It is shown that the classical description of pair production effect is possible, i.e. one can describe pair production without a reference to quantum principles. Pair production appears at statistical description of stochastic relativistic particles. There is a special force field which is responsible for pair production. This field is a reasonable consequence of quantum stochasticity. Consideration of quantum systems as stochastic systems and statistical description of them generates hydrodynamic interpretation of quantum phenomena. In the collision problem the hydrodynamic interpretation appears to be alternative to the conventional interpretation, based on quantum principles and on consideration of the wave function as a principal object of dynamics. Hydrodynamic interpretation leads to such a statement of the collision problem, which is alternative to the conventional S-matrix theory.It is shown that the classical description of pair production effect is possible, i.e. one can describe pair production without a reference to quantum principles. Pair production appears at statistical description of stochastic relativistic particles. There is a special force field which is responsible for pair production. This field is a reasonable consequence of quantum stochasticity. Consideration of quantum systems as stochastic systems and statistical description of them generates hydrodynamic interpretation of quantum phenomena. In the collision problem the hydrodynamic interpretation appears to be alternative to the conventional interpretation, based on quantum principles and on consideration of the wave function as a principal object of dynamics. Hydrodynamic interpretation leads to such a statement of the collision problem, which is alternative to the conventional S-matrix theory.

arXiv:physics/0301020Jan 12, 200313 citations

How to Define Quantum Dynamical Systems

Andrew Petrov

Physics EssaysSep 1, 19911 citation

Alternative linear structures associated with regular Lagrangians. Weyl quantization and the Von Neumann uniqueness theorem

Elisa Ercolessi, Alberto Ibort, Giuseppe Marmo +1 more

We discuss how the existence of a regular Lagrangian description on the tangent bundle $TQ$ of some configuration space $Q$ allows for the construction of a linear structure on $TQ$ that can be considered as "adapted" to the given dynamical system. The fact then that many dynamical systems admit alternative Lagrangian descriptions opens the possibility to use the Weyl scheme to quantize the system in different non equivalent ways, "evading", so to speak, the von Neumann uniqueness theorem.We discuss how the existence of a regular Lagrangian description on the tangent bundle $TQ$ of some configuration space $Q$ allows for the construction of a linear structure on $TQ$ that can be considered as "adapted" to the given dynamical system. The fact then that many dynamical systems admit alternative Lagrangian descriptions opens the possibility to use the Weyl scheme to quantize the system in different non equivalent ways, "evading", so to speak, the von Neumann uniqueness theorem.

arXiv:math-ph/0602011Feb 3, 20063 citations

AN ABSTRACT FORMULATION OF QUANTUM DYNAMICS

Włodzimierz M. Tulczyjew

Jan 1, 19650 citations

A Limitation of the Nakajima-Zwanzig projection method

M. Arsenijević, J. Jeknić-Dugić, M. Dugić

There is current interest in dynamical description of dif- ferent decompositions of a quantum system into subsystems. We investi- gate usefulness of the Nakajima-Zwanzig projection method in this context. Particularly, we are interested in simultaneous description of dynamics of open systems pertaining to dierent system-environment splits (decompo- sitions). We find that the Nakajima-Zwanzig and related projection meth- ods are system-environment split specific, that every system-environment split requires specific projector, and that projector adapted to a split nei- ther provides information about nor commute with a projector adapted to an alternative system-environment split. Our findings refer to finite- and infinite-dimensional systems and to arbitrary kinds of system-environment splitting. These findings are a direct consequence of the recently established quantum correlations relativity. We emphasize the subtlety and delicacy re- quired of the task of simultaneously describing the dynamics of alternate system-environment splits.There is current interest in dynamical description of dif- ferent decompositions of a quantum system into subsystems. We investi- gate usefulness of the Nakajima-Zwanzig projection method in this context. Particularly, we are interested in simultaneous description of dynamics of open systems pertaining to dierent system-environment splits (decompo- sitions). We find that the Nakajima-Zwanzig and related projection meth- ods are system-environment split specific, that every system-environment split requires specific projector, and that projector adapted to a split nei- ther provides information about nor commute with a projector adapted to an alternative system-environment split. Our findings refer to finite- and infinite-dimensional systems and to arbitrary kinds of system-environment splitting. These findings are a direct consequence of the recently established quantum correlations relativity. We emphasize the subtlety and delicacy re- quired of the task of simultaneously describing the dynamics of alternate system-environment splits.

arXiv:1301.1005Jan 6, 20134 citations

Quantum dynamics and open quantum systems

Dmitry Mozyrsky

Feb 1, 19990 citations

We discuss how the existence of a regular Lagrangian description on the tangent bundle

TQ

of some configuration space

Q

allows for the construction of a linear structure on

TQ

that can be considered as "adapted" to the given dynamical system. The fact then that many dynamical systems admit alternative Lagrangian descriptions opens the possibility to use the Weyl scheme to quantize the system in different non equivalent ways, "evading", so to speak, the von Neumann uniqueness theorem.