Position, spin and orbital angular momentum of a relativistic electron

Motivated by recent interest in relativistic electron vortex states, we revisit the spin and orbital angular momentum properties of Dirac electrons. These are uniquely determined by the choice of the position operator for a relativistic electron. We overview two main approaches discussed in the literature: (i) the projection of operators onto the positive-energy subspace, which removes the zitterbewegung effects and correctly describes spin-orbit interaction effects, and (ii) the use of Newton-Wigner-Foldy-Wouthuysen operators based on the inverse Foldy-Wouthuysen transformation. We argue that the first approach [previously described in application to Dirac vortex beams in K.Y. Bliokh et al., Phys. Rev. Lett. 107, 174802 (2011)] has a more natural physical interpretation, including spin-orbit interactions and a nonsingular zero-mass limit, than the second one [S.M. Barnett, Phys. Rev. Lett. 118, 114802 (2017)].Comment: 10 pages, 1 table, to appear in Phys. Rev.

Flavor Changing Neutral Currents, an Extended Scalar Sector, and the Higgs Production Rate at the LHC

We study extensions of the standard model with additional colored scalar fields which can couple directly to quarks. Natural suppression of flavor changing neutral currents implies minimal flavor violation, and fixes the scalars to transform as (8,2)_1/2 under the SU(3) X SU(2) X U(1) gauge symmetry. We explore the phenomenology of the standard model with one additional (8,2)_1/2 scalar, and discuss how this extension can modify flavor physics and the Higgs boson production rate at the LHC. Custodial SU(2) symmetry can be implemented for the octet scalars since they transform as a real color representation. Additional weak scale degrees of freedom needed for gauge unification are discussed.Comment: Minor change

Theory of the Stark Effect for P donors in Si

We develop a multi-valley effective mass theory for substitutional donors in silicon in an inhomogeneous environment. Valley-orbit coupling is treated perturbatively. We apply the theory to the Stark effect in Si:P. The method becomes more accurate at high fields, and it is designed to give correct experimental binding energies at zero field. Unexpectedly, the ground state energy for the donor electron is found to increase with electric field as a consequence of spectrum narrowing of the 1s manifold. Our results are of particular importance for the Kane quantum computer.Comment: published versio

A Unified and Complete Construction of All Finite Dimensional Irreducible Representations of gl(2|2)

Representations of the non-semisimple superalgebra $gl(2|2)$ in the standard basis are investigated by means of the vector coherent state method and boson-fermion realization. All finite-dimensional irreducible typical and atypical representations and lowest weight (indecomposable) Kac modules of $gl(2|2)$ are constructed explicitly through the explicit construction of all $gl(2)\oplus gl(2)$ particle states (multiplets) in terms of boson and fermion creation operators in the super-Fock space. This gives a unified and complete treatment of finite-dimensional representations of $gl(2|2)$ in explicit form, essential for the construction of primary fields of the corresponding current superalgebra at arbitrary level.Comment: LaTex file, 23 pages, two references and a comment added, to appear in J. Math. Phy

Geometric phases in 2D and 3D polarized fields: geometrical, dynamical, and topological aspects

Geometric phases are a universal concept that underpins numerous phenomena involving multi-component wave fields. These polarization-dependent phases are inherent in interference effects, spin-orbit interaction phenomena, and topological properties of vector wave fields. Geometric phases have been thoroughly studied in two-component fields, such as two-level quantum systems or paraxial optical waves. However, their description for fields with three or more components, such as generic nonparaxial optical fields routinely used in modern nano-optics, constitutes a nontrivial problem. Here we describe geometric, dynamical, and total phases calculated along a closed spatial contour in a multi-component complex field, with particular emphasis on 2D (paraxial) and 3D (nonparaxial) optical fields. We present several equivalent approaches: (i) an algebraic formalism, universal for any multi-component field; (ii) a dynamical approach using the Coriolis coupling between the spin angular momentum and reference-frame rotations; and (iii) a geometric representation, which unifies the Pancharatnam-Berry phase for the 2D polarization on the Poincar\'e sphere and the Majorana-sphere representation for the 3D polarized fields. Most importantly, we reveal close connections between geometric phases, angular-momentum properties of the field, and topological properties of polarization singularities in 2D and 3D fields, such as C-points and polarization M\"obius strips.Comment: 21 pages, 11 figures, to appear in Rep. Prog. Phy

Spin-Statistics Violations in Superstring Theory

I describe how superstring theory may violate spin-statistics in an experimentally observable manner. Reviewing the basics of superstring interactions and how to utilize these to produce a statistical phase, I then apply these ideas to two specific examples. The first is the case of heterotic worldsheet linkings, whereby one small closed string momentarily enlarges sufficiently to pass over another, producing such a statistical phase. The second is the braneworld model with noncommutative geometry, whereby matter composed of open strings may couple to a background in which spacetime coordinates do not commute, modifying the field (anti)commutator algebra. I conclude with ways to sharpen and experimentally test these exciting avenues to possibly verify superstring theory.Comment: 18 pages, 3 figures; v2: references added and typos correcte