaos creation in three-body systems by A. V. Bogdanov, A. S. Gevorkyan, and A. G. Grigoryan Random motion of quantum harmonic oscillator-Thermodynamics of nonrelativistic vacuum by A. V. Bogdanov, A. S. Gevorkyan, and A. G. Grigoryan A new formulation of Lax pairs for generalized Calogero-Moser models by A. J. Bordner Four-point correlation functions in the AdS/CFT correspondence by G. Chalmers and K. Schalm Gravitational instantons and moduli spaces by S. A. Cherkis Superdualities and twisted self-duality by E. Cremmer, B. Julia, H. Lu, and C. N. Pope Boomerons in field theory by I. Dasgupta A layman's guide to $M$-theory by M. J. Duff Family symmetry, the anomalous $U(1)$, and neutrino mixing by J. K. Elwood Stochastic quantization approach to $c \leq 1$ open-closed string field theories by D. Ennyu, H. Kawabe, and N. Nakazawa Gauge invariance and effective actions at finite temperature by C. D. Fosco Superconformal deformations and space-time symmetries by I. Giannakis Nonlinear patterns in microstructures by M. E. Glicksman Non-thermalizability of a quantum field theory by C. R. Hagen Field theory for chemical spaces by R. A. Hefferlin From functions to matrices by J. Hoppe Duality and construction of quantum integrable systems by E. Horozov and A. Kasman Geometric concepts for the mass in general relativity by G. Huisken Crystallographic topology 2: Overview and work in progress by C. K. Johnson Gravitationally dressed RG flows, zigzag symmetry and zero-tension strings by I. I. Kogan and O. A. Soloviev Einstein metrics and the Yamabe problem by C. LeBrun Numerical evolution in time of curvature perturbations in Kerr black holes by R. Lopez-Aleman Nonlinearity and self-similarity: Wavelets and compactons on a physical background by A. Ludu and J. P. Draayer On analytic approach to perturbative quantum chromodynamics by B. A. Magradze Lattice gauge theory by C. Michael Integrable models with boundary by R. I. Nepomechie Mathematical aspects of chiral gauge theories on the lattice by H. Neuberger The statistical entropy of black holes and the $AdS_3$ geometry by L. A. Pando Zayas Canonical treatment of regular Lagrangians with holonomic constraints as singular systems by E. M. Rabei Algebraic shape invariant models by C. Rasinariu, U. P. Sukhatme, and A. Gangopadhyaya Molecular configurations and Euclidean distance matrices by W. Rivera-Gallego Derivative expansion of the one-loop effective action in QED by I. A. Shovkovy Nonlinear generalizations of a 3-manifold's Dirac operator by C. H. Taubes Dynamical symmetry approach to quantum many-body problems by C.-L. Wu.