Exceptional Point and Gauge Invariance in Particle Models and Related Field Theories

We propose appearance of Exceptional Point (EP) in a real parameter space, in a novel type of Hermitian model. This is possible because the constraint structure changes discontinuously at the EP leading to a coalescence of a full tower of quantum (Harmonic Oscillator) states. We also find interesting consequences of complexifying the parameter space. We show that this model is a descendent of a well known relativistic field theory in 1 + 1-dimensionthe bosonized Chiral Schwinger Model and in the latter the features of EP are retained. We also show that the Cranking Model, recently studied in the context of EP, is a descendent of another well studied relativistic field theory in 2 + 1-dimensionthe Maxwell-Chern-Simons-Proca Model. Introduction: The study of Exceptional Points (EP) and the underlying quantum instability has created a lot of interest in recent times [1, 2, 3]. Generically this phenomenon is associated with some points (EPs) in the parameter space of the theory where energy eigenvalue becomes singular and for parameter values beyond EPs the energy eigenvalue turn into complex from real ones (or vice versa). Clearly there is a dramatic change in the behavior of the system while crossing the EPs. To the best of our knowledge, so far the studies of EPs have been restricted to finite dimensional (classical and quantum) mechanical models where the presence of EP is entirely dictated by the behavior of the energy value over the E-mail: sudipta [email protected] E-mail: [email protected]