109 research outputs found
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
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
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
Neutral pion decay in dense skyrmion matter
We study the density dependence of the decay using
the Skyrme Lagrangian to describe simultaneously both the matter background and
mesonic fluctuations. Pion properties such as mass and decay constant are
modified by the medium. This leads to large suppression at high density of both
photo-production from the neutral pion and the reverse process. The in-medium
effective charge of are also discussed in the same framework.Comment: 8 pages, 4 figures. Corrections in light of referee comment
Quantum Electrodynamics in the Light-Front Weyl Gauge
We examine QED(3+1) quantised in the `front form' with finite `volume'
regularisation, namely in Discretised Light-Cone Quantisation. Instead of the
light-cone or Coulomb gauges, we impose the light-front Weyl gauge . The
Dirac method is used to arrive at the quantum commutation relations for the
independent variables. We apply `quantum mechanical gauge fixing' to implement
Gau{\ss}' law, and derive the physical Hamiltonian in terms of unconstrained
variables. As in the instant form, this Hamiltonian is invariant under global
residual gauge transformations, namely displacements. On the light-cone the
symmetry manifests itself quite differently.Comment: LaTeX file, 30 pages (A4 size), no figures. Submitted to Physical
review D. January 18, 1996. Originally posted, erroneously, with missing
`Weyl' in title. Otherwise, paper is identica
Weyl group, CP and the kink-like field configurations in the effective SU(3) gauge theory
Effective Lagrangian for pure Yang-Mills gauge fields invariant under the
standard space-time and local gauge SU(3) transformations is considered. It is
demonstrated that a set of twelve degenerated minima exists as soon as a
nonzero gluon condensate is postulated. The minima are connected to each other
by the parity transformations and Weyl group transformations associated with
the color su(3) algebra. The presence of degenerated discrete minima in the
effective potential leads to the solutions of the effective Euclidean equations
of motion in the form of the kink-like gauge field configurations interpolating
between different minima. Spectrum of charged scalar field in the kink
background is discussed.Comment: 10 pages, 1 figure, added references for sections 1 and
Dimensional renormalization: ladders to rainbows
Renormalization factors are most easily extracted by going to the massless
limit of the quantum field theory and retaining only a single momentum scale.
We derive factors and renormalized Green functions to all orders in
perturbation theory for rainbow graphs and vertex (or scattering diagrams) at
zero momentum transfer, in the context of dimensional renormalization, and we
prove that the correct anomalous dimensions for those processes emerge in the
limit D -> 4.Comment: RevTeX, no figure
Quantum Mechanics of Dynamical Zero Mode in on the Light-Cone
Motivated by the work of Kalloniatis, Pauli and Pinsky, we consider the
theory of light-cone quantized on a spatial circle with periodic
and anti-periodic boundary conditions on the gluon and quark fields
respectively. This approach is based on Discretized Light-Cone Quantization
(DLCQ). We investigate the canonical structures of the theory. We show that the
traditional light-cone gauge is not available and the zero mode (ZM)
is a dynamical field, which might contribute to the vacuum structure
nontrivially. We construct the full ground state of the system and obtain the
Schr\"{o}dinger equation for ZM in a certain approximation. The results
obtained here are compared to those of Kalloniatis et al. in a specific
coupling region.Comment: 19 pages, LaTeX file, no figure
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
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