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Title: Quantum Supersymmetric Models in the Causal Approach

Abstract

We consider the massless supersymmetric vector multiplet in a purely quantum framework. First order gauge invariance determines uniquely the interaction Lagrangian as in the case of Yang-Mills models. Going to the second order of perturbation theory produces an anomaly which cannot be eliminated. We make the analysis of the model working only with the component fields.

Authors:
 [1]
  1. Department of Theoretical Physics, 'Horia Hulubei' National Institute for Physics and Nuclear Engineering (IFIN-HH), Inst. Atomic Phys., 407 Atomistilor, Bucharest-Magurele, MG 6, 077125 (Romania)
Publication Date:
OSTI Identifier:
21057123
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 899; Journal Issue: 1; Conference: 6. international conference of the Balkan Physical Union, Istanbul (Turkey), 22-26 Aug 2006; Other Information: DOI: 10.1063/1.2733104; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BASIC INTERACTIONS; GAUGE INVARIANCE; LAGRANGIAN FIELD THEORY; LAGRANGIAN FUNCTION; NUMERICAL ANALYSIS; PERTURBATION THEORY; SUPERSYMMETRY; VECTORS; YANG-MILLS THEORY

Citation Formats

Grigore, Dan-Radu. Quantum Supersymmetric Models in the Causal Approach. United States: N. p., 2007. Web. doi:10.1063/1.2733104.
Grigore, Dan-Radu. Quantum Supersymmetric Models in the Causal Approach. United States. doi:10.1063/1.2733104.
Grigore, Dan-Radu. Mon . "Quantum Supersymmetric Models in the Causal Approach". United States. doi:10.1063/1.2733104.
@article{osti_21057123,
title = {Quantum Supersymmetric Models in the Causal Approach},
author = {Grigore, Dan-Radu},
abstractNote = {We consider the massless supersymmetric vector multiplet in a purely quantum framework. First order gauge invariance determines uniquely the interaction Lagrangian as in the case of Yang-Mills models. Going to the second order of perturbation theory produces an anomaly which cannot be eliminated. We make the analysis of the model working only with the component fields.},
doi = {10.1063/1.2733104},
journal = {AIP Conference Proceedings},
number = 1,
volume = 899,
place = {United States},
year = {Mon Apr 23 00:00:00 EDT 2007},
month = {Mon Apr 23 00:00:00 EDT 2007}
}
  • The authors analyze phase-space approaches to relativistic quantum mechanics from the viewpoint of the causal interpretation. In particular, they discuss the canonical phase space associated with stochastic quantization, its relation to Hilbert space, and the Wigner-Moyal formalism. They then consider the nature of Feynman paths, and the problem of nonlocality, and conclude that a perfectly consistent relativistically covariant interpretation of quantum mechanics which retains the notion of particle trajectory is possible.
  • Combining the methods of scattering theory and supersymmetric quantum mechanics we obtain relations between the S matrix and its supersymmetric partner. These relations involve only asymptotic quantities and do not require knowledge of the dynamical details. For example, for coupled channels with no threshold differences the relations involve the asymptotic normalization constant of the bound state removed by supersymmetry.
  • We show that for the class of gauge-field configurations which reduce the Dirac operator to the one-dimensional Witten Hamiltonian, an appropriate semiclassical quantization rule permits the computation of the bound-state spectrum in an accurate way.
  • It is argued that the noncommutativity approach to fully supersymmetric field theories on the lattice suffers from an inconsistency. Supersymmetric quantum mechanics is worked out in this formalism and the inconsistency is shown both in general and explicitly for that system, as well as for the Abelian super BF model.
  • We study exact solutions of the Schrödinger equation for some potentials. We introduce a parametric approach to supersymmetric quantum mechanics to calculate energy eigenvalues and corresponding wave functions exactly. As an application we solve Schrödinger equation for the generalized Morse potential, modified Hulthen potential, deformed Rosen-Morse potential and Poschl-Teller potential. The method is simple and effective to get the results.