Linear space of spinor monomials and realization of the Nambu-Goldstone fermion in the Volkov-Akulov and Komargodski-Seiberg Lagrangians

2010/12/12 by A. A. Zheltukhin, Zheltukhin, A. A.
Mathematics · Physics and Astronomy · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #gr-qc #hep-th #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1012.2568

10 pages

arxiv created 2010/12/12 · arxiv updated 2010/12/14

Abstract

The analytical algorithm previously proposed by the author for matching the Volkov-Akulov (VA) and Komargodski-Seiberg (KS) actions describing the Nambu-Goldstone (NG) fermion, is discussed. The essence of the algotithm is explained, its consistency is proved and the recent results obtained with computer assistance are reproduced, when the proper Fierz rearrangements for Majorana bispinors are taken into account. We reveal a linear space of composite spinorial monomials Δ_m which are the solutions of the scalar constraint (∂^mψΔ_m)=0. This space is used to clarify relations between the KS and VA realizations of the NG fermionic field ψ.

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