17271450
Harmonic BRST quantization of systems with irreducible holomorphic bosonic and fermionic constraints.
We consider systems with second-class constraints or, equivalently, first-class holomorphic constraints. We show that the harmonic Becchi-Rouet-Stora-Tyutin method of quantizing systems with bosonic holomorphic constraints extends to systems having both bosonic and fermionic holomorphic constraints. The ghosts for bosonic holomorphic constraints in the harmonic BRST method have a Poisson brackets structure different from that of the ghosts in the usual BRST method, which applies to systems with real first-class constraints. Apart from this exotic ghost structure for bosonic constraints, the new feature of the harmonic BRST method is the introduction of two new holomorphic BRST charges [Theta] and [bar [Theta]] and the addition of an extra term [minus][beta][l brace][Theta],[bar [Theta]][r brace] to the BRST-invariant Hamiltonian. We apply the Fradkin-Vilkovisky theorem to general systems with mixed bosonic and fermionic holomorphic constraints and show that, taking an appropriate limit, the extra term in the harmonic BRST-modified path integral reproduces the correct Senjanovic measure.
18449042
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.
29392446
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 analytically the bound state spectrum of the light degrees of freedom for a spinless, massless quark in scalar, time-component vector, and string confinement through semi-classical quantization.
17624939
TOPOLOGICAL MASS GENERATION IN 3+1 DIMENSIONS
The 4-dimensional theory of a 1-form Abelian gauge field A coupled to a 2-form (antisymmetric tensor) potential B is studied. The two gauge invariances of the theory admit a coupling mB ∧ F where F is the field strength (F=dA) of A. It is shown that this theory is a unitary, renormalizable theory of a massive spin-one field with no additional degrees of freedom. In this sense, it is a generalization to four dimensions of topological mechanisms in two dimensions (the Schwinger model) and three dimensions (Chern-Simons theory). The issue of spontaneous symmetry breaking is also examined.
121348066
Flux tube vibrations and the excited glue spectroscopy
As a step toward a fundamental understanding of hybrid states we demonstrate the close relationship between the relativistic string and lattice simulation results for excited glue states with two fixed color sources.
119941265
Scalar and QCD string confinement
We compare scalar and string confinement mechanisms. Solutions for the massless quark case are found and discussed.
14961957
Long-range effects of cosmic string structure.
We combine and further develop ideas and techniques of Allen & Ottewill, Phys. Rev. D, 42, 2669 (1990) and Kay & Studer Commun. Math. Phys., 139, 103 (1991) for calculating the long range effects of cosmic string cores on classical and quantum field quantities far from an (infinitely long, straight) cosmic string. We find analytical approximations for (a) the gravity-induced ground state renormalized expectation values of ˆ ϕ 2 and ˆ Tµ � for a non-minimally coupled quantum scalar field far from a cosmic string (b) the classical electrostatic self force on a test charge far from a superconducting cosmic string. Surprisingly – even at cosmologically large distances – all these quantities would be very badly approximated by idealizing the string as having zero thickness and imposing regular boundary conditions; instead they are well approximated by suitably fitted strengths of logarithmic divergence at the string core. Our formula for h ˆ ϕ 2 i reproduces (with much less effort and much more generality) the earlier numerical results of Allen & Ottewill. Both h ˆ
14972039
Analytic results for the gravitational radiation from a class of cosmic string loops.
Cosmic string loops are defined by a pair of periodic functions ${\bf a}$ and ${\bf b}$, which trace out unit-length closed curves in three-dimensional space. We consider a particular class of loops, for which ${\bf a}$ lies along a line and ${\bf b}$ lies in the plane orthogonal to that line. For this class of cosmic string loops one may give a simple analytic expression for the power $\gamma$ radiated in gravitational waves. We evaluate $\gamma$ exactly in closed form for several special cases: (1) ${\bf b}$ a circle traversed $M$ times; (2) ${\bf b}$ a regular polygon with $N$ sides and interior vertex angle $\pi-2\pi M/N$; (3) ${\bf b}$ an isosceles triangle with semi-angle $\theta$. We prove that case (1) with $M=1$ is the absolute minimum of $\gamma$ within our special class of loops, and identify all the stationary points of $\gamma$ in this class.