arXiv subjects

Theodore J. Allen

Publications and source records attributed to Theodore J. Allen.

18 recordsLinked to original sources

arXiv2021

Spin in Schrödinger-quantized Pseudoclassical Systems

We examine the construction of the spin angular momentum in systems with pseudoclassical Grassmann variables. In constrained systems there are many different algebraic forms for the dynamical variables that will all agree on the constraint surface. For the angular momentum, a particular form of the generators is preferred, which yields superselection sectors of irreducible spin^c(n) representations rather than reducible so(n) representations when quantized in the Schrödinger realization.

quant-ph↗

arXiv2020

Quantization of Pseudoclassical Systems in the Schrödinger Realization

We examine the quantization of pseudoclassical dynamical systems, models that have classically anticommuting variables, in the Schrödinger picture. We quantize these systems, which can be viewed as classical models of particle spin, using the generalized Gupta-Bleuler method as well as the reduced phase space method in even dimensions. With minimal modifications, the standard constructions of Schrödinger quantum mechanics of constrained systems work for pseudoclassical systems. We generalize the standard Schrödinger norm and implement the correct adjointness properties of observables and constraints. We construct the state space corresponding to spinors as physical wave functions of anticommuting variables, finding that there are superselection sectors in both the physical and ghost subspaces. The physical states are isomorphic to those of the Dirac-Kähler formulation of fermions though the inner product in Dirac-Kähler theory is not equivalent to ours.

hep-th↗

arXiv2004

Direct experimental test of scalar confinement

The concept of Lorentz scalar quark confinement has a long history and is still widely used despite its well-known theoretical faults. We point out here that the predictions of scalar confinement also conflict directly with experiment. We investigate the dependence of heavy-light meson mass differences on the mass of the light quark. In particular, we examine the strange and non-strange D mesons. We find that the predictions of scalar confinement are in considerable conflict with measured values.

hep-ph↗

arXiv2003

Universal light quark mass dependence and heavy-light meson spectroscopy

Clean predictions are presented for all the spin-averaged heavy-light meson spectroscopies. A new symmetry is identified wherein the energy eigenstates have a universal dependence on both the light and heavy quark masses. This universality is used in an efficient analysis of these mesons within the QCD string/flux tube picture. Unique predictions for all the D, D_s, B, and B_s type mesons in terms of just four measured quantities.

hep-ph↗

arXiv2003

QCD strings with spinning quarks

We construct a consistent action for a massive spinning quark on the end of a QCD string that leads to pure Thomas precession of the quark's spin. The string action is modified by the addition of Grassmann degrees of freedom to the string such that the equations of motion for the quark spin follow from boundary conditions, just as do those for the quark's position.

hep-ph↗

arXiv2003

Reduction of the QCD string to a time component vector potential

We demonstrate the equivalence of the relativistic flux tube model of mesons to a simple potential model in the regime of large radial excitation. We make no restriction on the quark masses; either quark may have a zero or finite mass. Our primary result shows that for fixed angular momentum and large radial excitation, the flux tube/QCD string meson with a short-range Coulomb interaction is described by a spinless Salpeter equation with a time component vector potential V(r) = ar - k/r.

hep-ph↗

arXiv2003

QCD String Structure in Vector Confinement

We demonstrate that the Nambu-Goto string spectroscopy with massless quarks is replicated in highly excited states of the linear vector confinement potential. For deep radial excitations we observe that the Regge slope, spacing between daughter trajectories, and absolute state energies agree with those of the QCD string.

hep-ph↗

arXiv2002

A Mechanism for Charge Quantization

We analyze a potential that produces background charges which are automatically quantized. This introduces a new mechanism for charge quantization, although so far it has only been implemented for background charges. We show that this same mechanism can also lead to an alternative means of hiding extra dimensions that is analogous to the Kaluza-Klein approach.

hep-th↗

arXiv2001

Analytic Quantization of the QCD String

We perform an analytic semi-classical quantization of the straight QCD string with one end fixed and a massless quark on the other, in the limits of orbital and radial dominant motion. We compare our results to the exact numerical semi-classical quantization. We observe that the numerical semi-classical quantization agrees well with our exact numerical canonical quantization.

