(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 $\theta$-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)$/Z_2$, which possesses nontrivial topology. In particular, there are two topological sectors and the physical vacuum state has a structure analogous to a $\theta$ vacuum. We formulate the model using periodicity conditions in $x^\pm$ for infrared regulation, and consider a solution in which the gauge field zero mode is treated as a constrained operator. We obtain the expected $Z_2$ 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 QCD1+1QCD_{1+1} on the Light-Cone

Motivated by the work of Kalloniatis, Pauli and Pinsky, we consider the theory of light-cone quantized $QCD_{1+1}$ 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 $A_- = 0$ 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 ϕ4\bf \phi^4 theory in light-front field theory (III)

We investigate (1+1)-dimensional $\phi^4$ 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 $\gamma$ which we determine explicitly as a function of the noise intensity \sigma and the frequency \omega. We find uniform two-parameter asymptotic expressions for $\gamma$ which allow us to evaluate $\gamma$ 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