3,576 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
Delay-bandwidth and delay-loss limitations for cloaking of large objects
Based on a simple model of ground-plane cloaking, we argue that the diffculty
of cloaking is fundamentally limited by delay-loss and delaylbandwidth/size
limitations that worsen as the size of the object to be cloaked increases
relative to the wavelength. These considerations must be taken into account
when scaling experimental cloaking demonstrations from wavelength-scale objects
towards larger sizes, and suggest quantitative material/loss challenges in
cloaking human-scale objects.Comment: 4 pages, 2 figure
Non-Perturbative Spectrum of Two Dimensional (1,1) Super Yang-Mills at Finite and Large N
We consider the dimensional reduction of N = 1 SYM_{2+1} to 1+1 dimensions,
which has (1,1) supersymmetry. The gauge groups we consider are U(N) and SU(N),
where N is a finite variable. We implement Discrete Light-Cone Quantization to
determine non-perturbatively the bound states in this theory. A careful
analysis of the spectrum is performed at various values of N, including the
case where N is large (but finite), allowing a precise measurement of the 1/N
effects in the quantum theory. The low energy sector of the theory is shown to
be dominated by string-like states. The techniques developed here may be
applied to any two dimensional field theory with or without supersymmetry.Comment: LaTex 18 pages; 5 Encapsulated PostScript figure
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
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
Modal expansions and non-perturbative quantum field theory in Minkowski space
We introduce a spectral approach to non-perturbative field theory within the
periodic field formalism. As an example we calculate the real and imaginary
parts of the propagator in 1+1 dimensional phi^4 theory, identifying both
one-particle and multi-particle contributions. We discuss the computational
limits of existing diagonalization algorithms and suggest new quasi-sparse
eigenvector methods to handle very large Fock spaces and higher dimensional
field theories.Comment: new material added, 12 pages, 6 figure
Spontaneous symmetry breaking of (1+1)-dimensional theory in light-front field theory (III)
We investigate (1+1)-dimensional field theory in the symmetric and
broken phases using discrete light-front quantization. We calculate the
perturbative solution of the zero-mode constraint equation for both the
symmetric and broken phases and show that standard renormalization of the
theory yields finite results. We study the perturbative zero-mode contribution
to two diagrams and show that the light-front formulation gives the same result
as the equal-time formulation. In the broken phase of the theory, we obtain the
nonperturbative solutions of the constraint equation and confirm our previous
speculation that the critical coupling is logarithmically divergent. We discuss
the renormalization of this divergence but are not able to find a satisfactory
nonperturbative technique. Finally we investigate properties that are
insensitive to this divergence, calculate the critical exponent of the theory,
and find agreement with mean field theory as expected.Comment: 21 pages; OHSTPY-HEP-TH-94-014 and DOE/ER/01545-6
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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