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Atomic supersymmetry is a quantum-mechanical supersymmetry connecting the properties of different atoms and ions. A short description of some established results in the subject are provided and a few recent developments are discussed including the extension to parabolic coordinates and the calculation of Stark maps using supersymmetry-based models.
Atomic supersymmetry provides an analytical effective-potential model useful for describing certain aspects of Rydberg atoms. Experiments have recently demonstrated the existence of Rydberg wave packets localized in the radial coordinated with p-state angular distribution. This paper shows how atomic supersymmetry can be used to treat radial Rydberg wave packets via a particular analytical type of squeezed state, called a radial squeezed state.
The internal space-time symmetry and simple supersymmetry of relativistic particles are briefly discussed in terms of the little group of the Poincare group. The little group generators in a finite-dimensional matrix representation of the N = 1 super-Poincare algebra are explicitly constructed. The supergeometry of a massive case continuously becomes that of a massless case in the infinite-momentum limit. The origin of the gage transformations associated with the massless supermultiplets becomes transparent in that limit.
The physics of the annihilation of photinos is considered as a function of mass in detail, in order to obtain the energy spectra of the cosmic ray antiprotons produced under the assumption that photinos make up the missing mass in the galactic halo. The modulated spectrum is at 1 a.w. with the cosmic ray antiprotons data. A very intriguing fit is obtained to all of the present antiprotons up to 13.4 GeV data for similar to 15 GeV. A cutoff is predicted in the antiprotons spectrum at E = photino mass above which only a small flux from secondary production should remain.
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It is pointed out that radiative decay of massive fermions can distort the cosmic background radiation. The present investigation is concerned with a study of decay lifetimes in the range from 10 to 100,000 years. Attention is given to the physics involved in determining the effect of radiative decay of massive fermions on observed photon backgrounds. The case of particles which decoupled when the effective number of species in equilibrium was in the range from 50 to 100 is considered, and constraints on particle masses and lifetimes are placed on the basis of observed photon fluxes. This approach provides results with special applications to particles predicted by supersymmetry theories and to right-handed neutrinos. Implications for galaxy formation are also discussed.
Production models were developed and the confirmation of each one had significant astrophysical impact. These include radical modifications of propagation models, cosmic ray antiprotons injection from neighboring domains of antimatter, p production by evaporating primordial black holes, and cosmic ray p's as annihilation products of supersymmetry particles that might make up the dark dynamical mass of the Galaxy. It is that p's originating from supersymmetric parents might have distinct spectral features that would survive solar modulation; in one model, higgsino annihilation proceeds through the bb quark-antiquark channel, producing a spectral bump at approx. 0.3 GeV in the p spectrum.
Stable photinos, the photino being the supersymmetry partner of the photon, can explain both the 'missing mass' in galactic halos and the cosmic-ray antiproton spectrum up to the highest energies observed so far. This requires a photino mass around 15 GeV; significantly higher masses are cosmologically disfavored. As a consequence, the observed cosmic-ray antiproton-to-proton ratio is predicted to decrease abruptly just above the measured energy range, at E = m(x). If observed, this striking effect would strongly support the hypothesis that photinos make up the missing matter in the galaxy and also lead to a measurement of the photino mass from cosmic-ray data.
Various theoretical arguments make exotic heavy neutral weakly interacting fermions, particularly those predicted by supersymmetry theory, attractive candidates for making up the large amount of unseen gravitating mass in galactic halos. Such particles can annihilate with each other, producing secondary particles of cosmic-ray energies, among which are antiprotons, positrons, neutrinos, and gamma-rays. Spectra and fluxes of these annihilation products can be calculated, partly by making use of positron electron collider data and quantum chromodynamic models of particle production derived therefrom. These spectra may provide detectable signatures of exotic particle remnants of the big bang.
The divergent part of the self force of a radiating string coupled to gravity, an antisymmetric tensor and a dilaton in four dimensions are calculated to first order in classical perturbation theory. While this divergence can be absorbed into a renormalization of the string tension, demanding that both it and the divergence in the energy momentum tensor vanish forces the string to have the couplings of compactified N = 1 D = 10 supergravity. In effect, supersymmetry cures the classical infinities.
A method is developed for obtaining coherent states of a system admitting a supersymmetry. These states are called supercoherent states. The presented approach is based on an extension to supergroups of the usual group-theoretic approach. The example of the supersymmetric harmonic oscillator is discussed, thereby illustrating some of the attractive features of the method. Supercoherent states of an electron moving in a constant magnetic field are also described.
It is well known that Parafermi and Parabose statistics are natural extensions of the usual Fermi and Bose ones, enhancing trilinear (anti)commutation relations instead of bilinear ones. Due to this generalization, positive parameters appear: the so-called orders of paraquantization p (= 1, 2, 3, ...) and h sub 0 (= 1/2, 1, 3/2, ...), respectively, the first value leading in each case to the usual statistics. The superpostion of the parabosonic and parafermionic operators gives rise to parasupermultiplets for which mixed trilinear relations have already been studied leading to two (nonequivalent) sets: the relative Parabose and the relative Parafermi ones. For the specific values p = 1 = 2h sub 0, these sets reduce to the well known supersymmetry. Coherent states associated with this last model have been recently put in evidence through the annihilation operator point of view and the group theoretical approach or displacement operator context. We propose to realize the corresponding studies within the new context p = 2 = 2h sub 0, being then directly extended to any order of paraquantization.
We define the Berry phase for the Heisenberg operators. This definition is motivated by the calculation of the phase shifts by different techniques. These techniques are: the solution of the Heisenberg equations of motion, the solution of the Schrodinger equation in coherent-state representation, and the direct computation of the evolution operator. Our definition of the Berry phase in the Heisenberg representation is consistent with the underlying supersymmetry of the model in the following sense. The structural blocks of the Hamiltonians of supersymmetrical quantum mechanics ('superpairs') are connected by transformations which conserve the similarity in structure of the energy levels of superpairs. These transformations include transformation of phase of the creation-annihilation operators, which are generated by adiabatic cyclic evolution of the parameters of the system.
We show that the supersymmetric structure (in the sense of supersymmetric quantum mechanics) appears in Helmholtz optics describing light propagation in waveguides. For the case of elliptical waveguides, with the accuracy of paraxial approximation it admits a simple physical interpretation. The supersymmetry connects light beams of different colors. The difference in light frequencies for the supersymmetric beams is determined by the transverse gradient of the refractive index. These beams have the save wavelength in the propagation direction and can form a stable interference pattern.
In this paper ,the unitary squeezing operator of 'superspace' is introduced and by making this operator act on the supercoherent state, the squeezing supercoherent states are obtained, then come out the four orthonormalization eigenstates of the square of annihilation operator A of the supersymmetry harmonic oscillator, and their squeezing character is also studied.
Light scalar fields called moduli arise from a variety of different models involving supersymmetry and/or string theory; thus their existence is a generic prediction of leading theories for physics beyond the standard model. They also present a formidable, long-standing problem for cosmology. We argue that an anthropic solution to the moduli problem exists in the case of small moduli masses and that it automatically leads to dark matter in the form of moduli. The recent discovery of the 125 GeV Higgs boson implies a lower bound on the moduli mass of about a keV. This form of dark matter is consistent with the observed properties of structure formation, and it is amenable to detection with the help of x-ray telescopes. We present the results of a search for such dark matter particles using spectra extracted from the first deep x-ray observations of the Draco and Ursa Minor dwarf spheroidal galaxies, which are darkmatter- dominated systems with extreme mass-to-light ratios and low intrinsic backgrounds. No emission line is positively detected, and we set new constraints on the relevant new physics.