Do metric independent classical actions lead to topological field theories?

Abstract We investigate the quantum theory of non-abelian BF -systems (gauge theories with the classical metric independent action ∫ tr BF A ). The fact that due to a complicated (on-shell reducible) gauge structure the quantum action of these theories does not differ only by a BRST commutator from the classical action, and that moreover the BRST operator turns out to be metric dependent, renders the standard arguments for metric independence inapplicable. We establish the topological nature of these models and argue that in gauge theories the information on gauge invariance is contained entirely in the metric independent part of the BRST operator. We make some general remarks on the relati…

Topological field theory

Behavior of alloying elements during anodizing of Mg-Cu and Mg-W alloys in a fluoride/glycerol electrolyte

Anodizing of sputtering-deposited magnesium and Mg-0.75at.%Cu and Mg-1.23at.%W alloys has been carried out in a fluoride/ glycerol electrolyte. The aims of the study were to investigate the enrichment of alloying elements in the alloy immediately beneath the anodic film and the migration of alloying element species in the film. The specimens were examined by electron microscopy and ion beam analysis. An enrichment of copper is revealed in the Mg-Cu alloy that increases with the anodizing time up to ∼6×1015 Cu atoms cm-2. Copper species are then incorporated into the anodic film and migrate outwards. In contrast, no enrichment of tungsten occurs in the Mg-W alloy, and tungsten species are im…

N=2 topological gauge theory, the Euler characteristic of moduli spaces, and the Casson invariant

We discuss gauge theory with a topological N=2 symmetry. This theory captures the de Rham complex and Riemannian geometry of some underlying moduli space $\cal M$ and the partition function equals the Euler number of $\cal M$. We explicitly deal with moduli spaces of instantons and of flat connections in two and three dimensions. To motivate our constructions we explain the relation between the Mathai-Quillen formalism and supersymmetric quantum mechanics and introduce a new kind of supersymmetric quantum mechanics based on the Gauss-Codazzi equations. We interpret the gauge theory actions from the Atiyah-Jeffrey point of view and relate them to supersymmetric quantum mechanics on spaces of…

QUANTUM YANG-MILLS THEORY ON ARBITRARY SURFACES

We study quantum Maxwell and Yang-Mills theory on orientable two-dimensional surfaces with an arbitrary number of handles and boundaries. Using path integral methods we derive general and explicit expressions for the partition function and expectation values of contractible and noncontractible Wilson loops on closed surfaces of any genus, as well as for the kernels on manifolds with handles and boundaries. In the Abelian case we also compute correlation functions of intersecting and self-intersecting loops on closed surfaces, and discuss the role of large gauge transformations and topologically nontrivial bundles.

Relativistic SU(6) wave functions as the basis of modern approaches to hadronic wave functions

The connections between various models of hadrons and the relativistic SU(6) wave functions are established. In formal terms and by concrete example it is shown how the Bargman-Wigner fields of freely moving quarks and antiquarks of equal velocity form the basis of the above approaches. This places modern attempts in their historical setting and allows for a more unified analysis of the various schemes.

Tailoring of the Solid State Properties of Al–Nb Mixed Oxides: A Photoelectrochemical Study

Al–Nb containing mixed oxides were grown by anodizing sputter-deposited Al–Nb alloys of different compositions. A photoelectrochemical investigation was carried out in order to estimate the band gap, flat band potential, and conductivity type of these oxides as a function of their composition. The dependence of the band gap on the composition of mixed sp–d metal oxides has been rationalized by using a semiempirical correlation between the difference of electronegativity and band gap of oxides proposed in the literature some years ago and recently tested for regular d–d metal mixed oxides. The band gap increase observed as a function of Al content into the oxides seems mainly depending on th…

Covariant trace formalism for heavy mesons-wave top-wave transitions

Heavy meson,s- top-wave, weakb→c transitions are studied in the context of the heavy quark effective theory using covariant meson wave functions. We use the trace formalism to evaluate the weak transitions. As expected from heavy quark symmetry, the eight transitions betweens- andp-wave states are described in terms of only two universal form factors which are given in terms of explicit wave function overlap integrals. We present our results in terms of both invariant and helicity amplitudes. Using our helicity amplitude expressions we discuss rate formulae, helicity structure functions and joint angular decay distributions in the decays $$\bar B \to D^{**} ( \to (D,D^* ) + \pi ) + W^ - ( \…

Non-commutative geometry and supersymmetry II

Abstract Extending results of a previous work [Phys. Lett. B 260 (1991) 359], we establis that anothe non-commutative model proposed by Balakrishna, Gursey and Wali may be expressed as a Yang-Mills theory of a graded Lie group.

On heavy baryon decay form factors

We consider in detail the consequences of the heavy quark mass limit in the weak decay of 1/2+ heavy baryons to 1/2+ and 3/2+ heavy baryon final states. We also analyze heavy baryon to light baryon transitions as well ase+e−-annihilation into heavy baryon-antibaryonpairs. We discuss possible approximations to the most general approach and some of their implications for future experiments.

TOPOLOGICAL GAUGE THEORIES FROM SUPERSYMMETRIC QUANTUM MECHANICS ON SPACES OF CONNECTIONS

We rederive the recently introduced $N=2$ topological gauge theories, representing the Euler characteristic of moduli spaces ${\cal M}$ of connections, from supersymmetric quantum mechanics on the infinite dimensional spaces ${\cal A}/{\cal G}$ of gauge orbits. To that end we discuss variants of ordinary supersymmetric quantum mechanics which have meaningful extensions to infinite-dimensional target spaces and introduce supersymmetric quantum mechanics actions modelling the Riemannian geometry of submersions and embeddings, relevant to the projections ${\cal A}\rightarrow {\cal A}/{\cal G}$ and inclusions ${\cal M}\subset{\cal A}/{\cal G}$ respectively. We explain the relation between Donal…