On the Hamilton-Jacobi equation for second class constrained systems

We discuss a general procedure for arriving at the Hamilton-Jacobi equation of second-class constrained systems, and illustrate it in terms of a number of examples by explicitely obtaining the respective Hamilton principal function, and verifying that it leads to the correct solution to the Euler-Lagrange equations.Comment: 17 pages, to appear in Ann. Phy

Quantum Fluctuations of Particles and Fields in Smooth Path Integrals

An approach to evaluation of the smooth Feynman path integrals is developed for the study of quantum fluctuations of particles and fields in Euclidean time-space. The paths are described by sum of Gauss functions and are weighted with exp(-S) by appropriate methods. The weighted smooth paths reproduce properties of the ground state of the harmonic oscillator in one dimension with high accuracy. Quantum fluctuations of U(1) and SU(2) gauge fields in four dimensions are also evaluated in our approach.Comment: 4 pages, 1 figure, talk given at the 12th Asia Pacific Physics Conference of AAPPS (APPC12), Makuhari, Japan, 14-19 July 201

Binary spinning black hole Hamiltonian in canonical center-of-mass and rest-frame coordinates through higher post-Newtonian order

The recently constructed Hamiltonians for spinless binary black holes through third post-Newtonian order and for spinning ones through formal second post-Newtonian order, where the spins are counted of zero post-Newtonian order, are transformed into fully canonical center-of-mass and rest-frame variables. The mixture terms in the Hamiltonians between center-of-mass and rest-frame variables are in accordance with the relation between the total linear momentum and the center-of-mass velocity as demanded by global Lorentz invariance. The various generating functions for the center-of-mass and rest-frame canonical variables are explicitly given in terms of the single-particle canonical variables. The no-interaction theorem does not apply because the world-line condition of Lorentz covariant position variables is not imposed.Comment: 18 pages, no figure

Lattice sum rules for the colour fields

We analyse the sum rules describing the action and energy in the colour fields around glueballs, torelons and static potentials.Comment: 9 pages LATEX, (typos corrected, to appear in Phys Rev D

All-electric qubit control in heavy hole quantum dots via non-Abelian geometric phases

We demonstrate how non-Abelian geometric phases can be used to universally process a spin qubit in heavy hole quantum dots in the absence of magnetic fields. A time dependent electric quadrupole field is used to perform any desired single qubit operation by virtue of non-Abelian holonomy. During the proposed operations, the degeneracy of the time dependent two level system representing the qubit is not split. Since time reversal symmetry is preserved and hyperfine coupling is known to be weak in spin qubits based on heavy holes, we expect very long coherence times in the proposed setup

Off-diagonal Gluon Mass Generation and Infrared Abelian Dominance in Maximally Abelian Gauge in SU(3) Lattice QCD

In SU(3) lattice QCD formalism, we propose a method to extract gauge fields from link-variables analytically. With this method, we perform the first study on effective mass generation of off-diagonal gluons and infrared Abelian dominance in the maximally Abelian (MA) gauge in the SU(3) case. Using SU(3) lattice QCD, we investigate the propagator and the effective mass of the gluon fields in the MA gauge with U(1)_3 \timesU(1)_8 Landau gauge fixing. The Monte Carlo simulation is performed on $16^4$ at $\beta$=5.7, 5.8 and 6.0 at the quenched level. The off-diagonal gluons behave as massive vector bosons with the approximate effective mass $M_{\mathrm{off}} \simeq 1.1-1.2\mathrm{GeV}$ in the region of $r =0.3-0.8$fm, and the propagation is limited within a short range, while the propagation of diagonal gluons remains even in a large range. In this way, infrared Abelian dominance is shown in terms of short-range propagation of off-diagonal gluons. Furthermore, we investigate the functional form of the off-diagonal gluon propagator. The functional form is well described by the four-dimensional Euclidean Yukawa-type function $e^{-m_{\rm off}r}/r$ with $m_{\rm off} \simeq 1.3-1.4\mathrm{GeV}$ for $r = 0.1- 0.8$ fm. This also indicates that the spectral function of off-diagonal gluons has the negative-value region

Hilbert Space of Isomorphic Representations of Bosonized Chiral QCD2QCD_2

We analyse the Hilbert space structure of the isomorphic gauge non-invariant and gauge invariant bosonized formulations of chiral $QCD_2$ for the particular case of the Jackiw-Rajaraman parameter $a = 2$. The BRST subsidiary conditions are found not to provide a sufficient criterium for defining physical states in the Hilbert space and additional superselection rules must to be taken into account. We examine the effect of the use of a redundant field algebra in deriving basic properties of the model. We also discuss the constraint structure of the gauge invariant formulation and show that the only primary constraints are of first class.Comment: LaTeX, 19 page

A new look at the modified Coulomb potential in a strong magnetic field

The static Coulomb potential of Quantum Electrodynamics (QED) is calculated in the presence of a strong magnetic field in the lowest Landau level (LLL) approximation using two different methods. First, the vacuum expectation value of the corresponding Wilson loop is calculated perturbatively in two different regimes of dynamical mass $m_{dyn.}$, {\it i.e.}, $|{\mathbf{q}}_{\|}^{2}|\ll m_{dyn.}^{2}\ll |eB|$ and $m_{dyn.}^{2}\ll |\mathbf{q}_{\|}^{2}|\ll|eB|$, where $\mathbf{q}_{\|}$ is the longitudinal components of the momentum relative to the external magnetic field $B$. The result is then compared with the static potential arising from Born approximation. Both results coincide. Although the arising potentials show different behavior in the aforementioned regimes, a novel dependence on the angle $\theta$ between the particle-antiparticle's axis and the direction of the magnetic field is observed. In the regime $|{\mathbf{q}}_{\|}^{2}|\ll m_{dyn.}^{2}\ll |eB|$, for strong enough magnetic field and depending on the angle $\theta$, a qualitative change occurs in the Coulomb-like potential; Whereas for $\theta=0,\pi$ the potential is repulsive, it exhibits a minimum for angles $\theta\in]0,\pi[$.Comment: V1: 26 pages, 8 figures, latex format, V2: Accepted for publication in PRD (2007