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

References in corpus (38)

• Gauge Invariant Lagrangians for Free and Interacting Higher Spin Fields. A Review of the BRST formulation
• BRST approach to Lagrangian construction for fermionic higher spin fields in AdS space
• BRST-BV approach to cubic interaction vertices for massive and massless higher-spin fields
• Higher-Spin Theory and Space-Time Metamorphoses
• Off-shell nilpotent finite BRST/anti-BRST transformations
• Is soft breaking of BRST symmetry consistent?
• Application of finite field-dependent BRS transformations to problems of the Coulomb gauge
• Finite BRST Transformations for the Bagger-Lambert-Gustavasson Theory
• Field-dependent BRST transformations in Yang-Mills theory
• Relating Gribov-Zwanziger theory to effective Yang-Mills theory
• Finite nilpotent symmetry in Batalin-Vilkovisky formalism
• Field-dependent BRST-antiBRST Transformations in Yang-Mills and Gribov-Zwanziger Theories
• General Lagrangian Formulation for Higher Spin Fields with Arbitrary Index Symmetry. 2. Fermionic fields
• Generalized BRST transformation in Abelian rank-2 antisymmetric tensor field theory
• Field dependent nilpotent symmetry for gauge theories
• BRST symmetry and $W$-algebra in higher derivative models
• Aspects of finite field-dependent symmetry in SU(2) Cho-Faddeev-Niemi decomposition
• Finite BRST transformation and constrained systems
• ABJM theory in Batalin-Vilkovisky formulation
• The noncovariant gauges in 3-form theories
• Finite BRST-antiBRST Transformations in Lagrangian Formalism
• Finite field-dependent symmetries in perturbative quantum gravity
• Generalized BRST Symmetry and Gaugeon Formalism for Perturbative Quantum Gravity: Novel Observation
• Generalized BRST symmetry for arbitrary spin conformal field theory
• Field-dependent quantum gauge transformation
• Quantum gauge symmetry from finite field dependent BRST transformations
• A systematic study of finite BRST-BV transformations in field-antifield formalism
• Field-dependent symmetries in Friedmann-Robertson-Walker models
• N=1 super-Chern-Simons theory in Batalin-Vilkovisky formulation
• Generalized supersymmetry and sigma models
• The conformal gauge to the derivative gauge for worldsheet gravity
• Perturbative quantum gravity in Batalin-Vilkovisky formalism
• Field-Dependent BRST-antiBRST Lagrangian Transformations
• Supersymmetry Transformation of Quantum Fields II: Supersymmetric Yang-Mills Theory
• Supersymmetry Transformation of Quantum Fields
• Finite BRST-antiBRST Transformations in Generalized Hamiltonian Formalism
• A systematic study of finite BRST-BFV transformations in $Sp(2)$-extended generalized Hamiltonian formalism
• On Gauge Independence for Gauge Models with Soft Breaking of BRST Symmetry

Cited by in corpus (12)

• BRST Quantization of Unimodular Gravity
• BRST Symmetry for Torus Knot
• On the BRST and finite field dependent BRST of a model where vector and axial vector interaction get mixed up with different weight
• Generalized quantum electrodynamics in the framework of Generalized BRST transformation
• Finite BRST Mapping in Higher Derivative Models
• Conformal to Harmonic Gauge for Bosonic Strings
• Generalization of Faddeev--Popov Rules in Yang--Mills Theories: N=3,4 BRST Symmetries
• Soft-Collinear Effective Theory: BRST Formulation
• Quantum gauge symmetry of reducible gauge theory
• On finite $N=1,2$ BRST transformations: Jacobians and Standard Model with gauge-invariant Gribov horizon
• Non-Abelian gauge theories with composite fields in the background field method
• Equivalence of two solutions of physical massive gravity