Rotations and e, $\nu$ Propagators, Part II

TL;DR

This paper derives spacetime-invariant propagators for neutrinos from rotation-based projection operators, extending previous work on electron propagators and providing a novel approach to understanding neutrino behavior in quantum field theory.

Contribution

It introduces rotation-invariant projection operators for four-component quantities and constructs neutrino propagators, expanding the rotation-based framework from Part I to neutrinos.

Findings

Derived rotation-invariant projection operators for four-component quantities.

Constructed spacetime-invariant neutrino propagators.

Extended the rotation-based derivation method from electrons to neutrinos.

Abstract

We continue to derive spacetime quantities and spin 1/2 propagators from rotations. Rotation-invariant projection operators are found for each element of a four element basis, i.e. a basis for four component quantities with specific transformation rules under rotations. With these four projection operators, we make two spacetime invariant projection operators, i.e. once space, time, energy, and momentum are identified. The spacetime invariant operators are propagators for free neutrinos. Except for the substitute basis, the process is the same as the one that gave electron propagators in Part I. PACS number(s): 11.30.-j, 11.30.Cp, and 03.65.Fd