THERMAL LIE-GROUPS, CLASSICAL MECHANICS, AND THERMOFIELD DYNAMICS

The concept of thermoalgebra, a kind of representation for the Lie-sym metries developed in connection with thermal quantum field theory, is extended to study unitary representations of the Galilei group for the rmal classical systems. One of the representations results in the firs t-quantized Schonberg formalism for the classical statistical mechanic s. Furthermore, the close analogy between thermal classical mechanics and thermal quantum field theory is analysed, and such an analogy is a lmost exact for harmonic oscillator systems. The other unitary represe ntation studied results in a field-operator version of the Schonberg a pproach. As a consequence, in this case the counterpart of the thermof ield dynamics (TFD) in classical theory is identified as both the firs t and second-quantized form of the Liouville equation. Non-unitary rep resentations are also studied, being, in this case, the Lie product of the thermoalgebra identified as the Poisson brackets. A representatio n of the thermal SU(1, 1) is analysed, such that the tilde variables ( introduced in TFD) are functions in a double phase space. As a result the equations of motion for dissipative classical oscillators are deri ved. (C) 1996 Academic Press, Inc.