# Faculty Publications and Research

Permanent link for this collectionhttps://hdl.handle.net/2022/17486

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Item Evidence for a phenomenological supersymmetry in atomic physics(American Physical Society, 1984) Kostelecký, V.A.; Nieto, M.M.We show that supersymmetric quantum mechanics may be used to interrelate the spectra of different atoms and ions. This supersymmetry is broken by electron-electron interactions.Item The neutrino as a tachyon(Physics Letters B, 1985) Chodos, Alan; Hauser, Avi I.; Kostelecký, V.A.We investigate the hypothesis that at least one of the known neutrinos travels faster than light. The current experimental situation is examined within this purview.Item Supersymmetry and the relationship between the Coulomb and oscillator problems in arbitrary dimensions(American Physical Society, 1985) Kostelecký, V.A.; Nieto, M.M.; Truax, D.R.We construct the relationship between the radial equations of the $d$-dimensional hydrogen atom and the $D$-dimensional simple harmonic oscillator. The supersymmetric partners of each of these systems are obtained, and a series of maps between the various systems is delineated. We present an explicit physical example of our maps. Finally, we generalize to D dimensions the recent work of Balantekin on the supersymmetric oscillator with spin-orbit coupling, and we demonstrate that this supersymmetry is different from the one we study.Item Analytical wave functions for atomic quantum-defect theory(American Physical Society, 1985) Kostelecký, V.A.; Nieto, M.M.We present an exactly solvable effective potential that reproduces atomic spectra in the limit of exact quantum-defect theory, i.e., the limit in which, for a fixed l, the principal quantum number is modified by a constant: $n^*=\text{n}-\delta (\text{l})$. Transition probabilities for alkali atoms are calculated using the analytical wave functions obtained and agree well with accepted values. This allows us to make phenomenological predictions for certain unknown transition probabilities. Our analytical wave functions might serve as useful trial wave functions for detailed calculations.Item Evidence from alkali-metal-atom transition probabilities for a phenomenological atomic supersymmetry(American Physical Society, 1985) Kostelecký, V.A.; Nieto, M.M.We review the proposal that relationships between physical spectra of certain atoms can be considered as evidence for a phenomenological supersymmetry. Next, a comparison is made between the supersymmetric and the hydrogenic approximations. We then present the calculation of low-Z alkali-metal-atom transition probabilities between low-n states, using supersymmetric wave functions. These probabilities agree more closely with accepted values than do those obtained with use of the hydrogenic approximation. This shows that, in simple radial Schrödinger theory, supersymmetry is a concept providing insight into the true, fermionic, many-body physics of these atoms.Item Kostelecký and Nieto respond(American Physical Society, 1986) Kostelecký, V.A.; Nieto, M.M.A reply to the comment on evidence for a phenomenological supersymmetr in atomic physics is presented.Item Supersymmetric quantum mechanics in a first-order Dirac equation(American Physical Society, 1986) Hughes, R.J.; Kostelecký, V.A.; Nieto, M.M.We demonstrate the realization of supersymmetric quantum mechanics in the standard first-order Dirac equation describing a massless Dirac particle in a magnetic field. This system is relevant to the integer quantum Hall effect. In obtaining the first-order supersymmetry, square-root operators are used and justified. A detailed discussion is also provided of the simpler problem of supersymmetry in the context of the relativistic Pauli Hamiltonian squared. In addition we discuss a realization of the superalgebra osp(1/2) obtained from this system.Item Lorentzian algebra for the superstring(American Physical Society, 1987) Kostelecký, V.A.; Lechtenfeld, O.A Lorentzian algebra is constructed that underlies the covariant formulation of the spinning string. It is a simply laced hyperbolic Kac-Moody algebra having a realization on the ghost-extended spectrum of string states. From the weight space of this algebra, we obtain a unique indefinite superalgebra that has a realization on the superstring spectrum and that automatically implements the Gliozzi-Scherk-Olive projection.Item Fine structure and analytical quantum-defect wave functions(American Physical Society, 1988) Kostelecký, V.A.; Nieto, M.M.; Truax, D.R.We investigate the domain of validity of previously proposed analytical wave functions for atomic quantum-defect theory. This is done by considering the fine-structure splitting of alkali-metal and singly ionized alkaline-earth atoms. The Landé formula is found to be naturally incorporated. A supersymmetric-type integer is necessary for finite results. Calculated splittings correctly reproduce the principal features of experimental values for alkali-like atoms.Item Toy superstrings(American Physical Society, 1989) Corvi, M.; Kostelecký, V.A.; Moxhay, P.Superstrings with critical dimension two and two real bosonic spacetime coordinates may serve as useful toy models for the study of string properties. We present details of several such toy superstrings including open, closed, and heterotic models. Conformal methods are used to establish the spectrum and dimensionality. The spin fields are provided and Becchi-Rouet-Stora-Tyutin- (BRST-) invariant vertex operators are constructed. Four-point tree-level and four-point one-loop amplitudes in these models are obtained. The closed and heterotic toy superstrings are shown to be modular invariant to this order.Item $CP$ violation in supersymmetric models(American Physical Society, 1989) Branco, G.C.; Kostelecký, V.A.For supersymmetric extensions of the standard model, we obtain necessary conditions for $CP$ invariance expressed in terms of weak-basis invariants. Among other applications, these conditions allow a simple identification of independent sources of $CP$ violation and a simple exact count of $CP$-violating phases for any choice of couplings and