Quantum field theory of a hyper-complex scalar field on a commutative ring

TL;DR

This paper develops a hypercomplex scalar field theory unifying U(1) and SO(1,1) gauge groups using a commutative ring, revealing novel neutral bosons and vacuum energy cancellation, with potential quantum information applications.

Contribution

It introduces a hypercomplex field theory that unifies gauge groups and demonstrates vacuum energy cancellation without normal ordering, extending quantum field theory frameworks.

Findings

Hypercomplex field encodes two charged bosons forming a neutral boson.

Vacuum energy cancels exactly due to contributions from boson partners.

Potential applications in quantum teleportation and squeezed boson states.

Abstract

Inspired by the structural unification of unitary groups (quantum field theory) with orthogonal groups (relativity) proposed recently through a non-division algebra, we construct a hypercomplex field theory with an internal symmetry that unifies the U(1) compact gauge group with the SO(1,1) noncompact gauge group, using the commutative ring of hypercomplex numbers. From the quantum field theory point of view, the hypercomplex field encodes two charged bosons with opposite charge, and corresponds thus to a neutral compound boson. Furthermore, normal or- dering of operators is not required for controling the vacuum divergences; in an analogy with SUSY, the theory under study contains U(1) boson particles and their hyperbolic SO(1,1) boson partners, whose contributions to the vacuum energy cancel out exactly to a zero value. In fact the present scheme allows us to compare finite measuments of squeezed boson-number statistics obtained with and without normal ordering. Additionally we discuss on the potential applications of the squeezed boson states constructed on the commutative ring, in quantum teleportation and in related areas.