1,418 research outputs found
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
Quantum States of String-Inspired Lineal Gravity
We construct quantum states for a (1+1) dimensional gravity-matter model that
is also a gauge theory based on the centrally extended Poincar\'e group.
Explicit formulas are found, which exhibit interesting structures. For example
wave functionals are gauge invariant except for a gauge non-invariant phase
factor that is the Kirillov-Kostant 1-form on the (co-) adjoint orbit of the
group. However no evidence for gravity-matter forces is found.Comment: 23 pages in REVTEX, MIT-CTP-227
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
Effective Hamiltonian approach to adiabatic approximation in open systems
The adiabatic approximation in open systems is formulated through the
effective Hamiltonian approach. By introducing an ancilla, we embed the open
system dynamics into a non-Hermitian quantum dynamics of a composite system,
the adiabatic evolution of the open system is then defined as the adiabatic
dynamics of the composite system. Validity and invalidity conditions for this
approximation are established and discussed. A High-order adiabatic
approximation for open systems is introduced. As an example, the adiabatic
condition for an open spin- particle in time-dependent magnetic
fields is analyzed.Comment: 6 pages, 2 figure
Unfrustrated Qudit Chains and their Ground States
We investigate chains of 'd' dimensional quantum spins (qudits) on a line
with generic nearest neighbor interactions without translational invariance. We
find the conditions under which these systems are not frustrated, i.e. when the
ground states are also the common ground states of all the local terms in the
Hamiltonians. The states of a quantum spin chain are naturally represented in
the Matrix Product States (MPS) framework. Using imaginary time evolution in
the MPS ansatz, we numerically investigate the range of parameters in which we
expect the ground states to be highly entangled and find them hard to
approximate using our MPS method.Comment: 5 pages, 5 figures. Typos correcte
Calculating the Rest Tension for a Polymer of String Bits
We explore the application of approximation schemes from many body physics,
including the Hartree-Fock method and random phase approximation (RPA), to the
problem of analyzing the low energy excitations of a polymer chain made up of
bosonic string bits. We accordingly obtain an expression for the rest tension
of the bosonic relativistic string in terms of the parameters
characterizing the microscopic string bit dynamics. We first derive an exact
connection between the string tension and a certain correlation function of the
many-body string bit system. This connection is made for an arbitrary
interaction potential between string bits and relies on an exact dipole sum
rule. We then review an earlier calculation by Goldstone of the low energy
excitations of a polymer chain using RPA. We assess the accuracy of the RPA by
calculating the first order corrections. For this purpose we specialize to the
unique scale invariant potential, namely an attractive delta function potential
in two (transverse) dimensions. We find that the corrections are large, and
discuss a method for summing the large terms. The corrections to this improved
RPA are roughly 15\%.Comment: 44 pages, phyzzx, psfig required, Univ. of Florida preprint,
UFIFT-HEP-94
Quantization of Field Theories Generalizing Gravity-Yang-Mills Systems on the Cylinder
Pure gravity and gauge theories in two dimensions are shown to be special
cases of a much more general class of field theories each of which is
characterized by a Poisson structure on a finite dimensional target space. A
general scheme for the quantization of these theories is formulated. Explicit
examples are studied in some detail. In particular gravity and gauge theories
with equivalent actions are compared. Big gauge transformations as well as the
condition of metric nondegeneracy in gravity turn out to cause significant
differences in the structure of the corresponding reduced phase spaces and the
quantum spectra of Dirac observables. For gravity coupled to SU(2) Yang
Mills the question of quantum dynamics (`problem of time') is addressed. [This
article is a contribution to the proceedings (to appear in LNP) of the 3rd
Baltic RIM Student Seminar (1993). Importance is attached to concrete examples.
A more abstract presentation of the ideas underlying this article (including
new developments) is found in hep-th/9405110.]Comment: 26, pages, TUW-94-
Spontaneous Symmetry Breaking with Abnormal Number of Nambu-Goldstone Bosons and Kaon Condensate
We describe a class of relativistic models incorporating finite density of
matter in which spontaneous breakdown of continuous symmetries leads to a
lesser number of Nambu-Goldstone bosons than that required by the Goldstone
theorem. This class, in particular, describes the dynamics of the kaon
condensate in the color-flavor locked phase of high density QCD. We describe
the spectrum of low energy excitations in this dynamics and show that, despite
the presence of a condensate and gapless excitations, this system is not a
superfluid.Comment: 5 pages, 1 figure, REVTeX. Minor revisions made and 2 new references
added. To appear in Phys. Rev. Let
On The Existence of Roton Excitations in Bose Einstein Condensates: Signature of Proximity to a Mott Insulating Phase
Within the last decade, artificially engineered Bose Einstein Condensation
has been achieved in atomic systems. Bose Einstein Condensates are superfluids
just like bosonic Helium is and all interacting bosonic fluids are expected to
be at low enough temperatures. One difference between the two systems is that
superfluid Helium exhibits roton excitations while Bose Einstein Condensates
have never been observed to have such excitations. The reason for the roton
minimum in Helium is its proximity to a solid phase. The roton minimum is a
consequence of enhanced density fluctuations at the reciprocal lattice vector
of the stillborn solid. Bose Einstein Condensates in atomic traps are not near
a solid phase and therefore do not exhibit roton minimum. We conclude that if
Bose Einstein Condensates in an optical lattice are tuned near a transition to
a Mott insulating phase, a roton minimum will develop at a reciprocal lattice
vector of the lattice. Equivalently, a peak in the structure factor will appear
at such a wavevector. The smallness of the roton gap or the largeness of the
structure factor peak are experimental signatures of the proximity to the Mott
transition.Comment: 4 pages, 5 figure
Finite-Size Studies on the SO(5) Symmetry of the Hubbard Model
We present numerical evidence for the approximate SO(5) symmetry of the
Hubbard model on a 10 site cluster. Various dynamic correlation functions
involving the operators, the generators of the SO(5) algebra, are studied
using exact diagonalisation, and are found to possess sharp collective peaks.
Our numerical results also lend support on the interpretation of the recent
resonant neutron scattering peaks in the YBCO superconductors in terms of the
Goldstone modes of the spontaneously broken SO(5) symmetry.Comment: 4 pages, Rev-Tex, includes 2 eps figure
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