Quantum Degenerate Systems

TL;DR

This paper investigates whether classical disconnected regions in degenerate dynamical systems remain disconnected in quantum theory, concluding that in irreducible cases, quantum tunneling does not occur across degeneracy surfaces, preserving classical boundaries.

Contribution

It demonstrates that in irreducible degenerate systems, quantum theory preserves classical disconnectedness, showing degeneracy surfaces act as quantum boundaries.

Findings

Quantum tunneling is absent across degeneracy surfaces in irreducible systems.

Degeneracy surfaces serve as boundaries in both classical and quantum descriptions.

Disconnection persists in quantum theory, affecting interpretations of gravitation and Chern-Simons theories.

Abstract

Degenerate dynamical systems are characterized by symplectic structures whose rank is not constant throughout phase space. Their phase spaces are divided into causally disconnected, nonoverlapping regions such that there are no classical orbits connecting two different regions. Here the question of whether this classical disconnectedness survives quantization is addressed. Our conclusion is that in irreducible degenerate systems --in which the degeneracy cannot be eliminated by redefining variables in the action--, the disconnectedness is maintained in the quantum theory: there is no quantum tunnelling across degeneracy surfaces. This shows that the degeneracy surfaces are boundaries separating distinct physical systems, not only classically, but in the quantum realm as well. The relevance of this feature for gravitation and Chern-Simons theories in higher dimensions cannot be overstated.