A new way to unify all fermion and boson fields, including gravity

2025/12/09 by N. S. Mankoč Borštnik, Borštnik, N. S. Mankoč
Mathematics · Physics and Astronomy · Social Sciences · #Algebraic and Geometric Analysis #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #International Science and Diplomacy #Quantum Physics (quant-ph) #Quantum and Classical Electrodynamics

paper · pdf · doi:10.48550/arxiv.2512.09008

openalex publication_date 2025/12/09 · openalex created_date 2025/12/12 · openalex updated_date 2026/07/28

Abstract

The description of the internal spaces of fermion and boson fields with "basis vectors", which are the superposition of odd and even products of the operators γ^a, offers in d=2(2n+1)-dimensions, such as d=(13+1), a unified picture of all so far observed fermions (quarks, leptons, antiquarks and antileptons that appear in families) and bosons (gravitons, photons, weak bosons, gluons and scalars), under the condition that all fields have non-zero angular momenta only in the d =(3+1), SO(3,1), of ordinary space-time. Bosons, which also carry the spatial index α (which is for tensors and vectors μ=(0,1,2,3) and for scalars σ≥ 5) appear in two orthogonal groups. In any d=2(2n+1)-dimensional space the number of internal states of fermions in all families and their Hermitian conjugate partners is equal to the number of internal states of boson states. The article presents general properties of massless fermion and boson fields and their mutual interactions in this theory, which determine the Lagrangian density of both fields and their interactions. It particularly illustrates "basis vectors" and their properties in d=(13+1) and d=(5+1). The article presents new results and discusses open problems in this theory.

Citations

• Can the "basis vectors", describing the internal spaces of fermion and boson fields with the Clifford odd (for fermion) and Clifford even (for boson) objects, explain interactions among fields, with gravitons included?
• Clifford odd and even objects in even and odd dimensional spaces describing internal spaces of fermion and boson fields
• New experimental data for the quarks mixing matrix are in better agreement with the spin-charge-family theory predictions
• Clifford algebra, geometric algebra, and applications

Related

• How to present and interpret the Feynman diagrams in this theory describing fermion and boson fields in a unique way, in comparison with the Feynman diagrams so far presented and interpreted?
• Clifford odd and even objects in even and odd dimensional spaces describing internal spaces of fermion and boson fields
• Can the "basis vectors", describing the internal spaces of fermion and boson fields with the Clifford odd (for fermion) and Clifford even (for boson) objects, explain interactions among fields, with gravitons included?
• Clifford odd and even objects offer the description of the internal space of fermions and bosons, respectively, opening new insight into the second quantization of fields
• How Clifford algebra can help understand second quantization of fermion and boson fields