2,595 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
Renormalization of Tamm-Dancoff Integral Equations
During the last few years, interest has arisen in using light-front
Tamm-Dancoff field theory to describe relativistic bound states for theories
such as QCD. Unfortunately, difficult renormalization problems stand in the
way. We introduce a general, non-perturbative approach to renormalization that
is well suited for the ultraviolet and, presumably, the infrared divergences
found in these systems. We reexpress the renormalization problem in terms of a
set of coupled inhomogeneous integral equations, the ``counterterm equation.''
The solution of this equation provides a kernel for the Tamm-Dancoff integral
equations which generates states that are independent of any cutoffs. We also
introduce a Rayleigh-Ritz approach to numerical solution of the counterterm
equation. Using our approach to renormalization, we examine several ultraviolet
divergent models. Finally, we use the Rayleigh-Ritz approach to find the
counterterms in terms of allowed operators of a theory.Comment: 19 pages, OHSTPY-HEP-T-92-01
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
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
Inversion formula and Parsval theorem for complex continuous wavelet transforms studied by entangled state representation
In a preceding Letter (Opt. Lett. 32, 554 (2007)) we have proposed complex
continuous wavelet transforms (CCWTs) and found Laguerre--Gaussian mother
wavelets family. In this work we present the inversion formula and Parsval
theorem for CCWT by virtue of the entangled state representation, which makes
the CCWT theory complete. A new orthogonal property of mother wavelet in
parameter space is revealed.Comment: 4 pages no figur
On inversions and Doob -transforms of linear diffusions
Let be a regular linear diffusion whose state space is an open interval
. We consider a diffusion which probability law is
obtained as a Doob -transform of the law of , where is a positive
harmonic function for the infinitesimal generator of on . This is the
dual of with respect to where is the speed measure of
. Examples include the case where is conditioned to stay above
some fixed level. We provide a construction of as a deterministic
inversion of , time changed with some random clock. The study involves the
construction of some inversions which generalize the Euclidean inversions.
Brownian motion with drift and Bessel processes are considered in details.Comment: 19 page
Electromagnetic Fields Produced by Moving Sources in a Curved Beam Pipe
A new geometrical perturbation scheme is developed in order to calculate the
electromagnetic fields produced by charged sources in prescribed motion moving
in a non-straight perfectly conducting beam pipe. The pipe is regarded as a
perturbed infinitely long hollow right-circular cylinder. The perturbation
maintains the pipe's circular cross-section while deforming its axis into a
planar space-curve with, in general, non-constant curvature. Various charged
source models are considered including a charged bunch and an off-axis point
particle. In the ultra-relativistic limit this permits a calculation of the
longitudinal wake potential in terms of powers of the product of the pipe
radius and the arbitrarily varying curvature of the axial space-curve. Analytic
expressions to leading order are presented for beam pipes with piecewise
defined constant curvature modelling pipes with straight segments linked by
circular arcs of finite length. The language of differential forms is used
throughout and to illustrate the power of this formalism a pedagogical
introduction is developed by deriving the theory ab-initio from Maxwell's
equations expressed intrinsically as a differential system on (Minkowski)
spacetime.Comment: 43pages, 7figure
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
Variational Calculation of the Effective Action
An indication of spontaneous symmetry breaking is found in the
two-dimensional model, where attention is paid to the
functional form of an effective action. An effective energy, which is an
effective action for a static field, is obtained as a functional of the
classical field from the ground state of the hamiltonian interacting
with a constant external field. The energy and wavefunction of the ground state
are calculated in terms of DLCQ (Discretized Light-Cone Quantization) under
antiperiodic boundary conditions. A field configuration that is physically
meaningful is found as a solution of the quantum mechanical Euler-Lagrange
equation in the limit. It is shown that there exists a nonzero field
configuration in the broken phase of symmetry because of a boundary
effect.Comment: 26 pages, REVTeX, 7 postscript figures, typos corrected and two
references adde
Vacuum Structures of Supersymmetric Yang-Mills Theories in Dimensions
Vacuum structures of supersymmetric (SUSY) Yang-Mills theories in
dimensions are studied with the spatial direction compactified. SUSY allows
only periodic boundary conditions for both fermions and bosons. By using the
Born-Oppenheimer approximation for the weak coupling limit, we find that the
vacuum energy vanishes, and hence the SUSY is unbroken. Other boundary
conditions are also studied, especially the antiperiodic boundary condition for
fermions which is related to the system in finite temperatures. In that case we
find for gaugino bilinears a nonvanishing vacuum condensation which indicates
instanton contributions.Comment: LaTeX file, 25 page, 3 eps figure, some references adde
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