https://doi.org/10.1140/epjc/s10052-016-4213-7
Regular Article - Theoretical Physics
Comments on interactions in the SUSY models
1
Department of Physics, Banaras Hindu University, Varanasi, 221005, India
2
Institute of Strength Physics and Materials Science of SB RAS, Tomsk, 634021, Russia
* e-mail: bhabani.mandal@gmail.com
Received:
2
November
2015
Accepted:
16
June
2016
Published online:
12
July
2016
We consider special supersymmetry (SUSY) transformations with m generators for some class of models and study the physical consequences when making the Grassmann-odd transformations to form an Abelian supergroup with finite parameters and a set of group-like elements with finite parameters being functionals of the field variables. The SUSY-invariant path integral measure within conventional quantization scheme leads to the appearance of the Jacobian under a change of variables generated by such SUSY transformations, 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 the and 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 have a corresponding SUSY-exact form: generated naturally under such generalized formulation. We argue that the case of a non-trivial interaction cannot be obtained in such a way.
© The Author(s), 2016