In several previous papers we have argued for a global and non-entropic approach to the problem of the arrow of time, according to which the " arrow " is only a metaphorical way of expressing the geometrical time-asymmetry of the universe. We have also shown that, under definite conditions, this global time-asymmetry can be transferred to local contexts as… (More)
The upside-down simple harmonic oscillator system is studied in the contexts of quantum mechanics and classical statistical mechanics. It is shown that in order to study in a simple manner the creation and decay of a physical system by ways of Gamow vectors we must formulate the theory in a time-asymmetric fashion, namely using two different rigged Hilbert… (More)
The classical-statistical limit of quantum mechanics is studied. It is proved that the limit → 0 is the good limit for the operators algebra but it si not so for the state compact set. In the last case decoherence must be invoked to obtain the classical-statistical limit.
We introduce a 'proper time' formalism to study the instability of the vacuum in a uniform external electric field due to particle production. This formalism allows us to reduce a quantum field theoretical problem to a quantum-mechanical one in a higher dimension. The instability results from the inverted oscillator structure which appears in the… (More)
After an appropriate restatement of the GNS construction for topological *-algebras we prove that there exists an isomorphism among the set Cycl(A) of weakly continuous strongly cyclic *-representations of a barreled dual-separable *-algebra with unit A, the space Hilb A (A *) of the Hilbert spaces that are continuously embedded in A * and are *-invariant… (More)
We obtain the precise form of two Gamow functionals, representing the exponentially decaying part of a quantum resonance and its mirror image that grows exponentially, as a linear, positive and continuous functional on an algebra containing observables. These functionals do not admit normalization and, with an appropiate choice of the algebra, are time… (More)
It is demonstrated how a convenient choice of the mathematical structure of the quantum cosmology superspace, precisely the definition of a convenient regular state superspace and the restriction of the dynamics to this space, yields directly to an irreversible evolution, in the classical (and semiclassical) phase of the universe, where: • Decoherence and… (More)
It is demonstrated that almost any S-matrix of quantum field theory in curved spaces posses an infinite set of complex poles (or branch cuts). These poles can be transformed into complex eigenvalues, the corresponding eigenvectors being Gamow vectors. All this formalism, which is heuristic in ordinary Hilbert space, becomes a rigorous one within the… (More)