Maurer-Cartan forms and equations for two-dimensional superdiffeomorphisms

We present explicit expressions for the Maurer-Cartan forms of the superdiffeomorphism group associated to a super Riemann surface. As an application to superconformal field theory, we use these forms to evaluate the effective action for the factorized superdiffeomorphism anomaly.Comment: (LATEX, 8 pages), MPI-Ph/92-4

About Symmetries in Physics

The goal of this introduction to symmetries is to present some general ideas, to outline the fundamental concepts and results of the subject and to situate a bit the following lectures of this school. [These notes represent the write-up of a lecture presented at the fifth ``Seminaire Rhodanien de Physique: Sur les Symetries en Physique" held at Dolomieu (France), 17-21 March 1997. Up to the appendix and the graphics, it is to be published in "Symmetries in Physics", F.Gieres, M.Kibler,C.Lucchesi and O.Piguet, eds. (Editions Frontieres, 1998).]Comment: Latex, 42 pages, 4 figure

Conformal covariance in 2d conformal and integrable models, in W-algebras and in their supersymmetric extensions

Conformal symmetry underlies the mathematical description of various two-dimensional integrable models (e.g. for their Lax representation, Poisson algebra, zero curvature representation,...) or of conformal models (for the anomalous Ward identities, operator product expansion, Krichever-Novikov algebra,...) and of W-algebras. Here, we review the construction of conformally covariant differential operators which allow to render the conformal covariance manifest. The N=1 and N=2 supersymmetric generalizations of these results are also indicated and it is shown that they involve nonstandard matrix formats of Lie superalgebras.Comment: Proceedings of the workshop "Supersymmetries and Quantum Symmetries" (SQS'99, Dubna, July 1999

Superconformally covariant operators and super W algebras

We study superdifferential operators of order $2n+1$ which are covariant with respect to superconformal changes of coordinates on a compact super Riemann surface. We show that all such operators arise from super M\"obius covariant ones. A canonical matrix representation is presented and applications to classical super W algebras are discussed.Comment: 23 pages, LATEX, MPI-Ph/92-66 and KA-THEP-7/9

Classical N=1N=1 and N=2N=2 super W-algebras from a zero-curvature condition

Starting from superdifferential operators in an $N=1$ superfield formulation, we present a systematic prescription for the derivation of classical $N=1$ and $N=2$ super W-algebras by imposing a zero-curvature condition on the connection of the corresponding first order system. We illustrate the procedure on the first non-trivial example (beyond the $N=1$ superconformal algebra) and also comment on the relation with the Gelfand-Dickey construction of $W$-algebras.Comment: 18 pages, tex, LMU-TPW 93-0

Relating Weyl and diffeomorphism anomalies on super Riemann surfaces

Starting from the Wess-Zumino action associated to the super Weyl anomaly, we determine the local counterterm which allows to pass from this anomaly to the chirally split superdiffeomorphism anomaly (as defined on a compact super Riemann surface without boundary). The counterterm involves the graded extension of the Verlinde functional and the results can be applied to the study of holomorphic factorization of partition functions in superconformal field theory.Comment: (LATEX, 18 pages), MPI-Ph/92-38, LPTB 92-

The Energy-Momentum Tensor(s) in Classical Gauge Theories

We give an introduction to, and review of, the energy-momentum tensors in classical gauge field theories in Minkowski space, and to some extent also in curved space-time. For the canonical energy-momentum tensor of non-Abelian gauge fields and of matter fields coupled to such fields, we present a new and simple improvement procedure based on gauge invariance for constructing a gauge invariant, symmetric energy-momentum tensor. The relationship with the Einstein-Hilbert tensor following from the coupling to a gravitational field is also discussed.Comment: 34 pages; v2: Slightly expanded version with some improvements of presentation; Contribution to Mathematical Foundations of Quantum Field Theory, special issue in memory of Raymond Stora, Nucl. Phys.

Wong's Equations and Charged Relativistic Particles in Non-Commutative Space

In analogy to Wong's equations describing the motion of a charged relativistic point particle in the presence of an external Yang-Mills field, we discuss the motion of such a particle in non-commutative space subject to an external $U_\star(1)$ gauge field. We conclude that the latter equations are only consistent in the case of a constant field strength. This formulation, which is based on an action written in Moyal space, provides a coarser level of description than full QED on non-commutative space. The results are compared with those obtained from the different Hamiltonian approaches. Furthermore, a continuum version for Wong's equations and for the motion of a particle in non-commutative space is derived

New solution of the N=2\mathcal{N}=2 Supersymmetric KdV equation via Hirota methods

We consider the resolution of the $\mathcal{N}=2$ supersymmetric KdV equation with $a=-2$ ($SKdV_{a=-2}$) from the Hirota formalism. For the first time, a bilinear form of the $SKdV_{a=-2}$ equation is constructed. We construct multisoliton solutions and rational similarity solutions.Comment: 7 pages, 9 figures. arXiv admin note: significant text overlap with arXiv:1104.059