Affine Lie Algebras in Massive Field Theory and Form-Factors from Vertex Operators

We present a new application of affine Lie algebras to massive quantum field theory in 2 dimensions, by investigating the $q\to 1$ limit of the q-deformed affine $\hat{sl(2)}$ symmetry of the sine-Gordon theory, this limit occurring at the free fermion point. Working in radial quantization leads to a quasi-chiral factorization of the space of fields. The conserved charges which generate the affine Lie algebra split into two independent affine algebras on this factorized space, each with level 1 in the anti-periodic sector, and level $0$ in the periodic sector. The space of fields in the anti-periodic sector can be organized using level-$1$ highest weight representations, if one supplements the \slh algebra with the usual local integrals of motion. Introducing a particle-field duality leads to a new way of computing form-factors in radial quantization. Using the integrals of motion, a momentum space bosonization involving vertex operators is formulated. Form-factors are computed as vacuum expectation values in momentum space. (Based on talks given at the Berkeley Strings 93 conference, May 1993, and the III International Conference on Mathematical Physics, String Theory, and Quantum Gravity, Alushta, Ukraine, June 1993.)Comment: 13 pages, CLNS 93/125

QED for a Fibrillar Medium of Two-Level Atoms

We consider a fibrillar medium with a continuous distribution of two-level atoms coupled to quantized electromagnetic fields. Perturbation theory is developed based on the current algebra satisfied by the atomic operators. The one-loop corrections to the dispersion relation for the polaritons and the dielectric constant are computed. Renormalization group equations are derived which demonstrate a screening of the two-level splitting at higher energies. Our results are compared with known results in the slowly varying envelope and rotating wave approximations. We also discuss the quantum sine-Gordon theory as an approximate theory.Comment: 32 pages, 4 figures, uses harvmac and epsf. In this revised version, infra-red divergences are more properly handle

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Particle-Field Duality and Form Factors from Vertex Operators

Using a duality between the space of particles and the space of fields, we show how one can compute form factors directly in the space of fields. This introduces the notion of vertex operators, and form factors are vacuum expectation values of such vertex operators in the space of fields. The vertex operators can be constructed explicitly in radial quantization. Furthermore, these vertex operators can be exactly bosonized in momentum space. We develop these ideas by studying the free-fermion point of the sine-Gordon theory, and use this scheme to compute some form-factors of some non-free fields in the sine-Gordon theory. This work further clarifies earlier work of one of the authors, and extends it to include the periodic sector.Comment: 17 pages, 2 figures, CLNS 93/??

Chiral Vertex Operators in Off-Conformal Theory: The Sine-Gordon Example

We study chiral vertex operators in the sine-Gordon [SG] theory, viewed as an off-conformal system. We find that these operators, which would have been primary fields in the conformal limit, have interesting and, in some ways, unexpected properties in the SG model. Some of them continue to have scale- invariant dynamics even in the presence of the non-conformal cosine interaction. For instance, it is shown that the Mandelstam operator for the bosonic representation of the Fermi field does {\it not} develop a mass term in the SG theory, contrary to what the real Fermi field in the massive Thirring model is expected to do. It is also shown that in the presence of the non-conformal interactions, some vertex operators have unique Lorentz spins, while others do not.Comment: 32 pages, Univ. of Illinois Preprint # ILL-(TH)-93-1

On the Beta Function for Anisotropic Current Interactions in 2D

By making use of current-algebra Ward identities we study renormalization of general anisotropic current-current interactions in 2D. We obtain a set of algebraic conditions that ensure the renormalizability of the theory to all orders. In a certain minimal prescription we compute the beta function to all orders.Comment: 7 pages, 6 figures. v2: References added and typos corrected; v3: cancellation of finite parts more accurately state

A central extension of \cD Y_{\hbar}(\gtgl_2) and its vertex representations

A central extension of \cD Y_{\hbar}(\gtgl_2) is proposed. The bosonization of level $1$ module and vertex operators are also given.Comment: 10 pages, AmsLatex, to appear in Lett. in Math. Phy

One-point functions in massive integrable QFT with boundaries

We consider the expectation value of a local operator on a strip with non-trivial boundaries in 1+1 dimensional massive integrable QFT. Using finite volume regularisation in the crossed channel and extending the boundary state formalism to the finite volume case we give a series expansion for the one-point function in terms of the exact form factors of the theory. The truncated series is compared with the numerical results of the truncated conformal space approach in the scaling Lee-Yang model. We discuss the relevance of our results to quantum quench problems.Comment: 43 pages, 20 figures, v2: typos correcte

Sign reversal of spin polarization in Co/Ru/Al2O3/Co magnetic tunnel junctions

Utilizing ultrathin Ru interfacial layers in Co/Al2O3/Co tunnel junctions, we demonstrate that not only does the tunnel magnetoresistance decrease strongly as the Ru thickness increases as found for Cu or Cr interlayers, in contrast, even the sign of the apparent tunneling spin polarization may be changed. Further, the magnitude and sign of the apparent polarization is strongly dependent on applied voltage. The results are explained by a strong density-of-states modification at the (interdiffused) Co/Ru interface, consistent with theoretical calculations and experiments on Co/Ru metallic multilayers and Co-Ru alloys

Freezing transitions and the density of states of 2D random Dirac Hamiltonians

Using an exact mapping to disordered Coulomb gases, we introduce a novel method to study two dimensional Dirac fermions with quenched disorder in two dimensions which allows to treat non perturbative freezing phenomena. For purely random gauge disorder it is known that the exact zero energy eigenstate exhibits a freezing-like transition at a threshold value of disorder $\sigma=\sigma_{th}=2$. Here we compute the dynamical exponent $z$ which characterizes the critical behaviour of the density of states around zero energy, and find that it also exhibits a phase transition. Specifically, we find that $\rho(E=0 + i \epsilon) \sim \epsilon^{2/z-1}$ (and $\rho(E) \sim E^{2/z-1}$) with $z=1 + \sigma$ for $\sigma < 2$ and $z=\sqrt{8 \sigma} - 1$ for $\sigma > 2$. For a finite system size $L<\epsilon^{-1/z}$ we find large sample to sample fluctuations with a typical $\rho_{\epsilon}(0) \sim L^{z-2}$. Adding a scalar random potential of small variance $\delta$, as in the corresponding quantum Hall system, yields a finite noncritical $\rho(0) \sim \delta^{\alpha}$ whose scaling exponent $\alpha$ exhibits two transitions, one at $\sigma_{th}/4$ and the other at $\sigma_{th}$. These transitions are shown to be related to the one of a directed polymer on a Cayley tree with random signs (or complex) Boltzmann weights. Some observations are made for the strong disorder regime relevant to describe transport in the quantum Hall system