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

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.

27 pages

References in corpus (3)

• Adinkras: A Graphical Technology for Supersymmetric Representation Theory
• When Superspace Is Not Enough
• The Landscape of Theoretical Physics: A Global View; From Point Particles to the Brane World and Beyond, in Search of a Unifying Principle

Cited by in corpus (15)

• Spin Gauge Theory of Gravity in Clifford Space: A Realization of Kaluza-Klein Theory in 4-Dimensional Spacetime
• Kaluza-Klein Theory without Extra Dimensions: Curved Clifford Space
• On Negative Energies, Strings, Branes, and Braneworlds: A Review of Novel Approaches
• Classical Cancellation of the Cosmological Constant Re-Considered
• On a Unified Theory of Generalized Branes Coupled to Gauge Fields, Including the Gravitational and Kalb-Ramond Fields
• Quantum Field Theories in Spaces with Neutral Signatures
• An Extra Structure of Spacetime: A Space of Points, Areas and Volumes
• Towards a New Paradigm: Relativity in Configuration Space
• Branes and Quantized Fields
• Electroweak and Majorana Sector Higgs Bosons and Pseudo-Nambu-Goldstone Bosons
• On the Stueckelberg Like Generalization of General Relativity
• Towards the Unification of Gravity and other Interactions: What has been Missed?
• A Non-Trivial Zero Length Limit of the Nambu-Goto String
• On an Alternative Approach to the Relation between Bosons and Fermions: Employing Clifford Space
• Extended Relativity: Beyond