masses.Item Phenomenological gravitational constraints on strings and higher-dimensional theories(American Physical Society, 1989) Kostelecký, V.A.; Samuel, S.We investigate measurable gravitational and cosmological effects in four dimensions that can arise from the compactification of higher-dimensional theories incorporating gravity. We identify the nature of effects due to massless scalar components of the compactified higher-dimensional metric and due to modifications of cosmological dynamics. Current experimental data impose constraints on the viability of many higher-dimensional theories, including Kaluza-Klein, supergravity, and string theories. The phenomenological problems can be avoided if the components of the metric in the higher dimensions acquire an effective mass. We survey some possible mechanisms for mass generation.Item Gravitational phenomenology in higher-dimensional theories and strings(American Physical Society, 1989) Kostelecký, V.A.; Samuel, S.We investigate gravitational phenomenology in compactified higher-dimensional theories, with particular emphasis on the consequences in string theory of tensor-induced spontaneous Lorentz-symmetry breaking. The role played by this mechanism in causing a gravitational version of the Higgs effect and in compactification is explored. The experimental viability of compactified theories with zero modes is considered by examining nonleading but observable gravitational effects. Additional constraints from the observed cosmological properties of the Universe are uncovered. Our investigations significantly constrain many theories involving extra dimensions in their perturbative regime. To resolve the phenomenological difficulties one must generate masses for the higher-dimensional components of the metric while leaving massless the physical spacetime components. Some possibilities for overcoming this metric-mass problem are suggested. An open issue is whether the metric-mass problem is resolved in string theory.Item Spontaneous breaking of Lorentz symmetry in string theory(American Physical Society, 1989) Kostelecký, V.A.; Samuel, S.The possibility of spontaneous breakdown of Lorentz symmetry in string theory is explored via covariant string field theory. A potential mechanism is suggested for the Lorentz breaking that may be generic in many string theories.Item Nonperturbative many-body physics in the open bosonic string(American Physical Society, 1990) Kostelecký, V.A.; Samuel, S.We use covariant string field theory to explore many-body string physics. A candidate nonperturbative vacuum is identified via a level-truncation scheme. The breaking of internal and Lorentz symmetries is investigated. We show that tree-level string physics exhibits similarities to loop-level particle physics. The effective string coupling runs at tree level, inducing asymptotic freedom. This is a feature of any string theory. The running coupling has significant effects on the spectrum in the nonperturbative vacuum, including the disappearance of states.Item Collective physics in the closed bosonic string(American Physical Society, 1990) Kostelecký, V.A.; Samuel, S.A second-quantized analysis is performed to examine many-body phenomena in closed bosonic strings. The covariant nonpolynomial closed-string field theory is developed in terms of particle fields and shown to contain interactions triggering a nonperturbative condensation of the tachyon field. We study the possibility that the higher-dimensional Lorentz symmetry spontaneously breaks. We show that the theory has asymptotic freedom due to a tree-level running coupling. The spectrum of states in the nonperturbative ground state is radically changed relative to the free caseItem Reply to "Comment on 'Fine-structure and analytical quantum-defect wave functions'"(American Physical Society, 1990) Kostelecký, V.A.; Nieto, M.M.; Truax, D.R.The preceding Comment by Goodfriend [Phys. Rev. A 41, 1730 (1990)] contains three criticisms of our model for analytical quantum-defect wave functions vis-á-vis the atomic Fues potential of Simons [J. Phys. Chem. 55, 756 (1971)]. We rebut the first two criticisms explicitly. This makes the third criticism moot. We stand by our resultsItem Photon and graviton masses in string theories(American Physical Society, 1991) Kostelecký, V.A.; Samuel, S.We show that string theories allow interactions potentially leading to photon and graviton-mass terms when one or more scalar fields acquire vacuum expectation values. A general analysis is presented for the case when one of these scalars is the electroweak Higgs-boson doublet. The results provide a new constraint on model building for string theories.Item Reply to "Comment on 'Analytical wave functions for atomic quantum-defect theory'"(American Physical Society, 1991) Kostelecký, V.A.; Nieto, M.M.The preceding paper, by Martin and Barrientos [Phys. Rev. A 43, 4061 (1991)], comments on our supersymmetry-inspired model of atomic physics. We relate this to other Comments [Rau, Phys. Rev. Lett. 56, 95 (1986) and Goodfriend, Phys. Rev. A 41, 1730 (1990)] and point out that, although the mathematics and physics of the 1974 Simons model [J. Chem. Phys. 60, 645 (1974)] is similar to ours, it is not identical. This is elucidated by explicitly comparing our symmetry-based approach to the more phenomenological approach of Martin and Barrientos.Item Supercoherent states(American Physical Society, 1991) Fatyga, B.W.; Kostelecký, V.A.; Nieto, M.M.; Truax, D.R.A general approach is presented for constructing coherent states for supersymmetric systems. It uses Rogers's supermanifold formulation of supergroups to extend the group-theoretic method. Supercoherent states are explicitly obtained for the supersymmetric harmonic oscillator. They are shown to be eigenstates of the supersymmetric annihilation operator and to be minimum-uncertainty states. Two more-complex situations with extended physical supersymmetries are also considered: an electron moving in a constant magnetic field, and the electron-monopole system. The supercoherent states for these systems are found using super Baker-Campbell-Hausdorff relations and their interpretation is elucidated.