Dynamical q-deformation in quantum theory and the stochastic limit

Abstract

A model of particle interacting with quantum field is considered. The model includes as particular cases the polaron model and non-relativistic quantum electrodynamics. We show that the field operators obey q-commutation relations with q depending on time. After the stochastic (or van Hove) limit, due to the nonlinearity, the atomic and field degrees of freedom become entangled in the sense that the field and the atomic variables no longer commute but give rise to a new algebra with new commutation relations replacing the Boson ones. This new algebra allows to give a simple proof of the fact that the non crossing half-planar diagrams give the dominating contribution in a weak coupling regime and to calculate explicitly the correlations associated to the new algebra. The above results depend crucially on the fact that we do not introduce any dipole or multipole approximation.

Latex, 11 pages

References in corpus (1)

• The Stochastic Sector of Interacting-Free Quantum Field Theory

Cited by in corpus (8)

• Quantum stochastic equation for test particle interacting with dilute Bose gas
• Non-Exponential Decay for Polaron Model
• Noncommutative probability in classical systems
• p-Adic representation of the Cuntz algebra and the free coherent states
• The Contextual Quantization and the Principle of Complementarity of Probabilities
• Weak coupling limit for quantum systems with unbounded weakly commuting system operators
• q-Deformation and free statistics for interaction of a field and a particle
• The stochastic limit of the Fröhlich Hamiltonian: relations with the quantum Hall effect