Clifford Space as a Generalization of Spacetime: Prospects for QFT of Point Particles and Strings

TL;DR

This paper explores replacing traditional spacetime with Clifford space (C-space) to generalize quantum field theory and string theory, offering solutions to the cosmological constant problem and reformulating string theory without central charges.

Contribution

It introduces Clifford space as a novel framework for QFT and string theory, addressing longstanding issues like the cosmological constant and algebraic anomalies.

Findings

C-space's pseudo-Euclidean signature helps solve the cosmological constant problem

String theory can be formulated without central terms in C-space

A toy model demonstrates properties of harmonic oscillators in pseudo-Euclidean space

Abstract

The idea that spacetime has to be replaced by Clifford space (C-space) is explored. Quantum field theory (QFT) and string theory are generalized to C-space. It is shown how one can solve the cosmological constant problem and formulate string theory without central terms in the Virasoro algebra by exploiting the peculiar pseudo-Euclidean signature of C-space and the Jackiw definition of the vacuum state. As an introduction into the subject, a toy model of the harmonic oscillator in pseudo-Euclidean space is studied.