Generalized probability and current densities: A field theory approach

TL;DR

This paper develops a novel field theory approach to quantum mechanics by introducing a generalized Lagrangian density with a non-Hermitian kinetic term, leading to extended probability and current densities that satisfy the continuity equation.

Contribution

It introduces a new generalized Lagrangian density for quantum particles with a non-Hermitian kinetic term, deriving a modified Schrödinger equation and extended densities.

Findings

Derived a generalized Schrödinger equation from the new Lagrangian

Found extended probability and current densities satisfying the continuity equation

Established a field theory framework for quantum particles with non-Hermitian kinetic terms

Abstract

We introduce a generalized Lagrangian density - involving a non-Hermitian kinetic term - for a quantum particle with the generalized momentum operator. Upon variation of the Lagrangian, we obtain the corresponding Schrodinger equation. The extended probability and particle current densities are found which satisfy the continuity equation.