Comments on interactions in the SUSY models

Abstract

We consider special supersymmetry (SUSY) transformations with m generators ← − s α , 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 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 SUSYexact form:← − s ← − s generated naturally under such generalized formulation. We argue that the case of a non-trivial interaction cannot be obtained in such a way.

Electrical conductivity of waxes as model systems for polyethylene: Role of water

“…Theoretical models predict that above~10 kV mm −1 the measured conductivity is strongly influenced by the applied field and this is borne out by experiment. 7 For instance, electrical conductivity is reported to be independent of applied field in the range 2-15 kV/mm 14 while, elsewhere, 15 it was reported that the electrical conductivity is strongly dependent on applied field above 20 kV mm −1 . In the work reported here, we sought to work in a regime where the measurements are not unduly influenced by the applied electric field, which suggests that: (1), a constant applied field is used and (2) all work is performed with fields <20 kV mm −1 .…”

“…However, another complication is evident in working under constant field conditions; that is, the current is observed to fall over a period of hours. 15,16 Therefore, sufficient measurement time must be allowed if a reliable steady-state current is to be assured. Additional complications are posed by the influences of both water 9,13 and impurities 17 and so these factors must either be eliminated or controlled.…”

“…Additional complications are posed by the influences of both water 9,13 and impurities 17 and so these factors must either be eliminated or controlled. Additionally, temperature can influence electrical conductivity 15,18 and, therefore, this variable also needs to be properly controlled. Here, we have sought to overcome many of these difficulties by employing two high-purity alkanebased systems whose chemical composition is well defined.…”

The Quantum Description of BF Model in Superspace

“…The BV method also address the possible violations of symmetries of the action by quantum effects. The BV formulation (independently introduced by Zinn-Justin [21]) extends the BRST approach [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]. In fact, the BRST symmetry [37,38] is a very important symmetry for gauge theories [26,[39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54].…”

Quantum Gauge Symmetry of Reducible Gauge Theory

“…The problem of graviton propagator divergences is a also addressed [46]. The supersymmetry is also generalized by making transformation parameter finite and field dependent [47]. The finite BRST-antiBRST symmetry to the case of general gauge theories is discussed [48,49].…”