Fun with supersymmetric quantum mechanics
One reason for studying supersymmetric quantum mechanics is that there are a class of superpotentials W(x) which behave at large x as x/sup ..cap alpha../ for which we know from general arguments whether SUSY is broken or unbroken. Thus one can use these superpotentials to test various ideas about how to see if supersymmetry is broken in an arbitrary model. Recently, Witten proposed a topological invariant, the Witten index ..delta.. which counts the number of bosons minus the number of fermions having ground state energy zero. Since if supersymmetry is broken, the ground state energy cannot be zero, one expects if ..delta.. is not zero, SUSY is preserved and the theory is not a good candidate for a realistic model. In this study we evaluate ..delta.. for several examples, and show some unexpected peculiarities of the Witten index for certain choice of superpotentials W(x). We also discuss two other nonperturbative methods of studying supersymmetry breakdown. One involves relating supersymmetric quantum mechanics to a stochastic classical problem and the other involves considering a discrete (but not supersymmetric) version of the theory and studying its behavior as one removes the lattice cuttoff. In this survey we review the Hamiltonian and path integral approaches to supersymmetric quantum mechanics. We then discuss the related path integrals for the Witten Index and for stochastic processes and show how they are indications for supersymmetry breakdown. We then discuss a system where the superpotential W(x) has assymetrical values at +-infinity. We finally discuss nonperturbative strategies for studying supersymmetry breakdown based on introducing a lattice and studying the behavior of the ground state energy as the lattice cutoff is removed. 17 references.
- Research Organization:
- Illinois Univ., Urbana (USA). Dept. of Physics; Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- DOE Contract Number:
- W-7405-ENG-36
- OSTI ID:
- 7000703
- Report Number(s):
- LA-UR-84-1311; CONF-831267-4; ON: DE84011329
- Resource Relation:
- Conference: Workshop on supersymmetry in physics, Los Alamos, NM, USA, 15 Dec 1983
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
SUPERSYMMETRY
QUANTUM MECHANICS
SYMMETRY BREAKING
FIELD THEORIES
HAMILTONIANS
LATTICE FIELD THEORY
REVIEWS
SOLITONS
DOCUMENT TYPES
MATHEMATICAL OPERATORS
MECHANICS
QUANTUM FIELD THEORY
QUANTUM OPERATORS
QUASI PARTICLES
SYMMETRY
645400* - High Energy Physics- Field Theory