Interacting non-Abelian vector spinor and nilpotent spinor charges

摘要

We formulate an interacting theory of a vector-spinor field associated with anticommuting Majorana spinor charges {Q(alpha)(I), Q(beta)(J)} = 0 in arbitrary spacetime dimensions. The field content of the system is (psi(alpha I)(mu), chi(alpha IJ), A(mu)(I)), where psi(alpha I)(mu) is a vector spinor in the adjoint representation of an arbitrary gauge group, and A(mu)(I) is its gauge field, while chi(alpha IJ) is an extra spinor with antisymmetric adjoint indices IJ. Contrary to common wisdom, the consistency of the vector-spinor field equation is maintained, despite its non-trivial interactions and nilpotency of the spinor charges. After establishing the classical system, we perform its quantization with gauge-fixing and Faddeev-Popov ghost terms, confirming the BRST invariance of the total action.