Quantum mechanics and the direction of time

Journal Article · Fri Mar 01 00:00:00 EST 1991 · Foundations of Physics; (United States)

DOI:https://doi.org/10.1007/BF01883634· OSTI ID:5616183

Hasegawa, H; Petrosky, T ^[1]; Prigogine, I ^[2]; Tasaki, S ^[3]

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1. Univ. of Texas, Austin (United States)
2. Univ. of Texas, Austin (United States) International Solvay Inst. for Physics and Chemistry, Brussels (Belgium)
3. International Solvay Inst. for Physics and Chemistry, Brussels (Belgium)

In recent papers the authors have discussed the dynamical properties of large Poincare systems (LPS), that is, nonintegrable systems with a continuous spectrum (both classical and quantum). An interesting example of LPS is given by the Friedrichs model of field theory. As is well known, perturbation methods analytic in the coupling constant diverge because of resonant denominators. They show that this Poincare catastrophe can be eliminated by a natural time ordering of the dynamical states. They obtain then a dynamical theory which incorporates a privileged direction of time (and therefore the second law of thermodynamics). However, it is only in very simple situations that his time ordering can be performed in an extended Hilbert space. In general, they need to go to the Liouville space (superspace) and introduce a time ordering of dynamical states according to the number of particles involved in correlations. This leads then to a generalization of quantum mechanics in which the usual Heisenberg's eigenvalue problem is replaced by a complex eigenvalue problem in the Liouville space.

• DOE Contract Number: FG05-88ER13897
• OSTI ID: 5616183
• Journal Information: Foundations of Physics; (United States), Journal Name: Foundations of Physics; (United States) Vol. 21:3; ISSN FNDPA; ISSN 0015-9018
• Country of Publication: United States
• Language: English

Related Subjects

661100* -- Classical & Quantum Mechanics-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BANACH SPACE
CLASSICAL MECHANICS
CORRELATIONS
COUPLING CONSTANTS
DYNAMICS
EIGENVALUES
FIELD THEORIES
HEISENBERG PICTURE
HILBERT SPACE
IRREVERSIBLE PROCESSES
LIOUVILLE THEOREM
MATHEMATICAL SPACE
MECHANICS
PERTURBATION THEORY
QUANTUM MECHANICS
SPACE
TIME DEPENDENCE