Brief Summary of Each Supplement
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
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.