International Journal of Modern Physics A

We review aspects of broken symmetry and the nature of long range order in theories of anyons starting with bosons with a statistical interaction. We introduce a novel gauge invariant quantization scheme that allows the identification of local and gauge invariant order parameters. The connection between spin and statistics is reviewed and the consequences of broken symmetries in the anyon representation are discussed. An anyon gas is studied in the Bogoliubov approximation, it is determined that the ground state is a condensate of charge-flux composites with “quasi-long-range order” at zero temperature, a “weak” gap in the spectrum and finite helicity modulus. The system is disordered at nonzero temperatures. The disorder is not caused by Goldstone bosons but by the strong infrared behavior arising from the Coulomb interaction induced by the long-range statistical interaction. The properties of topological vortices in nonrelativistic and in relativistic Landau-Ginzburg theories are studied in detail. We study the physics of the mean-field ansatz and quasi-long range order in a simple exactly soluble relativistic model. This model exhibits a novel phenomenon of charge redistribution to the boundaries and restoration of translational invariance in the infinite volume limit. It also illuminates the physics of quasi-long-range order with a gap in the spectrum, statistical charge polarization by external magnetic fields and the role of “large” gauge transformations.

A generalization of relativistic particle and string dynamics based on a notion of twistor shift and containing a fundamental length constant is considered, which results in a modification of particle (or string) interactions with background fields.

The extrinsic geometry of N=1 world-sheet supersymmetry is studied through generalized super-Gauss map. The world sheet, realized as a conformally immersed super-Riemann surface S in Rⁿ (n=3 is studied for simplicity) is mapped into the supersymmetric Grassmannian G_2,3. In order for the Grassmannian fields to form (super) tangent planes to S, certain integrability conditions are satisfied by G_2,n fields. These conditions are explicitly derived. The supersymmetric invariant action for the Kähler σ-model G_2,3 is reexpressed in terms of the world-sheet coordinates, thereby an off-shell supersymmetric generalization of the action proportional to the extrinsic curvature of the immersed surface is obtained.

We extend a recent formulation of the D=10, GS heterotic string with (2, 0) world sheet supersymmetry involving pure spinors. The new model exhibits an (8, 0) world sheet supersymmetry which can be interpreted as κ symmetry in disguise.

We show that classical U(∞) gauge theories can be obtained from the dimensional reduction of a certain class of higher-derivative theories. In general, the exact symmetry is attained in the limit of degenerate metric; otherwise, the infinite-dimensional symmetry can be taken as spontaneously broken. Monopole solutions are examined in the model for scalar and gauge fields. An extension to gravity is also discussed.

We discuss the polarized photon structure function and focus on the first moment of , where we explore the role of the axial QED and strong U(1) anomalies. Electromagnetic gauge invariance determines an exact sum rule for the first moment of . If we accept a recently proposed definition of “spin content” then we must also accept a polarized gluon component of Δg^γ=2π/α_s in the spin-one photon.

We analyze the W_N^(l) algebras according to their conjectured realization as the second Hamiltonian structure of the integrable hierarchy resulting from the interchange of x and t in the l th flow of the sl(N) KdV hierarchy. The W₄⁽³⁾ algebra is derived explicitly along these lines, thus providing further support for the conjecture. This algebra is found to be equivalent to that obtained by the method of Hamiltonian reduction. Furthermore, its twisted version reproduces the algebra associated to a certain nonprincipal embedding of sl(2) into sl(4), or equivalently, the u(2) quasi-superconformal algebra. General aspects of the W_N^(l) algebras are also presented. We point out in particular that the x↔t interchange approach of the W_N^(l) algebra appears straightforward only when N and l are coprime.

The phenomenology of mixing involves four parameters: average width Γ, mixing ratio |q|p|, mass difference proportional to x, and width difference proportional to y. We point out the types of experimental inputs that are eventually needed in order to determine the four parameters completely and in a model-independent way. For the sign of y we suggest the measurement (at ϒ(4S) factories) of a certain time-asymmetry when one of the neutral B mesons is tagged and the other decays to a CP-eigenstate. For the sign of x we propose similar time-asymmetries when one of the B mesons undergoes the chain decay: B→KJ/ψ, and the neutral kaon→πlν or π⁺π⁻.

Random matrix models based on an integral over supermatrices are proposed as a natural extension of bosonic matrix models. The subtle nature of superspace integration allows these models to have very different properties from the analogous bosonic models. Two choices of integration slice are investigated. One leads to a perturbative structure which is reminiscent of, and perhaps identical to, the usual Hermitian matrix models. Another leads to an eigenvalue reduction which can be described by a two-component plasma in one dimension. A stationary point of the model is described.

It is argued that nonlocality is an essential ingredient in Relativistic Quantum Field Theory in order to have finite theory without recourse to a renormalisation program. A critical review of the physical constraints on the form the nonlocality can take is presented. The conclusion of this review is that nonlocality must be restricted to interactions with the vacuum sea of virtual particles. A successful formulation of such a theory, QNFT, is applied to scalar electrodynamics and serves to illustrate how gauge invariance and manifest finiteness can be achieved. The importance of the infinite dimensional symmetry groups that occur in QNFT are discussed as an alternative to supersymmetry, the ability to generate masses by breaking the nonlocal symmetry with a noninvariant functional measure is given a critical assessment. To demonstrate some of the many novel applications QNFT may make possible two examples are mooted, the existence of electroweak monopoles and the formulation of a finite perturbative theory of Quantum Gravity.

We examine the Wess-Zumino-Novikov-Witten (WZNW) model on a circle and compute the Poisson bracket algebra for left- and right-moving chiral group elements. Our computations apply for arbitrary groups and arbitrary boundary conditions, the latter being characterized by the monodromy matrix. Unlike in previous treatments, the Poisson brackets do not require specifying a particular parametrization of the group valued fields in terms of angles spanning the group. We do however find it necessary to make a gauge choice, as the chiral group elements are not gauge invariant observables. (On the other hand, the quadratic form of the Poisson brackets may be defined independently of a gauge fixing.) Gauge invariant observables can be formed from the monodromy matrix and these observbles are seen to commute in the quantum theory.