2,813 research outputs found
(1+1)-Dimensional Yang-Mills Theory Coupled to Adjoint Fermions on the Light Front
We consider SU(2) Yang-Mills theory in 1+1 dimensions coupled to massless
adjoint fermions. With all fields in the adjoint representation the gauge group
is actually SU(2)/Z_2, which possesses nontrivial topology. In particular,
there are two distinct topological sectors and the physical vacuum state has a
structure analogous to a \theta vacuum. We show how this feature is realized in
light-front quantization, with periodicity conditions used to regulate the
infrared and treating the gauge field zero mode as a dynamical quantity. We
find expressions for the degenerate vacuum states and construct the analog of
the \theta vacuum. We then calculate the bilinear condensate in the model. We
argue that the condensate does not affect the spectrum of the theory, although
it is related to the string tension that characterizes the potential between
fundamental test charges when the dynamical fermions are given a mass. We also
argue that this result is fundamentally different from calculations that use
periodicity conditions in x^1 as an infrared regulator.Comment: 20 pages, Revte
Quantum Spectra of Triangular Billiards on the Sphere
We study the quantal energy spectrum of triangular billiards on a spherical
surface. Group theory yields analytical results for tiling billiards while the
generic case is treated numerically. We find that the statistical properties of
the spectra do not follow the standard random matrix results and their peculiar
behaviour can be related to the corresponding classical phase space structure.Comment: 18 pages, 5 eps figure
Vacuum Structure of Two-Dimensional Gauge Theories on the Light Front
We discuss the problem of vacuum structure in light-front field theory in the
context of (1+1)-dimensional gauge theories. We begin by reviewing the known
light-front solution of the Schwinger model, highlighting the issues that are
relevant for reproducing the -structure of the vacuum. The most
important of these are the need to introduce degrees of freedom initialized on
two different null planes, the proper incorporation of gauge field zero modes
when periodicity conditions are used to regulate the infrared, and the
importance of carefully regulating singular operator products in a
gauge-invariant way. We then consider SU(2) Yang-Mills theory in 1+1 dimensions
coupled to massless adjoint fermions. With all fields in the adjoint
representation the gauge group is actually SU(2), which possesses
nontrivial topology. In particular, there are two topological sectors and the
physical vacuum state has a structure analogous to a vacuum. We
formulate the model using periodicity conditions in for infrared
regulation, and consider a solution in which the gauge field zero mode is
treated as a constrained operator. We obtain the expected vacuum
structure, and verify that the discrete vacuum angle which enters has no effect
on the spectrum of the theory. We then calculate the chiral condensate, which
is sensitive to the vacuum structure. The result is nonzero, but inversely
proportional to the periodicity length, a situation which is familiar from the
Schwinger model. The origin of this behavior is discussed.Comment: 29 pages, uses RevTeX. Improved discussion of the physical subspace
generally and the vacuum states in particular. Basic conclusions are
unchanged, but some specific results are modifie
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
The Light-Cone Vacuum in 1+1 Dimensional Super-Yang-Mills Theory
The Discrete Light-Cone Quantization (DLCQ) of a supersymmetric SU(N) gauge
theory in 1+1 dimensions is discussed, with particular emphasis given to the
inclusion of all dynamical zero modes. Interestingly, the notorious `zero-mode
problem' is now tractable because of special supersymmetric cancellations. In
particular, we show that anomalous zero-mode contributions to the currents are
absent, in contrast to what is observed in the non-supersymmetric case. We find
that the supersymmetric partner of the gauge zero mode is the diagonal
component of the fermion zero mode. An analysis of the vacuum structure is
provided and it is shown that the inclusion of zero modes is crucial for
probing the phase properties of the vacua. In particular, we find that the
ground state energy is zero and N-fold degenerate, and thus consistent with
unbroken supersymmetry. We also show that the inclusion of zero modes for the
light-cone supercharges leaves the supersymmetry algebra unchanged. Finally, we
remark that the dependence of the light-cone Fock vacuum in terms of the gauge
zero is unchanged in the presence of matter fields.Comment: REVTEX, 15 page
Lyapunov exponent of the random Schr\"{o}dinger operator with short-range correlated noise potential
We study the influence of disorder on propagation of waves in one-dimensional
structures. Transmission properties of the process governed by the
Schr\"{o}dinger equation with the white noise potential can be expressed
through the Lyapunov exponent which we determine explicitly as a
function of the noise intensity \sigma and the frequency \omega. We find
uniform two-parameter asymptotic expressions for which allow us to
evaluate for different relations between \sigma and \omega. The value
of the Lyapunov exponent is also obtained in the case of a short-range
correlated noise, which is shown to be less than its white noise counterpart.Comment: 20 pages, 4 figure
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