Comments on interactions in the SUSY models

Abstract

We consider special supersymmetry (SUSY) transformations with $m$ generators ${\overleftarrow{s}}_{\alpha }$ for a certain class of models and study some physical consequences of Grassmann-odd transformations which form an Abelian supergroup with finite parameters and respective group-like elements being functionals of field variables. The SUSY-invariant path integral measure within conventional quantization implies the appearance, under a change of variables related to such SUSY transformations, of a Jacobian which is explicitly calculated. The Jacobian implies, first of all, the appearance of trivial interactions in the transformed action, and, second, the presence of a modified Ward identity which reduces to the standard Ward identities in the case of constant parameters. We examine the case of $N=1$ and $N=2$ supersymmetric harmonic oscillators to illustrate the general concept by a simple free model with $(1,1)$ physical degrees of freedom. It is shown that the interaction terms $U_{tr}$ have a corresponding SUSY-exact form: $U_{tr}=$ naturally generated in this generalized formulation. We argue that the case of non-trivial interactions cannot be obtained in such a way.

Final version, to appear in EPJC

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Cited by in corpus (2)

• Finite BRST Mapping in Higher Derivative Models
• On finite $N=1,2$ BRST transformations: Jacobians and Standard Model with gauge-invariant Gribov horizon