| Budget Amount *help |
¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 1998: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1997: ¥900,000 (Direct Cost: ¥900,000)
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| Research Abstract |
To clarify the physical and mathematical meanings of spontaneous symmetry collapse discovered by D.Buchholz and myself in [2], I elaborated in 1997 on fundamental issues concerning relations among thermodynamic phases, order parameters to distinguish different phases, center of represented algebras and symmetry of systems. What I found is useful results involving the spectrum of centre, central ergodicity and approximate sequences of local operators tendeing to central elements, which exhibit interesting roles of the basic notions in quantum probability theory in connection with large deviations when applied to the discussions with low energy theorems. While some of these were reported in [3], I have been elaboraing on basic points in quantum-theoretical extensions of large deviation principle.
In the former half of 1998, 1 was invited by Academy of Sciences in Gottingen as Gauss Professor at Gottingen University where I collaborated with Profs.D.Buchholz and H.Roos on the mathematical
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formulation of local temperature states in algebraic QFT.I also elaborated upon the classification of symmetry breaking patterns [5], which answers the above-mentioned question by placing the result of [2] in a wider perspective with all possible patterns of symmetry breaking exhausted and classified. Concerning the former, its outline was reported at RIMS-meeting of "Mathematics of Quantum Information and Quantum Chaos" and a joint paper is in preparation. The idea is to map a given state to the set of all KMS states via suitable family of local observables in small neighbourhoods of each spacetime point to represent it as a mixture of various KMS states, through which a localized version of thermal equilibrium is attained in a novel way. There is a nontrivial example of such a local temperature state in the massless scalar field model which shows interesting aspects of nonequilibrium suggesting some promising direction of general-relativistic extension of thermodynamics and quantum statistical mechanicss. In the autumn of 1998, I had discussions with Prof.S.Maumary at Univ.de Lausanne on a homological-algebraic reformulation of BRS cohomology and we have been continuing a joint project to complete this work. Less
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