hep-ph↗

arXiv2000

Remark on the computation of mode sums

The computation of mode sums of the types encountered in basic quantum field theoretic applications is addressed with an emphasis on their expansions into functions of distance that can be interpreted as potentials. We show how to regularize and calculate the Casimir energy for the continuum Nambu-Goto string with massive ends as well as for the discrete Isgur-Paton non-relativistic string with massive ends. As an additional example, we examine the effect on the interquark potential of a constant Kalb-Ramond field strength interacting with a QCD string.

hep-th↗

arXiv2000

From scalar to string confinement

We outline a connection between scalar quark confinement, a phenomenologically successful concept heretofore lacking fundamental justification, and QCD. Although scalar confinement does not follow from QCD, there is an interesting and close relationship between them. We develop a simple model intermediate between scalar confinement and the QCD string for illustrative purposes. Finally, we find the bound state masses of scalar, time-component vector, and string confinement analytically through semi-classical quantization.

hep-ph↗

arXiv1999

Curved QCD string dynamics

We consider the effects of going beyond the approximation of a straight string in mesons by using a flexible flux tube model wherein a Nambu-Goto string bends in response to quark accelerations. The curved string is dynamically identical to the straight string even for ultra-relativistic mesons except for a small additional radial momentum. We numerically solve the curved string model in the case where both ends have equal mass quarks and also the case where one end is fixed. No approximation of non-relativistic motion is made. We note some small but interesting difference from the straight string.

hep-ph↗

arXiv1998

Excited glue and the vibrating flux tube

Recent lattice results for the energy of gluonic excitations as a function of quark separation are shown to correspond to transverse relativistic flux tube vibration modes. For large quark separations all states appear to degenerate into a few categories which are predicted uniquely, given the ground state.

hep-ph↗

arXiv1997

On quark confinement dynamics

Starting from Buchmüller's observation that a chromoelectric flux tube meson will exhibit only the Thomas type spin-orbit interaction, we show that a model built upon the related assumption that a quark feels only a constant radial chromoelectric field in its rest frame implies a complete relativistic effective Hamiltonian that can be written explicitly in terms of quark canonical variables. The model yields linear Regge trajectories and exhibits some similarities to scalar confinement, but with the advantage of being more closely linked to QCD.

hep-ph↗

arXiv1993

Phase Space Reduction and Vortex Statistics: An Anyon Quantization Ambiguity

We examine the quantization of the motion of two charged vortices in a Ginzburg--Landau theory for the fractional quantum Hall effect recently proposed by the first two authors. The system has two second-class constraints which can be implemented either in the reduced phase space or Dirac-Gupta-Bleuler formalism. Using the intrinsic formulation of statistics, we show that these two ways of implementing the constraints are inequivalent unless the vortices are quantized with conventional statistics; either fermionic or bosonic.

hep-th↗

arXiv1993

Harmonic BRST Quantization of Systems with Irreducible Holomorphic Boson and Fermion Constraints

We show that the harmonic Becchi-Rouet-Stora-Tyutin method of quantizing bosonic systems with second-class constraints or first-class holomorphic constraints extends to systems having both bosonic and fermionic second-class or first-class holomorphic constraints. Using a limit argument, we show that the harmonic BRST modified path integral reproduces the correct Senjanovic measure.

hep-th↗

arXiv1992

Collective Coordinate Action for Charged Sigma-Model Vortices in Finite Geometries

In this Letter the method of Lund is applied to formulate a variational principle for the motion of charged vortices in an effective non-linear Schrödinger field theory describing finite size two-dimensional quantum Hall samples under the influence of an arbitrary perpendicular magnetic field. Freezing out variations in the modulus of the effective field yields a $U(1)$ sigma-model. A duality transformation on the sigma-model reduces the problem to finding the Green function for a related electrostatics problem. This duality illuminates the plasma analogy to the Laughlin wave function.

hep-th↗

arXiv1992

Charged Vortex Dynamics in Ginzburg-Landau Theory of the Fractional Quantum Hall Effect

We write a Ginzburg-Landau Hamiltonian for a charged order parameter interacting with a background electromagnetic field in 2+1 dimensions. Using the method of Lund we derive a collective coordinate action for vortex defects in the order parameter and demonstrate that the vortices are charged. We examine the classical dynamics of the vortices and then quantize their motion, demonstrating that their peculiar classical motion is a result of the fact that the quantum motion takes place in the lowest Landau level. The classical and quantum motion in two dimensional regions with boundaries is also investigated. The quantum theory is not invariant under magnetic translations. Magnetic translations add total time derivative terms to the collective action, but no extra constants of the motion result.

hep-th↗