2,918 research outputs found
Classification of Type A N-fold supersymmetry
Type A N-fold supersymmetry of one-dimensional quantum mechanics can be
constructed by using sl(2) generators represented on a finite dimensional
functional space. Using this sl(2) formalism we show a general method of
constructing Type A N-fold supersymmetric models. We also present systematic
generation of known models and several new models using this method.Comment: 15 pages in LaTeX2e, some comments and a reference adde
N-fold Supersymmetry in Quantum Mechanics - General Formalism -
We report general properties of N-fold supersymmetry in one-dimensional
quantum mechanics. N-fold supersymmetry is characterized by supercharges which
are N-th polynomials of momentum. Relations between the anti-commutator of the
supercharges and the Hamiltonian, the spectra, the Witten index, the
non-renormalization theorems and the quasi-solvability are examined. We also
present further investigation about a particular class of N-fold supersymmetric
models which we dubbed type A. Algebraic equations which determine a part of
spectra of type A models are presented, and the non-renormalization theorem are
generalized. Finally, we present a possible generalization of N-fold
supersymmetry in multi-dimensional quantum mechanics.Comment: 25 page
N-fold Supersymmetry in Quantum Mechanics - Analyses of Particular Models -
We investigate particular models which can be N-fold supersymmetric at
specific values of a parameter in the Hamiltonians. The models to be
investigated are a periodic potential and a parity-symmetric sextic triple-well
potential. Through the quantitative analyses on the non-perturbative
contributions to the spectra by the use of the valley method, we show how the
characteristic features of N-fold supersymmetry which have been previously
reported by the authors can be observed. We also clarify the difference between
quasi-exactly solvable and quasi-perturbatively solvable case in view of the
dynamical property, that is, dynamical N-fold supersymmetry breaking.Comment: 32 pages, 10 figures, REVTeX
A New Family of N-fold Supersymmetry: Type B
We construct a new family of N-fold supersymmetric systems which is referred
to as ``type B''. A higher derivative representation of the N-fold supercharge
for this new family is given by a deformation of the type A N-fold supercharge.
By utilizing the same method as in the sl(2) construction of type A N-fold
supersymmetry, we show that this family includes two of the quasi-solvable
models of Post-Turbiner type.Comment: 12 pages, minor types corrected, references updated, DOI adde
General Forms of a N-fold Supersymmetric Family
We report general forms of one family of the N-fold supersymmetry in
one-dimensional quantum mechanics. The N-fold supersymmetry is characterized by
the supercharges which are N-th order in differential operators. The family
reported here is defined as a particular form of the supercharges and is
referred to as ``type A''. We show that a quartic and a periodic potentials,
which were previously found to be N-fold supersymmetric by the authors, are
realized as special cases of this type A family.Comment: 11pages, REVTeX, few errata correcte
Nonlinear supersymmetry in Quantum Mechanics: algebraic properties and differential representation
We study the Nonlinear (Polynomial, N-fold,...) Supersymmetry algebra in
one-dimensional QM. Its structure is determined by the type of conjugation
operation (Hermitian conjugation or transposition) and described with the help
of the Super-Hamiltonian projection on the zero-mode subspace of a supercharge.
We show that the SUSY algebra with transposition symmetry is always polynomial
in the Hamiltonian if supercharges represent differential operators of finite
order. The appearance of the extended SUSY with several (complex or real)
supercharges is analyzed in details and it is established that no more than two
independent supercharges may generate a Nonlinear superalgebra which can be
appropriately specified as {\cal N} = 2 SUSY. In this case we find a
non-trivial hidden symmetry operator and rephrase it as a non-linear function
of the Super-Hamiltonian on the physical state space. The full {\cal N} = 2
Non-linear SUSY algebra includes "central charges" both polynomial and
non-polynomial (due to a symmetry operator) in the Super-Hamiltonian.Comment: 28 pages, Latex, minor improvements and removed misprint
Testing new physics with the electron g-2
We argue that the anomalous magnetic moment of the electron (a_e) can be used
to probe new physics. We show that the present bound on new-physics
contributions to a_e is 8*10^-13, but the sensitivity can be improved by about
an order of magnitude with new measurements of a_e and more refined
determinations of alpha in atomic-physics experiments. Tests on new-physics
effects in a_e can play a crucial role in the interpretation of the observed
discrepancy in the anomalous magnetic moment of the muon (a_mu). In a large
class of models, new contributions to magnetic moments scale with the square of
lepton masses and thus the anomaly in a_mu suggests a new-physics effect in a_e
of (0.7 +- 0.2)*10^-13. We also present examples of new-physics theories in
which this scaling is violated and larger effects in a_e are expected. In such
models the value of a_e is correlated with specific predictions for processes
with violation of lepton number or lepton universality, and with the electric
dipole moment of the electron.Comment: 34 pages, 7 figures. Minor changes and references adde
In vitro effects of metals on the acid phosphatase from the microalgae Pseudokirchneriella subcapitata.
Phosphatases and antioxidant enzymes as potential biochemical indicators of toxicity in aquatic non-target organisms.
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