The Non-Relativistic Limit of Keldysh Spinors

TL;DR

This paper investigates the non-relativistic limit of Keldysh spinors, revealing that despite their unusual properties, they lead to standard quantum mechanics with a positive-definite Hamiltonian, and exhibit interesting decoupling behaviors.

Contribution

It demonstrates the well-defined non-relativistic limit of Keldysh spinors and explores their interaction with Dirac fields, highlighting novel decoupling phenomena.

Findings

Keldysh spinors yield a positive-definite Pauli Hamiltonian in the non-relativistic limit

Despite sign differences, Keldysh spinors have a consistent non-relativistic quantum mechanics

Decoupling observed between Dirac and Keldysh fields in certain interactions

Abstract

Keldysh spinors obey Dirac equation, but have the negative of the Dirac action and Hamiltonian. In an example of the U(1) EM coupling, we show that, despite the sign changes, they have a well-defined non-relativistic limit resulting in quantum mechanics with the positive-definite Pauli Hamiltonian. When non-relativistic Dirac and Keldysh fields are brought to interact, we observe curious decoupling of the two fields in mass-like and vector couplings.