Laboratory tests of Lorentz and CPTCPT symmetry with muons

The prospects are explored for testing Lorentz and $CPT$ symmetry in the muon sector via the spectroscopy of muonium and various muonic atoms, and via measurements of the anomalous magnetic moments of the muon and antimuon. The effects of Lorentz-violating operators of both renormalizable and nonrenormalizable dimensions are included. We derive observable signals, extract first constraints from existing data on a variety of coefficients for Lorentz and $CPT$ violation, and estimate sensitivities attainable in forthcoming experiments. The potential of Lorentz violation to resolve the proton radius puzzle and the muon anomaly discrepancy is discussed

Dyonic Integrable Models

A class of non abelian affine Toda models arising from the axial gauged two-loop WZW model is presented. Their zero curvature representation is constructed in terms of a graded Kac-Moody algebra. It is shown that the discrete multivacua structure of the potential together with non abelian nature of the zero grade subalgebra allows soliton solutions with non trivial electric and topological charges. The dressing transformation is employed to explicitly construct one and two soliton solutions and their bound states in terms of the tau functions. A discussion of the classical spectra of such solutions and the time delays are given in detail.Comment: Latex 30 pages, corrected some typo

T-duality of axial and vector dyonic integrable models

A general construction of affine Non Abelian (NA) - Toda models in terms of axial and vector gauged two loop WZNW model is discussed. They represent {\it integrable perturbations} of the conformal $\sigma$-models (with tachyons included) describing (charged) black hole type string backgrounds. We study the {\it off-critical} T-duality between certain families of axial and vector type of integrable models for the case of affine NA- Toda theories with one global U(1) symmetry. In particular we find the Lie algebraic condition defining a subclass of {\it T-selfdual} torsionless NA Toda models and their zero curvature representation.Comment: 20 pages, latex, no figures,improvments in the text of Sects.1,2 and 6;typos corrected,references added, to appear in Ann. of Physics (NY

Toda and Volterra Lattice Equations from Discrete Symmetries of KP Hierarchies

The discrete models of the Toda and Volterra chains are being constructed out of the continuum two-boson KP hierarchies. The main tool is the discrete symmetry preserving the Hamiltonian structure of the continuum models. The two-boson currents of KP hierarchy are being associated with sites of the corresponding chain by successive actions of discrete symmetry.Comment: 12 pgs, LaTeX, IFT-P.041/9

A symmetry reduction technique for higher order Painlev\'e systems

The symmetry reduction of higher order Painlev\'e systems is formulated in terms of Dirac procedure. A set of canonical variables that admit Dirac reduction procedure is proposed for Hamiltonian structures governing the ${A^{(1)}_{2M}}$ and ${A^{(1)}_{2M-1}}$ Painlev\'e systems for $M=2,3,...$.Comment: to appear in Phys. Lett.

Some comments on the bi(tri)-Hamiltonian structure of Generalized AKNS and DNLS hierarchies

We give the correct prescriptions for the terms involving the inverse of the derivative of the delta function, in the Hamiltonian structures of the AKNS and DNLS systems, in order for the Jacobi identities to hold. We also establish that the sl(2) AKNS and DNLS systems are tri-Hamiltonians and construct two compatible Hamiltonian structures for the sl(3) AKNS system. We also give a derivation of the recursion operator for the sl(n+1) DNLS system.Comment: 10 pages, LaTe

On Non-Linear W-Infinity Symmetry of Generalized Liouville and Conformal Toda Models

Invariance under non-linear ${\sf {\hat W}}_{\infty}$ algebra is shown for the two-boson Liouville type of model and its algebraic generalizations, the extended conformal Toda models. The realization of the corresponding generators in terms of two boson currents within KP hierarchy is presented.Comment: 10 pgs, LaTeX, IFT-P.038/9

Super WZNW with Reductions to Supersymmetric and Fermionic Integrable Models

A systematic construction for an action describing a class of supersymmetric integrable models as well as for pure fermionic theories is discussed in terms of the gauged WZNW model associated to twisted affine Kac-Moody algebras. Explicit examples of the $N=1,2$ super sinh(sine)-Gordon models are discussed in detail. Pure fermionic theories arises for cosets $sl(p,1)/sl(p)\otimes u(1)$ when a maximal kernel condition is fulfilled. The integrability condition for such models is discussed and it is shown that the simplest example when $p=2$ leads to the constrained Bukhvostov-Lipatov, Thirring, scalar massive and pseudo-scalar massless Gross-Neveu models.Comment: 28 pages, latex, added referenc

Hirota's Solitons in the Affine and the Conformal Affine Toda Models

We use Hirota's method formulated as a recursive scheme to construct complete set of soliton solutions for the affine Toda field theory based on an arbitrary Lie algebra. Our solutions include a new class of solitons connected with two different type of degeneracies encountered in the Hirota's perturbation approach. We also derive an universal mass formula for all Hirota's solutions to the Affine Toda model valid for all underlying Lie groups. Embedding of the Affine Toda model in the Conformal Affine Toda model plays a crucial role in this analysis.Comment: 36 pages, LaTe

Multicharged Dyonic Integrable Models

We introduce and study new integrable models of A_n^{(1)}-Non-Abelian Toda type which admit U(1)\otimes U(1) charged topological solitons. They correspond to the symmetry breaking SU(n+1) \to SU(2)\otimes SU(2)\otimes U(1)^{n-2} and are conjectured to describe charged dyonic domain walls of N=1 SU(n+1) SUSY gauge theory in large n limit. It is shown that this family of relativistic IMs corresponds to the first negative grade q={-1} member of a dyonic hierarchy of generalized cKP type. The explicit relation between the 1-soliton solutions (and the conserved charges as well) of the IMs of grades q=-1 and q=2 is found. The properties of the IMs corresponding to more general symmetry breaking SU(n+1) \to SU(2)^{\otimes p}\otimes U(1)^{n-p} as well as IM with global SU(2) symmetries are discussed.Comment: 48pages, latex, v2. typos in eqns. (1.7) and (3.20) corrected, small improvements in subsection 2.2, new reference added;v3. improvements in text of Sect. 1,2 and 6; new Sect 7 and new refs. added; version to appear in Nucl. Phys.