How to deal with the arrow of time in quantum field theory

The formalism of Quantum Mechanics is based by definition on conserving probabilities and thus there is no room for the description of dissipative systems in Quantum Mechanics. The treatment of time-irreversible evolution (the arrow of time) is therefore ruled out by definition in Quantum Mechanics. In Quantum Field Theory it is, however, possible to describe time-irreversible evolution by resorting to the existence of infinitely many unitarily inequivalent representations of the canonical commutation relations (ccr). In this paper I review such a result by discussing the canonical quantization of the damped harmonic oscillator (dho), a prototype of dissipative systems. The irreversibility of time evolution is expressed as tunneling among the unitarily inequivalent representations. The exact action for the dho is derived in the path integral formalism of the quantum Brownian motion developed by Schwinger and by Feynman and Vernon. The doubling of the phase-space degrees of freedom for dissipative systems is related to quantum noise effects. Finally, the role of dissipation in the quantum model of the brain and the occurrence that the cosmological arrow of time, the thermodynamical one and the biological one point into the same direction are shortly mentioned.Comment: 16 pages, Latex, Talk delivered at the XXIV International Workshop on Fundamental Problems of High Energy Physics and Field Theory, Protvino, June 2001 Proceeding available at http://dbserv.ihep.su/~pub

Fractals, coherent states and self-similarity induced noncommutative geometry

The self-similarity properties of fractals are studied in the framework of the theory of entire analytical functions and the $q$-deformed algebra of coherent states. Self-similar structures are related to dissipation and to noncommutative geometry in the plane. The examples of the Koch curve and logarithmic spiral are considered in detail. It is suggested that the dynamical formation of fractals originates from the coherent boson condensation induced by the generators of the squeezed coherent states, whose (fractal) geometrical properties thus become manifest. The macroscopic nature of fractals appears to emerge from microscopic coherent local deformation processes.Comment: 2 figure

QUANTUM DISSIPATION AND QUANTUM GROUPS

We discuss the r\^ole of quantum deformation of Weyl-Heisenberg algebra in dissipative systems and finite temperature systems. We express the time evolution generator of the damped harmonic oscillator and the generator of thermal Bogolubov transformations in terms of operators of the quantum Weyl-Heisenberg algebra. The quantum parameter acts as a label for the unitarily inequivalent representations of the canonical commutation relations in which the space of the states splits in the infinite volume limit.Comment: to appear in Annals of Physics (N.Y.

Quantum dissipation and neural net dynamics

Inspired by the dissipative quantum model of brain, we model the states of neural nets in terms of collective modes by the help of the formalism of Quantum Field Theory. We exhibit an explicit neural net model which allows to memorize a sequence of several informations without reciprocal destructive interference, namely we solve the overprinting problem in such a way last registered information does not destroy the ones previously registered. Moreover, the net is able to recall not only the last registered information in the sequence, but also anyone of those previously registered.Comment: latex file Published: Bioelectrochemistry and Bioenergetics, 48:339-342, 199

Spontaneous supersymmetry breaking probed by geometric invariants

The presence of the Aharonov-Anandan invariant in phenomena in which vacuum condensates are physically relevant can help to reveal the spontaneous supersymmetry breaking induced by condensates. The analysis is presented in the case of the Wess--Zumino model. The manifestation of the Aharonov-Anandan invariant of atoms and their superpartners, generated at non-zero temperature, could reveal the signature of SUSY violation in a recently proposed experimental setup based on an optical lattice in which SUSY is broken at non-zero temperature.Comment: 5 page

Geometric invariants as detector of Hawking and Unruh effects and quantum field theory in curved space

We report on the recent results revealing the presence of geometric invariants in all the phenomena in which vacuum condensates appear and we show that Aharonov--Anandan phase can be used to provide the evidence of phenomena like Hawking and Unruh effects and to test some behavior of quantum field theory in curved space. A very precise quantum thermometer can be also built by using geometric invariants.Comment: 7 pags. arXiv admin note: substantial text overlap with arXiv:1311.289