119136395
Exact solutions of the (2+1) Dimensional Dirac equation in a constant magnetic field in the presence of a minimal length
We study the (2+1) dimensional Dirac equation in an homogeneous magnetic field (relativistic Landau problem) within a minimal length, or generalized uncertainty principle -GUP-, scenario. We derive exact solutions for a given explicit representation of the GUP and provide expressions of the wave functions in the momentum representation. We find that in the minimal length case the degeneracy of the states is modified and that there are states that do not exist in the ordinary quantum mechanics limit (\beta -->0). We also discuss the mass-less case which may find application in describing the behavior of charged fermions in new materials like Graphene.
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.
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.
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.
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.
1691094
Electroweak Processes and Precision Tests
Review of the electroweak sector of the minimal standard model, Basic LEP processes at the tree level, 1-loop radiative corrections in the on-shell renormalization scheme, Star scheme and oblique corrections, Introduction to oblique parameters.
9655209
Probing the deviation from maximal mixing of atmospheric neutrinos
Pioneering atmospheric muon neutrino experiments have demonstrated the near-maximal magnitude of the flavor mixing angle ${\ensuremath{\theta}}_{23}$. But the precise value of the deviation $D\ensuremath{\equiv}1/2\ensuremath{-}{sin﻿}^{2}{\ensuremath{\theta}}_{23}$ from maximality (if nonzero) needs to be known, being of great interest\char22{}especially to builders of neutrino mass and mixing models. We quantitatively investigate in a three-generation framework the feasibility of determining $D$ in a statistically significant manner from studies of the atmospheric ${\ensuremath{\nu}}_{\ensuremath{\mu}},{\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}$ survival probability including both vacuum oscillations and matter effects. We show how this determination will be sharpened by considering the up-down ratios of observed ${\ensuremath{\nu}}_{\ensuremath{\mu}}$- and ${\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}$-induced events and the differences of these ratios in specified energy and zenith angle bins. We consider 1 Megaton year of exposure to a magnetized iron calorimeter such as the proposed India-based Neutrino Observatory detector ICAL, taking into account both energy and zenith angle resolution functions. The sensitivity of such an exposure and the dependence of the determination of $D$ on the concerned oscillation parameters are discussed in detail. The vital use of matter effects in fixing the octant of ${\ensuremath{\theta}}_{23}$ is highlighted.
15089264
Neutrinos at high energy accelerators
PREAMBLE, BRIEF HISTORY AND PRELIMINARIES, QUICK REVIEW OF BASIC NEUTRINO PROPERTIES, CHARGED CURRENT NEUTRINO PROCESSES, NEUTRAL CURRENT NEUTRINO PROCESSES, VERY HEAVY NEUTRINOS, CONCLUDING SUMMARY
120237473
An operatorially solved model of massless two-dimensional quantum chromodynamics
An operator solution is constructed in (1,1) dimensions to the massless quantum chromodynamics of n fermion quarks and n2 − 1 vector boson gluons with local colour SU(n) symmetry. The interacting quark field is a confined SU(n) Thirring field with zero Abelian coupling. The colour gluons are dependent Lie fields obeying the gluon-free fermionic current identity. Explicit local infinitesimal operator colour transformations (with an arbitrary coordinate-independent Lorentz vector coefficient defining the gauge) are given and the requirement of proper colour covariance linked to the vanishing of the coloured quark source currents and hence to the absence of coloured quark-composite states. The status of Noether's theorem is also clarified.
121409119
Explicit operator solution to thirring model with U(n) symmetry
Abstract Two explicit solutions to the Thirring model with U( n ) symmetry are constructed following Klaiber's approach. Products of fields are obtained in terms of those for the free case and scale dimensions of composite operators are computed.