121666860
DARBOUX TRANSFORMATION FOR THE ONE-DIMENSIONAL STATIONARY DIRAC EQUATION WITH NON-HERMITIAN INTERACTION
The Darboux algorithm is applied to an exactly solvable one-dimensional stationary Dirac equation, with non-Hermitian, pseudoscalar interaction V0(x). This generates a hierarchy of exactly solvable Dirac Hamiltonians, , defined by new non-Hermitian interactions V1(x), which are also pseudoscalar. It is shown that are isospectral to the initial Hamiltonian h0, except for certain missing states.
119312840
'Stringy' Coherent States Inspired By Generalized Uncertainty Principle
Abstract Coherent States with Fractional Revival property, that explicitly satisfy the Generalized Uncertainty Principle (GUP), have been constructed in the context of Generalized Harmonic Oscillator. The existence of such states is essential in motivating the GUP based phenomenological results present in the literature which otherwise would be of purely academic interest. The effective phase space is Non-Canonical (or Non-Commutative in popular terminology). Our results have a smooth commutative limit, equivalent to Heisenberg Uncertainty Principle. The Fractional Revival time analysis yields an independent bound on the GUP parameter. Using this and similar bounds obtained here, we derive the largest possible value of the (GUP induced) minimum length scale. Mandel parameter analysis shows that the statistics is Sub-Poissonian. Correspondence Principle is deformed in an interesting way. Our computational scheme is very simple as it requires only first order corrected energy values and undeformed basis states.
14129154
A new class of PT-symmetric Hamiltonians with real spectra
Abstract We investigate complex PT-symmetric potentials, associated with quasi-exactly solvable non-Hermitian models involving polynomials and a class of rational functions. We also look for special solutions of intertwining relations of SUSY quantum mechanics providing a partnership between a real and a complex PT-symmetric potential of the kind mentioned above. We investigate conditions sufficient to ensure the reality of the full spectrum or, for the quasi-exactly solvable systems, the reality of the energy of the finite number of levels.
8406718
Motion of a spin-½ particle in shape invariant scalar and magnetic fields
We study the motion of a spin-½ particle in a scalar as well as a magnetic field within the framework of supersymmetric quantum mechanics. We also introduce the concept of shape invariant scalar and magnetic fields and it is shown that the problem admits exact analytical solutions when such fields are considered.
119751583
On supersymmetry and random sources
We evaluate the one loop effective potential for the supersymmetric Higgs model in the presence of a gaussian random source and examine supersymmetry breaking at the one loop level.
120571457
Supersymmetric anyon quantum mechanics
Abstract We develop a framework for anyons within supersymmetric quantum mechanics. We prove that supersymmetry can be realized spectrally but necessarily requires a contact interaction which modifies in a specific way the usual regularity condition of the wavefunction at the origin.
13912698
Event shape discrimination of supersymmetry from large extra dimensions at a linear collider
The production of a charged lepton (l=e,μ) pair with a large missing energy at a linear collider is discussed as a means of distinguishing the minimal supersymmetry (MSSM) scenario from that with large extra dimensions (ADD) for parameter ranges where the total cross-sections are comparable for both. Analyses in terms of event shape variables, specifically sphericity and thrust, are shown to enable a clear discrimination in this regard.
119146278
Pseudo-Hermitian generalized Dirac oscillators
Abstract We study generalized Dirac oscillators with complex interactions in ( 1 + 1 ) dimensions. It is shown that for the choice of interactions considered here, the Dirac Hamiltonians are η -pseudo-Hermitian with respect to certain metric operators η . Exact solutions for the generalized Dirac oscillator for some choices of the interactions have also been obtained. It is also shown that generalized Dirac oscillators can be identified with an anti-Jaynes–Cummings-type model and by spin flipping they can also be identified with a Jaynes–Cummings-type model.
122353924
Light cone constraints and two asymptotic domains in lepton-nucleon and meson-nucleon scattering
Abstract Effective bare masses of the “current-quarks” are estimated from some testable inequalities, linking deep inelastic lepton-nucleon structure functions and high energy meson-nucleon total cross-sections, derived on the basis of the light-cone commutators of the pseudoscalar densities of quark-field theory.
119615417
What neutral current experiments can tell us about left-right symmetry
Abstract Neutral current consequences of left-right symmetry for the gauge group SUL(2) × SUR(2) × U(1) are derived in the form of experimentally testable relations. Additional results follow from the hypothesis of no exotic charges. Some of these tests can distinguish such theories from the Weinberg-Salam model.
119753398
Ultralight Dirac neutrinos from possible supergrand scenario
Persistent experimental suggestions about the electron neutrino being an ultralight Dirac particle in the mass range 20 to 55 eV have underlined the need to theoretically generate such a mass naturally, i.e., without any arbitrarily small Yukawa coupling or Higgs-field vacuum expectation value. A mechanism for this is proposed in this paper in terms of a 4\ifmmode\times\else\texttimes\fi{}4 neutral-fermion Majorana mass matrix for a single-generation world. The physical eigenstates turn out to be one ultralight and one very heavy Dirac neutrino within each fermion family. A general discussion (including the many-generation case) is given of the necessary and sufficient conditions for the emergence of such ultralight Dirac neutrinos. We also consider the skeleton of an illustrative, though incomplete, SO(10) supersymmetric (SUSY) grand unified theory (GUT) scenario\char22{}with a geometric type of hierarchy and some global symmetries\char22{}in which the aforesaid mass matrix is likely to arise. The ultralight neutrino Dirac mass is related at the tree level to that of its charge-$\frac{2}{3}$ family member by ${m}_{\ensuremath{\nu}}\ensuremath{\sim}m(\frac{2}{3})\frac{{M}_{\mathrm{SUSY}}}{{M}_{\mathrm{GUT}}}$ and radiative corrections are shown to be controllably small. Various implications of this result are brought out.