University Of Tasmania
142596 - SU(2-1) superchiral self-duality - print.pdf (423.61 kB)

SU(2/1) superchiral self-duality: a new quantum, algebraic and geometric paradigm to describe the electroweak interactions

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journal contribution
posted on 2023-05-20, 20:34 authored by Thierry-Mieg, J, Peter JarvisPeter Jarvis
We propose an extension of the Yang-Mills paradigm from Lie algebras to internal chiral superalgebras. We replace the Lie algebra-valued connection one-form A, by a superalgebra-valued polyform à mixing exterior-forms of all degrees and satisfying the chiral self-duality condition à =∗Ãχ, where χ denotes the superalgebra grading operator. This superconnection contains Yang-Mills vectors valued in the even Lie subalgebra, together with scalars and self-dual tensors valued in the odd module, all coupling only to the charge parity CP-positive Fermions. The Fermion quantum loops then induce the usual Yang-Mills-scalar Lagrangian, the self-dual Avdeev-Chizhov propagator of the tensors, plus a new vector-scalar-tensor vertex and several quartic terms which match the geometric definition of the supercurvature. Applied to the SU(2/1) Lie-Kac simple superalgebra, which naturally classifies all the elementary particles, the resulting quantum field theory is anomaly-free and the interactions are governed by the super-Killing metric and by the structure constants of the superalgebra.


Publication title

Journal of High Energy Physics








School of Natural Sciences


Int School Advanced Studies

Place of publication

Via Beirut 2-4, Trieste, Italy, I-34014

Rights statement

This is a U.S. government work and not under copyright protection in the U.S.; foreign copyright protection may apply 2021.

Repository Status

  • Open

Socio-economic Objectives

Expanding knowledge in the mathematical sciences; Expanding knowledge in the physical sciences