arXiv subjects
Publications and source records attributed to F. Gieres.
After a brief review of topological gravity, we present a superspace approach to this theory. This formulation allows us to recover in a natural manner various known results and to gain some insight into the precise relationship between different approaches to topological gravity. Though the main focus of our work is on the vielbein formalism, we also discuss the metric approach and its relationship with the former formalism.
Observables of topological Yang-Mills theory were defined by Witten as the classes of an equivariant cohomology. We propose to define them alternatively as the BRST cohomology classes of a superspace version of the theory, where BRST invariance is associated to super Yang-Mills invariance. We provide and discuss the general solution of this cohomology.
After recalling different formulations of the definition of supersymmetric quantum mechanics given in the literature, we discuss the relationships between them in order to provide an answer to the question raised in the title.
By a series of simple examples, we illustrate how the lack of mathematical concern can readily lead to surprising mathematical contradictions in wave mechanics. The basic mathematical notions allowing for a precise formulation of the theory are then summarized and it is shown how they lead to an elucidation and deeper understanding of the aforementioned problems. After stressing the equivalence between wave mechanics and the other formulations of quantum mechanics, i.e. matrix mechanics and Dirac's abstract Hilbert space formulation, we devote the second part of our paper to the latter approach: we discuss the problems and shortcomings of this formalism as well as those of the bra and ket notation introduced by Dirac in this context. In conclusion, we indicate how all of these problems can be solved or at least avoided.
The perturbative finiteness of various topological models (e.g. BF models) has its origin in an extra symmetry of the gauge-fixed action, the so-called vector supersymmetry. Since an invariance of this type also exists for gravity and since gravity is closely related to certain BF models, vector supersymmetry should also be useful for tackling various aspects of quantum gravity. With this motivation and goal in mind, we first extend vector supersymmetry of BF models to generic manifolds by incorporating it into the BRST symmetry within the Batalin-Vilkovisky framework. Thereafter, we address the relationship between gravity and BF models, in particular for three-dimensional space-time.
Topological field theories of Schwarz-type generally admit symmetries whose algebra does not close off-shell, e.g. the basic symmetries of BF models or vector supersymmetry of the gauge-fixed action for Chern-Simons theory (this symmetry being at the origin of the perturbative finiteness of the theory). We present a detailed discussion of all these symmetries within the algebraic approach to the Batalin-Vilkovisky formalism. Moreover, we discuss the general algebraic construction of topological models of both Schwarz- and Witten-type.
We study the gauge-fixing and symmetries (BRST-invariance and vector supersymmetry) of various six-dimensional topological models involving Abelian or non-Abelian 2-form potentials.
We present a simple derivation of vector supersymmetry transformations for topological field theories of Schwarz- and Witten-type. Our method is similar to the derivation of BRST-transformations from the so-called horizontality conditions or Russian formulae. We show that this procedure reproduces in a concise way the known vector supersymmetry transformations of various topological models and we use it to obtain some new transformations of this type for 4d topological YM-theories in different gauges.
Differents formalismes sont utilises en mecanique quantique pour la description des etats et des observables : la mecanique ondulatoire, la mecanique matricielle et le formalisme invariant. Nous discutons les problemes et inconvenients du formalisme invariant ainsi que ceux de la notation des bras et kets introduite par Dirac dans ce contexte. Nous indiquons comment tous les problemes peuvent etre resolus ou du moins evites. Une serie d'exemples illustre les points souleves et montre comment l'insouciance mathematique peut aisement conduire a des contradictions mathematiques surprenantes.
The standard format of matrices belonging to Lie superalgebras consists of partitioning the matrices into even and odd blocks. In this paper, we study other possible matrix formats and in particular the so-called diagonal format which naturally occurs in various applications, e.g. in superconformal field theory, superintegrable models, for super W-algebras and quantum supergroups.
CONTENTS: 1. Synopsis, 2. The MSSM Spectrum, 3. The Physical Parameters, 4. Higgs Boson Production and Decays, 5. SUSY Particle Production and Decays, 6. Experimental Bounds on SUSY Particle Masses, 7. References.
We construct and classify superconformally covariant differential operators defined on N=2 super Riemann surfaces. By contrast to the N=1 theory, these operators give rise to partial rather than ordinary differential equations which leads to novel features for their matrix representation. The latter is applied to the derivation of N=2 super W-algebras in terms of N=2 superfields.