Reformulation of spin pseudoclassical dynamics

Peter Prešnajder, V. Pažma

Jerry Paul Draayer, C. Bahri, S. A. Moszkowski

F. M. C. Witte

It is shown that pseudoclassical many-particle systems allow for observable consequences of the spin degrees of freedom, in contrast to the one-particle system, where a consistent formulation of spin space density is impossible. After quantization, this density can then be directly compared to the decomposition of the Wigner operator in terms of spin matrices, in both the nonrelativistic and the relativistic context. From an expansion of the Dirac spinors in terms of large and small components it is seen that in the nonrelativistic limit the pseudoscalar, the timelike component of the axial-vector current, and the spatial components of the vector current vanish. The spatial components of the axial-vector current vanish in the pseudoclassical limit. The pseudoclassical appearance of spin is due to the spin-tensor contribution.

Xiao-Chuan Wu, Ran Cheng, Di Xiao

Theodore J. Allen, Donald Spector, Christopher Wilson

We examine the quantization of pseudoclassical dynamical systems, models that have classically anticommuting variables, in the Schrödinger picture. We quantize these systems, which can be viewed as classical models of particle spin, using the generalized Gupta–Bleuler method as well as the reduced phase space method in even dimensions. With minimal modifications, the standard constructions of Schrödinger quantum mechanics of constrained systems work for pseudoclassical systems. We generalize the standard Schrödinger norm and implement the correct adjointness properties of observables and constraints. We construct the state space corresponding to spinors as physical wave functions of anticommuting variables, finding that there are superselection sectors in both the physical and ghost subspaces. The physical states are isomorphic to those of the Dirac–Kähler formulation of fermions, though the inner product in Dirac–Kähler theory is not equivalent to ours.

Zhixing Zou, Jiao Wang

The kicked rotor and the kicked top are two paradigms of quantum chaos. The notions of quantum resonance and the pseudoclassical limit, developed in the study of the kicked rotor, have revealed an intriguing and unconventional aspect of classical-quantum correspondence. Here, we show that, by extending these notions to the kicked top, its rich dynamical behavior can be appreciated more thoroughly; of special interest is the entanglement entropy. In particular, the periodic synchronization between systems subject to different kicking strength can be conveniently understood and elaborated from the pseudoclassical perspective. The applicability of the suggested general pseudoclassical theory to the kicked rotor is also discussed.