Metastable Cosmic Strings in Realistic Models

We investigate the stability of the electroweak Z-string at high temperatures. Our results show that while finite temperature corrections can improve the stability of the Z-string, their effect is not strong enough to stabilize the Z-string in the standard electroweak model. Consequently, the Z-string will be unstable even under the conditions present during the electroweak phase transition. We then consider phenomenologically viable models based on the gauge group $SU(2)_L \times SU(2)_R \times U(1)_{B-L}$ and show that metastable strings exist and are stable to small perturbations for a large region of the parameter space for these models. We also show that these strings are superconducting with bosonic charge carriers. The string superconductivity may be able to stabilize segments and loops against dynamical contraction. Possible implications of these strings for cosmology are discussed.Comment: 24 pages, 2 figures (available on request); HUTP-92/A032, Fermilab-Pub-92/228-

Re-entrant ferroelectricity in liquid crystals

The ferroelectric (Sm C$^*$) -- antiferroelectric (Sm C$^*_A$) -- reentrant ferroelectric (re Sm C$^*$) phase temperature sequence was observed for system with competing synclinic - anticlinic interactions. The basic properties of this system are as follows (1) the Sm C$^*$ phase is metastable in temperature range of the Sm C$^*_A$ stability (2) the double inversions of the helix handedness at Sm C$^*$ -- Sm C$^*_A$ and Sm C$^*_A$% -- re-Sm C$^*$ phase transitions were found (3) the threshold electric field that is necessary to induce synclinic ordering in the Sm C$^*_A$ phase decreases near both Sm C$^*_A$ -- Sm C$^*$ and Sm C$^*_A$ -- re-Sm C$^*$ phase boundaries, and it has maximum in the middle of the Sm C$^*_A$ stability region. All these properties are properly described by simple Landau model that accounts for nearest neighboring layer steric interactions and quadrupolar ordering only.Comment: 10 pages, 5 figures, submitted to PR

Minimal Family Unification

Absract It is proposed that there exist, within a new $SU(2)^{'}$, a gauged discrete group $Q_6$ (the order 12 double dihedral group) acting as a family symmetry. This nonabelian finite group can explain hierarchical features of families, using an assignment for quarks and leptons dictated by the requirements of anomaly cancellation and of no additional quarks.Comment: 10 pages, IFP-701-UNC;VAND-TH-94-

Quantum Mechanics of a Point Particle in 2+1 Dimensional Gravity

We study the phase space structure and the quantization of a pointlike particle in 2+1 dimensional gravity. By adding boundary terms to the first order Einstein Hilbert action, and removing all redundant gauge degrees of freedom, we arrive at a reduced action for a gravitating particle in 2+1 dimensions, which is invariant under Lorentz transformations and a group of generalized translations. The momentum space of the particle turns out to be the group manifold SL(2). Its position coordinates have non-vanishing Poisson brackets, resulting in a non-commutative quantum spacetime. We use the representation theory of SL(2) to investigate its structure. We find a discretization of time, and some semi-discrete structure of space. An uncertainty relation forbids a fully localized particle. The quantum dynamics is described by a discretized Klein Gordon equation.Comment: 58 pages, 3 eps figures, presentation of the classical theory improve

Renormalization of initial conditions and the trans-Planckian problem of inflation

Understanding how a field theory propagates the information contained in a given initial state is essential for quantifying the sensitivity of the cosmic microwave background to physics above the Hubble scale during inflation. Here we examine the renormalization of a scalar theory with nontrivial initial conditions in the simpler setting of flat space. The renormalization of the bulk theory proceeds exactly as for the standard vacuum state. However, the short distance features of the initial conditions can introduce new divergences which are confined to the surface on which the initial conditions are imposed. We show how the addition of boundary counterterms removes these divergences and induces a renormalization group flow in the space of initial conditions.Comment: 22 pages, 4 eps figures, uses RevTe

Examples of Embedded Defects (in Particle Physics and Condensed Matter)

We present a series of examples designed to clarify the formalism of the companion paper `Embedded Vortices'. After summarising this formalism in a prescriptive sense, we run through several examples: firstly, deriving the embedded defect spectrum for Weinberg-Salam theory, then discussing several examples designed to illustrate facets of the formalism. We then calculate the embedded defect spectrum for three physical Grand Unified Theories and conclude with a discussion of vortices formed in the superfluid $^3$He-A phase transition.Comment: final corrections. latex fil

How Efficient Is The Langacker-Pi Mechanism of Monopole Annihilation?

We investigate the dynamics of monopole annihilation by the Langacker-Pi mechanism. We find taht considerations of causality, flux-tube energetics and the friction from Aharonov-Bohm scatteering suggest that the monopole annihilation is most efficient if electromagnetism is spontaneously broken at the lowest temperature ($T_{em} \approx 10^6 GeV$) consistent with not having the monopoles dominate the energy density of the universe.Comment: 10 page

Irreducible decomposition for tensor prodect representations of Jordanian quantum algebras

Tensor products of irreducible representations of the Jordanian quantum algebras U_h(sl(2)) and U_h(su(1,1)) are considered. For both the highest weight finite dimensional representations of U_h(sl(2)) and lowest weight infinite dimensional ones of U_h(su(1,1)), it is shown that tensor product representations are reducible and that the decomposition rules to irreducible representations are exactly the same as those of corresponding Lie algebras.Comment: LaTeX, 14pages, no figur