181 research outputs found
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
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
Realisation of chiral symmetry in the domain model of QCD
The domain model for the QCD vacuum has previously been developed and shown
to exhibit confinement of quarks and strong correlation of the local chirality
of quark modes and duality of the background domain-like gluon field. Quark
fluctuations satisfy a chirality violating boundary conditions parametrized by
a random chiral angle on the domain. The free energy of an
ensemble of domains depends on through
the logarithm of the quark determinant. Its parity odd part is given by the
axial anomaly. The anomaly contribution to the free energy suppresses
continuous axial U(1) degeneracy in the ground state, leaving only a residual
axial Z(2) symmetry. This discrete symmetry and flavour chiral symmetry in turn are spontaneously broken with a quark
condensate arising due to the asymmetry of the spectrum of Dirac operator. In
order to illustrate the splitting between the from octet pseudoscalar
mesons realised in the domain model, we estimate the masses of light
pseudoscalar and vector mesons.Comment: 27 pages, uses RevTeX, 3 figures. v.2. includes additional references
and comment
Effect of Zero Modes on the Bound-State Spectrum in Light-Cone Quantisation
We study the role of bosonic zero modes in light-cone quantisation on the
invariant mass spectrum for the simplified setting of two-dimensional SU(2)
Yang-Mills theory coupled to massive scalar adjoint matter. Specifically, we
use discretised light-cone quantisation where the momentum modes become
discrete. Two types of zero momentum mode appear -- constrained and dynamical
zero modes. In fact only the latter type of modes turn out to mix with the Fock
vacuum. Omission of the constrained modes leads to the dynamical zero modes
being controlled by an infinite square-well potential. We find that taking into
account the wavefunctions for these modes in the computation of the full bound
state spectrum of the two dimensional theory leads to 21% shifts in the masses
of the lowest lying states.Comment: LaTeX with 5 postscript file
Model for SU(3) vacuum degeneracy using light-cone coordinates
Working in light-cone coordinates, we study the zero-modes and the vacuum in
a 2+1 dimensional SU(3) gauge model. Considering the fields as independent of
the tranverse variables, we dimensionally reduce this model to 1+1 dimensions.
After introducing an appropriate su(3) basis and gauge conditions, we extract
an adjoint field from the model. Quantization of this adjoint field and field
equations lead to two constrained and two dynamical zero-modes. We link the
dynamical zero-modes to the vacuum by writing down a Schrodinger equation and
prove the non-degeneracy of the SU(3) vacuum provided that we neglect the
contribution of constrained zero-modes.Comment: 22 pages, 5 figure
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
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