A Study of Anyon Statistics by Breit Hamiltonian Formalism

We study the anyon statistics of a $2 + 1$ dimensional Maxwell-Chern-Simons (MCS) gauge theory by using a systemmetic metheod, the Breit Hamiltonian formalism.Comment: 25 pages, LATE

Bethe ansatz at q=0 and periodic box-ball systems

A class of periodic soliton cellular automata is introduced associated with crystals of non-exceptional quantum affine algebras. Based on the Bethe ansatz at q=0, we propose explicit formulas for the dynamical period and the size of certain orbits under the time evolution in A^{(1)}_n case.Comment: 12 pages, Introduction expanded, Summary added and minor modifications mad

Creation of ballot sequences in a periodic cellular automaton

Motivated by an attempt to develop a method for solving initial value problems in a class of one dimensional periodic cellular automata (CA) associated with crystal bases and soliton equations, we consider a generalization of a simple proposition in elementary mathematics. The original proposition says that any sequence of letters 1 and 2, having no less 1's than 2's, can be changed into a ballot sequence via cyclic shifts only. We generalize it to treat sequences of cells of common capacity s > 1, each of them containing consecutive 2's (left) and 1's (right), and show that these sequences can be changed into a ballot sequence via two manipulations, cyclic and "quasi-cyclic" shifts. The latter is a new CA rule and we find that various kink-like structures are traveling along the system like particles under the time evolution of this rule.Comment: 31 pages. Section 1 changed and section 5 adde

Crystal Interpretation of Kerov-Kirillov-Reshetikhin Bijection II. Proof for sl_n Case

In proving the Fermionic formulae, combinatorial bijection called the Kerov--Kirillov--Reshetikhin (KKR) bijection plays the central role. It is a bijection between the set of highest paths and the set of rigged configurations. In this paper, we give a proof of crystal theoretic reformulation of the KKR bijection. It is the main claim of Part I (math.QA/0601630) written by A. Kuniba, M. Okado, T. Takagi, Y. Yamada, and the author. The proof is given by introducing a structure of affine combinatorial $R$ matrices on rigged configurations.Comment: 45 pages, version for publication. Introduction revised, more explanations added to the main tex

Form factor approach to dynamical correlation functions in critical models

We develop a form factor approach to the study of dynamical correlation functions of quantum integrable models in the critical regime. As an example, we consider the quantum non-linear Schr\"odinger model. We derive long-distance/long-time asymptotic behavior of various two-point functions of this model. We also compute edge exponents and amplitudes characterizing the power-law behavior of dynamical response functions on the particle/hole excitation thresholds. These last results confirm predictions based on the non-linear Luttinger liquid method. Our results rely on a first principles derivation, based on the microscopic analysis of the model, without invoking, at any stage, some correspondence with a continuous field theory. Furthermore, our approach only makes use of certain general properties of the model, so that it should be applicable, with possibly minor modifications, to a wide class of (not necessarily integrable) gapless one dimensional Hamiltonians.Comment: 33 page

Infinite-dimensional pp-adic groups, semigroups of double cosets, and inner functions on Bruhat--Tits builldings

We construct $p$-adic analogs of operator colligations and their characteristic functions. Consider a $p$-adic group $G=GL(\alpha+k\infty, Q_p)$, its subgroup $L=O(k\infty,Z_p)$, and the subgroup $K=O(\infty,Z_p)$ embedded to $L$ diagonally. We show that double cosets $\Gamma= K\setminus G/K$ admit a structure of a semigroup, $\Gamma$ acts naturally in $K$-fixed vectors of unitary representations of $G$. For each double coset we assign a 'characteristic function', which sends a certain Bruhat--Tits building to another building (buildings are finite-dimensional); image of the distinguished boundary is contained in the distinguished boundary. The latter building admits a structure of (Nazarov) semigroup, the product in $\Gamma$ corresponds to a point-wise product of characteristic functions.Comment: new version of the paper, 47pp, 3 figure

Two-dimensional Yang-Mills theory, Painleve equations and the six-vertex model

We show that the chiral partition function of two-dimensional Yang-Mills theory on the sphere can be mapped to the partition function of the homogeneous six-vertex model with domain wall boundary conditions in the ferroelectric phase. A discrete matrix model description in both cases is given by the Meixner ensemble, leading to a representation in terms of a stochastic growth model. We show that the partition function is a particular case of the z-measure on the set of Young diagrams, yielding a unitary matrix model for chiral Yang-Mills theory on the sphere and the identification of the partition function as a tau-function of the Painleve V equation. We describe the role played by generalized non-chiral Yang-Mills theory on the sphere in relating the Meixner matrix model to the Toda chain hierarchy encompassing the integrability of the six-vertex model. We also argue that the thermodynamic behaviour of the six-vertex model in the disordered and antiferroelectric phases are captured by particular q-deformations of two-dimensional Yang-Mills theory on the sphere.Comment: 27 pages, 1 figure; v2: Presentation of Section 2 improved; Final version to be published in Journal of Physics

Form factor approach to the asymptotic behavior of correlation functions in critical models

We propose a form factor approach for the computation of the large distance asymptotic behavior of correlation functions in quantum critical (integrable) models. In the large distance regime we reduce the summation over all excited states to one over the particle/hole excitations lying on the Fermi surface in the thermodynamic limit. We compute these sums, over the so-called critical form factors, exactly. Thus we obtain the leading large distance behavior of each oscillating harmonic of the correlation function asymptotic expansion, including the corresponding amplitudes. Our method is applicable to a wide variety of integrable models and yields precisely the results stemming from the Luttinger liquid approach, the conformal field theory predictions and our previous analysis of the correlation functions from their multiple integral representations. We argue that our scheme applies to a general class of non-integrable quantum critical models as well.Comment: 31 page