Bi-orthogonal eigen-spinors related to T-pseudo-Hermitian Pauli Hamiltonian : Time reversal and Clifford Algebra

TL;DR

This paper constructs bi-orthogonal eigen-spinors for a deformed pseudo-Hermitian Pauli Hamiltonian, explores their properties within Clifford algebra, and introduces a new variant of the Kustaanheimo-Stiefel transformation.

Contribution

It introduces a novel bi-orthogonal eigen-spinor framework for pseudo-Hermitian Hamiltonians using Clifford algebra and proposes a new spinor-based Kustaanheimo-Stiefel transformation.

Findings

Eigen-spinors are constructed for the deformed Hamiltonian.

An analogue of Kramers theorem is proposed in a pseudo-Hermitian context.

A new spinor-based Kustaanheimo-Stiefel transformation is introduced.

Abstract

A set of two-parameter bi-orthogonal eigen-spinors has been constructed from a deformed pseudo- Hermitian extension of Pauli Hamiltonian and its Hermitian conjugate. The Hamiltonians thus obtained are iso-spectral to the original Pauli Hamiltonian. A pair of spin-projection operators has been constructed as an essential ingredient of a possible bi-orthogonal quantum mechanics. An analogue of Kramers theorem in pseudo-Hermitian setting has also been inferred in a conjectural sense. The properties of time reversal and bi-orthogonality have been elaborated in the frame work of Clifford algebra Cl3, where the spinors have been viewed as elements of left ideal and the relevant inner-products are understood in terms of different involutions leading to elements of a division ring. The whole process of present construction is found to be based on both direct and time reversed Cl3 generators. A new variant of Kustaanheimo-Stiefel transformation has been introduced with the help of spinor operator.