30 research outputs found
Phases of a bilayer Fermi gas
We investigate a two-species Fermi gas in which one species is confined in
two parallel layers and interacts with the other species in the
three-dimensional space by a tunable short-range interaction. Based on the
controlled weak coupling analysis and the exact three-body calculation, we show
that the system has a rich phase diagram in the plane of the effective
scattering length and the layer separation. Resulting phases include an
interlayer s-wave pairing, an intralayer p-wave pairing, a dimer Bose-Einstein
condensation, and a Fermi gas of stable Efimov-like trimers. Our system
provides a widely applicable scheme to induce long-range interlayer
correlations in ultracold atoms.Comment: 5 pages, 5 figures; (v2) stability of trimer is emphasized; (v3)
published versio
Light-Front QCD(1+1) Coupled to Adjoint Scalar Matter
We consider adjoint scalar matter coupled to QCD(1+1) in light-cone
quantization on a finite `interval' with periodic boundary conditions. We work
with the gauge group SU(2) which is modified to by the
non-trivial topology. The model is interesting for various nonperturbative
approaches because it is the sector of zero transverse momentum gluons of pure
glue QCD(2+1), where the scalar field is the remnant of the transverse gluon
component. We use the Hamiltonian formalism in the gauge .
What survives is the dynamical zero mode of , which in other theories
gives topological structure and degenerate vacua. With a point-splitting
regularization designed to preserve symmetry under large gauge transformations,
an extra dependent term appears in the current . This is reminiscent
of an (unwanted) anomaly. In particular, the gauge invariant charge and the
similarly regulated no longer commute with the Hamiltonian. We show that
nonetheless one can construct physical states of definite momentum which are
not {\it invariant} under large gauge transformations but do {\it transform} in
a well-defined way. As well, in the physical subspace we recover vanishing {\it
expectation values} of the commutators between the gauge invariant charge,
momentum and Hamiltonian operators. It is argued that in this theory the vacuum
is nonetheless trivial and the spectrum is consistent with the results of
others who have treated the large N, SU(N), version of this theory in the
continuum limit.Comment: LaTex, 13 pages. Submitted to Physics Letters
Chord diagrams and BPHZ subtractions
The combinatorics of the BPHZ subtraction scheme for a class of ladder graphs
for the three point vertex in theory is transcribed into certain
connectivity relations for marked chord diagrams (knots with transversal
intersections). The resolution of the singular crossings using the equivalence
relations in these examples provides confirmation of a proposed fundamental
relationship between knot theory and renormalization in perturbative quantum
field theory.Comment: 12 pages, 5 Postscript figures, LaTex 2
CP-violating theta parameter in the domain model of the QCD vacuum
A non-zero CP-violating parameter is treated in the domain model
which assumes a cluster-like vacuum structure whose units are characterised in
particular by a topological charge which is not necessarily an integer number.
In the present paper we restrict consideration to rational values of the
charge. The model has previously been shown to manifest confinement,
spontaneous chiral symmetry breaking and the absence of an axial U(1) Goldstone
boson. We find that the specific structure of the minima of the free energy
density of the domain ensemble forces a -periodicity of observables in
for any number of light quarks, that vacuum doubling occurs at
for any and any value of topological charge . These
features are in agreement with expectations based on anomalous Ward identities
and large effective theories. We find also additional values of
depending on for which vacuum doubling occurs.Comment: 10 pages, 6 figures. Final version with modification of Eq.(2),
additional references, minor typographical correction
Poincar\'e recurrence theorem and the strong CP-problem
The existence in the physical QCD vacuum of nonzero gluon condensates, such
as , requires dominance of gluon fields with finite mean action
density. This naturally allows any real number value for the unit ``topological
charge'' characterising the fields approximating the gluon configurations
which should dominate the QCD partition function. If is an irrational
number then the critical values of the parameter for which CP is
spontaneously broken are dense in , which provides for a mechanism
of resolving the strong CP problem simultaneously with a correct implementation
of symmetry. We present an explicit realisation of this
mechanism within a QCD motivated domain model. Some model independent arguments
are given that suggest the relevance of this mechanism also to genuine QCD.Comment: 8 pages, RevTeX, 3 figures. Revised after referee suggestions. Now
includes model independent argument
On Zero Modes and the Vacuum Problem -- A Study of Scalar Adjoint Matter in Two-Dimensional Yang-Mills Theory via Light-Cone Quantisation
SU(2) Yang-Mills Theory coupled to massive adjoint scalar matter is studied
in (1+1) dimensions using Discretised Light-Cone Quantisation. This theory can
be obtained from pure Yang-Mills in 2+1 dimensions via dimensional reduction.
On the light-cone, the vacuum structure of this theory is encoded in the
dynamical zero mode of a gluon and a constrained mode of the scalar field. The
latter satisfies a linear constraint, suggesting no nontrivial vacua in the
present paradigm for symmetry breaking on the light-cone. I develop a
diagrammatic method to solve the constraint equation. In the adiabatic
approximation I compute the quantum mechanical potential governing the
dynamical gauge mode. Due to a condensation of the lowest omentum modes of the
dynamical gluons, a centrifugal barrier is generated in the adiabatic
potential. In the present theory however, the barrier height appears too small
to make any impact in this odel. Although the theory is superrenormalisable on
naive powercounting grounds, the removal of ultraviolet divergences is
nontrivial when the constrained mode is taken into account. The open aspects of
this problem are discussed in detail.Comment: LaTeX file, 26 pages. 14 postscript figure
QED(1+1) at Finite Temperature -- a Study with Light-Cone Quantisation
We explore quantum electrodynamics in (1+1) dimensions at finite temperature
using the method of Discretized Light-Cone Quantisation. The partition
function, energy and specific heat are computed in the canonical ensemble using
the spectrum of invariant masses computed with a standard DLCQ numerical
routine. In particular, the specific heat exhibits a peak which grows as the
continuum limit is numerically approached. A critical exponent is tentatively
extracted. The surprising result is that the density of states contains
significant finite size artifacts even for a relatively high harmonic
resolution. These and the other outstanding problems in the present calculation
are discussed.Comment: 10 pages, 11 Postscript figures, uses epsf.st
Towards Solving QCD - The Transverse Zero Modes in Light-Cone Quantization
We formulate QCD in (d+1) dimensions using Dirac's front form with periodic
boundary conditions, that is, within Discretized Light-Cone Quantization. The
formalism is worked out in detail for SU(2) pure glue theory in (2+1)
dimensions which is approximated by restriction to the lowest {\it transverse}
momentum gluons. The dimensionally-reduced theory turns out to be SU(2) gauge
theory coupled to adjoint scalar matter in (1+1) dimensions. The scalar field
is the remnant of the transverse gluon. This field has modes of both non-zero
and zero {\it longitudinal} momentum. We categorize the types of zero modes
that occur into three classes, dynamical, topological, and constrained, each
well known in separate contexts. The equation for the constrained mode is
explicitly worked out. The Gauss law is rather simply resolved to extract
physical, namely color singlet states. The topological gauge mode is treated
according to two alternative scenarios related to the In the one, a spectrum is
found consistent with pure SU(2) gluons in (1+1) dimensions. In the other, the
gauge mode excitations are estimated and their role in the spectrum with
genuine Fock excitations is explored. A color singlet state is given which
satisfies Gauss' law. Its invariant mass is estimated and discussed in the
physical limit.Comment: LaTex document, 26 pages, one figure (obtainable by contacting
authors). To appear in Physical. Review