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Progress of Theoretical Physics Supplement No. 127



Recent Developments of the Theory of Tunneling


By H. Aoyama, T. Harano, H. Kikuchi, I. Okouchi, M. Sato and S. Wada

Path-integral approach in imaginary and complex time has been proven successful in treating the tunneling phenomena in quantum mechanics and quantum field theories. Latest developments in this field, the proper valley method in imaginary time, its application to various quantum systems, complex time formalism, asympton theory for the large order analysis of the perturbation theory, are reviewed in a self-contained manner.


Dynamical Symmetry Breaking in Curved Spacetime
Four-Fermion Interactions


By T. Inagaki, T. Muta and S. D. Odintsov

Four-fermion interaction models are considered to be prototype models for dynamical symmetry breaking.The present review deals with recent developments in the studies of dynamical symmetry breaking in the four-fermion interaction models and their extension in curved spacetime. Starting with the Minkowski spacetime in dimension D (2 \leq D \leq 4) the effective potential in the leading order of 1/N-expansion is calculated and the phase structure of the theory is investigated. In curved spacetime curvature-induced phase transitions are discussed in the circumstances where fermion masses are dynamically generated. Subsequently a possibility of curvature- and temperature-induced or curvature- and topology-induced phase transitions is discussed. It is also argued that the chiral symmetry broken by a weak magnetic field may be restored due to the presence of gravitational field. Finally some applications of four-fermion models in quantum gravity are briefly described.


  Copyright © 2008 Progress of Theoretical Physics