Spectral Discontinuities in Constrained Dynamical Models

TL;DR

This paper investigates a quantum mechanical model derived from a relativistic field theory, revealing how parameter variations cause abrupt changes in constraints and uncovering new energy levels in complex parameter domains.

Contribution

It introduces a novel quantum mechanical model from the chiral Schwinger model, analyzing how constraints depend on parameters and exploring complex domain energy levels.

Findings

Parameter-dependent constraints alter dynamical modes.

Discovery of real energy levels in complex parameter regions.

Identification of higher derivative Pais-Uhlenbeck modes.

Abstract

As examples of models having interesting constraint structures, we derive a quantum mechanical model from the spatial freezing of a well known relativistic field theory - the chiral Schwinger model. We apply the Hamiltonian constraint analysis of Dirac [1] and find that the nature of constraints depends critically on a $c$-number parameter present in the model. Thus a change in the parameter alters the number of dynamical modes in an abrupt and non-perturbative way. We have obtained new {\it{real}} energy levels for the quantum mechanical model as we explore {\it{complex}} domains in the parameter space. These were forbidden in the parent chiral Schwinger field theory where the analogue Jackiw-Rajaraman parameter is restricted to be real. We explicitly show existence of modes that satisfy higher derivative Pais-Uhlenbeck form of dynamics [3]. We also show that the Cranking Model [7], well known in Nuclear Physics, can be interpreted as a spatially frozen version of another well studied relativistic field theory in 2+1-dimension- the Maxwell-Chern-Simons-Proca Model [8].