Spontaneously Broken Spacetime Symmetries and Goldstone's Theorem

Goldstone's theorem states that there is a massless mode for each broken symmetry generator. It has been known for a long time that the naive generalization of this counting fails to give the correct number of massless modes for spontaneously broken spacetime symmetries. We explain how to get the right count of massless modes in the general case, and discuss examples involving spontaneously broken Poincare and conformal invariance.Comment: 4 pages; 1 figure; v2: minor corrections. version to appear on PR

Anomaly Cancellation in 2+1 dimensions in the presence of a domainwall mass

A Fermion in 2+1 dimensions, with a mass function which depends on one spatial coordinate and passes through a zero ( a domain wall mass), is considered. In this model, originally proposed by Callan and Harvey, the gauge variation of the effective gauge action mainly consists of two terms. One comes from the induced Chern-Simons term and the other from the chiral fermions, bound to the 1+1 dimensional wall, and they are expected to cancel each other. Though there exist arguments in favour of this, based on the possible forms of the effective action valid far from the wall and some facts about theories of chiral fermions in 1+1 dimensions, a complete calculation is lacking. In this paper we present an explicit calculation of this cancellation at one loop valid even close to the wall. We show that, integrating out the ``massive'' modes of the theory does produce the Chern-Simons term, as appreciated previously. In addition we show that it generates a term that softens the high energy behaviour of the 1+1 dimensional effective chiral theory thereby resolving an ambiguity present in a general 1+1 dimensional theory.Comment: 17 pages, LaTex file, CU-TP-61

Pseudospin SU(2) Symmetry Breaking, Charge Density Wave and Superconductivity in the Hubbard Model

In this paper, we discuss physical consequences of pseudospin SU(2) symmetry breaking in the negative-U Hubbard model at half-filling. If pseudospin symmetry is spontaneously broken while its unique subgroup U(1) remains invariant, it will lead to the charge density wave (CDW) ground state. Furthermore, if the U(1) symmetry is also broken, the ground state will have the off-diagonal long range order (ODLRO), signaling a superconductor. In this case, CDW and superconductivity coexist to form a supersolid. Finally, we show that CDW suppresses, but does not destroy superconductivity.Comment: 7 page

Inclusion of non-spherical components of the Pauli blocking operator in (p,p') reactions

We present the first calculations of proton elastic and inelastic scattering in which the Pauli blocking operator contains the leading non-spherical components as well as the usual spherical (angle-averaged) part. We develop a formalism for including the contributions to the effective nucleon-nucleon interaction from the resulting new G-matrix elements that extend the usual two-nucleon spin structure and may not conserve angular momentum. We explore the consequences of parity conservation, time reversal invariance, and nucleon-nucleon antisymmetrization for the new effective interaction. Changes to the calculated cross section and spin observables are small in the energy range from 100 to 200 MeV.Comment: 24 pages, 4 figures, to be published in Physical Review

Damping of Tensor Modes in Cosmology

An analytic formula is given for the traceless transverse part of the anisotropic stress tensor due to free streaming neutrinos, and used to derive an integro-differential equation for the propagation of cosmological gravitational waves. The solution shows that anisotropic stress reduces the squared amplitude by 35.6 % for wavelengths that enter the horizon during the radiation-dominated phase, independent of any cosmological parameters. This decreases the tensor temperature and polarization correlation functions for these wavelengths by the same amount. The effect is less for wavelengths that enter the horizon at later times. At the longest wavelengths the decrease in the tensor correlation functions due to neutrino free streaming ranges from 10.7% for $\Omega_Mh^2=0.1$ to 9.0% for $\Omega_Mh^2=0.15$. An Appendix gives a general proof that tensor as well as scalar modes satisfy a conservation law for perturbations outside the horizon, even when the anisotropic stress tensor is not negligible.Comment: 14 pages. The original version of this paper has been expanded to deal with perturbations of any wavelength. While for wavelengths short enough to enter the horizon during radiation dominance, temperature and polarization correlations are damped by 35.6%, at the longest wavelengths the damping is from 9.0% to 11%. An added Appendix gives a general proof that tensor as well as scalar modes satisfy a conservation law outside the horizon, even during neutrino decoupling. Some references are also adde

