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The analytical algorithm previously proposed by the author for matching theVolkov-Akulov (VA) and Komargodski-Seiberg (KS) actions describing theNambu-Goldstone (NG) fermion, is discussed. The essence of the algotithm isexplained, its consistency is proved and the recent results obtained withcomputer assistance are reproduced, when the proper Fierz rearrangements forMajorana bispinors are taken into account. We reveal a linear space ofcomposite spinorial monomials $\Delta_{m}$ which are the solutions of thescalar constraint $(\partial^{m}\bar\psi\Delta_{m})=0$. This space is used toclarify relations between the KS and VA realizations of the NG fermionic field$\psi$.

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