Field theoretic description of the abelian and non-abelian Josephson effect

We formulate the Josephson effect in a field theoretic language which affords a straightforward generalization to the non-abelian case. Our formalism interprets Josephson tunneling as the excitation of pseudo-Goldstone bosons. We demonstrate the formalism through the consideration of a single junction separating two regions with a purely non-abelian order parameter and a sandwich of three regions where the central region is in a distinct phase. Applications to various non-abelian symmetry breaking systems in particle and condensed matter physics are given.Comment: 10 pages no figure

Emergence of a confined state in a weakly bent wire

In this paper we use a simple straightforward technique to investigate the emergence of a bound state in a weakly bent wire. We show that the bend behaves like an infinitely shallow potential well, and in the limit of small bending angle and low energy the bend can be presented by a simple 1D delta function potential.Comment: 4 pages, 3 Postscript figures (uses Revtex); added references and rewritte

Properties of Nambu-Goldstone Bosons in a Single-Component Bose-Einstein Condensate

We theoretically study the properties of Nambu-Goldstone bosons in an interacting single-component Bose-Einstein condensate (BEC). We first point out that the proofs of Goldstone's theorem by Goldstone, et al. [Phys. Rev. {\bf 127} (1962) 965] may be relevant to distinct massless modes of the BEC: whereas the first proof deals with the poles of the single-particle Green's function $\hat{G}$, the second one concerns those of the two-particle Green's function. Thus, there may be multiple Nambu-Goldstone bosons even in the single-component BEC with broken U(1) symmetry. The second mode turns out to have an infinite lifetime in the long-wavelength limit in agreement with the conventional viewpoint. In contrast, the first mode from $\hat{G}$, i.e., the Bogoliubov mode in the weak-coupling regime, is shown to be a "bubbling" mode fluctuating temporally out of and back into the condensate. The substantial lifetime originates from an "improper" structure of the self-energy inherent in the BEC, which has been overlooked so far and will be elucidated here, and removes various infrared divergences pointed out previously.Comment: 9 pages, 6 gigure

Polymers in Curved Boxes

We apply results derived in other contexts for the spectrum of the Laplace operator in curved geometries to the study of an ideal polymer chain confined to a spherical annulus in arbitrary space dimension D and conclude that the free energy compared to its value for an uncurved box of the same thickness and volume, is lower when $D < 3$, stays the same when $D = 3$, and is higher when \mbox{$D > 3$}. Thus confining an ideal polymer chain to a cylindrical shell, lowers the effective bending elasticity of the walls, and might induce spontaneous symmetry breaking, i.e. bending. (Actually, the above mentioned results show that {\em {any}} shell in $D = 3$ induces this effect, except for a spherical shell). We compute the contribution of this effect to the bending rigidities in the Helfrich free energy expression.Comment: 20 pages RevTeX, epsf; 4 figures; submitted to Macromoledule

Topological Excitations of One-Dimensional Correlated Electron Systems

Properties of low-energy excitations in one-dimensional superconductors and density-wave systems are examined by the bosonization technique. In addition to the usual spin and charge quantum numbers, a new, independently measurable attribute is introduced to describe elementary, low-energy excitations. It can be defined as a number w which determines, in multiple of $\pi$, how many times the phase of the order parameter winds as an excitation is transposed from far left to far right. The winding number is zero for electrons and holes with conventional quantum numbers, but it acquires a nontrivial value w=1 for neutral spin-1/2 excitations and for spinless excitations with a unit electron charge. It may even be irrational, if the charge is irrational. Thus, these excitations are topological, and they can be viewed as composite particles made of spin or charge degrees of freedom and dressed by kinks in the order parameter.Comment: 5 pages. And we are not only splitting point