6392662
Loop and Path Spaces and¶Four-Dimensional BF Theories:¶Connections, Holonomies and Observables
Abstract: We study the differential geometry of principal G-bundles whose base space is the space of free paths (loops) on a manifold M. In particular we consider connections defined in terms of pairs (A,B), where A is a connection for a fixed principal bundle P(M,G) and B is a 2-form on M. The relevant curvatures, parallel transports and holonomies are computed and their expressions in local coordinates are exhibited. When the 2-form B is given by the curvature of A, then the so-called non-abelian Stokes formula follows.For a generic 2-form B, we distinguish the cases when the parallel transport depends on the whole path of paths and when it depends only on the spanned surface. In particular we discuss generalizations of the non-abelian Stokes formula. We study also the invariance properties of the (trace of the) holonomy under suitable transformation groups acting on the pairs (A,B).In this way we are able to define observables for both topological and non-topological quantum field theories of the BF type. In the non-topological case, the surface terms may be relevant for the understanding of the quark-confinement problem. In the topological case the (perturbative) four-dimensional quantum BF-theory is expected to yield invariants of imbedded (or immersed) surfaces in a 4-manifold M.
117142608
On the algebraic structure of link-diagrams on a 2-dimensional surface
Following and generalizing a paper by Turaev, we consider some algebraic structures on the set of (generalized) link-diagrams, meant simply as collections of immersed loops on a two dimensional surface, with the specification of an over/undercrossing prescription at each double point. This definition is general enough to be relevant not only to traditional knot-theory, but possibly to some statistical mechanical models. A coalgebra structure is introduced on some modules (over polynomial rings), generated by these diagrams. The compatibility of this coalgebra structure with the skein invariance and the invariance under Reidemeister moves is discussed. A Hopf algebra structure results only in some special cases, which are thoroughly examined. It is shown that a special choice of the ground (polynomial) ring over which the diagram module is defined, allows us to define link-invariants for links (in the ordinary sense) in Σ×[0,1],where Σ is a (closed or open) two-dimensional surface. These invariants generalize in a nontrivial way the Jones polynomials and the Homfly polynomials (at least when the last ones are computed for some special values of the variables). In a sequel paper the relation between the algebraic structures of link-diagrams, some special types of quantum groups and the quantum holonomy will be discussed.
117924192
Generalized wess-zumino terms
119943646
Relation between representations of KN and virasoro algebras
Abstract Some aspects of conformal field theory over Riemann surfaces are examined. We study, in particular, on simple systems (b−c systems) the relation between representations of the Virasoro and the KN algebras. KN algebra representations decompose into an infinite sum of the Virasoro algebra representations. We argue that the KN algebra representations are the right tool in order to classify conformal field theories over higher genus Riemann surfaces.
121996237
The Sugawara construction on genus-g Riemann surfaces
Abstract By using the formalism recently developed by Krichever and Novikov, we carry out the Sugawara construction for a Kac-Moody algebra defined over a generic Riemann surface.
117730967
Generalized Wess-Zumino terms and global anomalies in string sigma models
8497922
Modified Dispersion Relations and trans-Planckian Physics
We consider modified dispersion relations in quantum field theory on curved space-time. Such relations, despite breaking the local Lorentz invariance at high energy, are considered in several phenomenological approaches to quantum gravity. Their existence involves a modification of the formalism of quantum field theory, starting from the problem of finding the scalar Green's functions up to the renormalization of various quantum expectation values. In this work we consider a simple example of such modifications, in the case of ultra-static metric. We show how to overcome the lack of Lorentz invariance by introducing a preferred frame, with respect to which we can express the Green's functions as an integral over all frequencies of a space-dependent function. The latter can be expanded in momentum space, and by integrating over all frequencies, we finally find the expansion of the Green's function up to four derivatives of the metric tensor. The relation with the proper-time formalism is also discussed.
209514446
OPERATIONAL EXPERIENCE WITH THE ELETTRA RF SYSTEM
The ELETTRA RF System has been in operation since October 1993 and has now exceeded 20000 running hours. With four 500 MHz cavities powered by four 60 kW transmitters, ELETTRA has successfully delivered synchrotron light to the users with 300 mA of stored current at 2 GeV in multibunch mode, which is 1.5 times the initial target value ( 200 mA at 2 GeV). The RF system has worked very satisfactorily. Apart from the usual problems of debugging a new system, the main problem encountered during the operation period came from the coaxial power transmission line. The global operational experience gained during these years of operation and the performances of the various elements making up the ELETTRA RF system will be reported.
119288395
A new approach to non-commutative inflation
We propose an inflationary scenario inspired by a recent formulation, in terms of coherent states, of non-commutative quantum field theory. We consider the semiclassical Einstein equations, and exploit the ultraviolet finiteness of the non-commutative propagator to construct the expectation value of the energy–momentum tensor associated with a generic scalar field. It turns out that the latter is always finite and dominated by an effective cosmological constant. By combining this general feature with the intrinsic fuzziness of spacetime, we show that non-commutativity governs the energy density of the early Universe in such a way that the strong energy condition is violated. Thus, there might be a bounce and a subsequent inflationary phase, which does not need any ad hoc scalar field.
16113420
Self-T-dual brane cosmology and the cosmological constant problem
We consider a codimension-one brane embedded in a gravity-dilaton bulk action, whose symmetries are compatible with T-duality along the space-like directions parallel to the brane, and the bulk time-like direction. The equations of motions in the string frame allow for a smooth background obtained by the union of two symmetric patches of AdS space. The Poincare invariance of the solution appears to hold independently of the value of the brane vacuum energy, through a self-tuning property of the dilaton ground state. Moreover, the effective cosmology displays a bounce, at which the scale factor does not shrink to zero. Finally, by exploiting the T-duality symmetry, we show how to construct an ever-expanding Universe, along the lines of the Pre-Big-Bang scenario.
53531318
PARTICLE PRODUCTION AND TRANSPLANCKIAN PROBLEM ON THE NONCOMMUTATIVE PLANE
We consider the coherent state approach to noncommutativity and we derive from it an effective quantum scalar field theory. We show how the noncommutativity can be taken into account by a suitable modification of the Klein–Gordon product, and of the equal-time commutation relations. We prove that, in curved space, the Bogoliubov coefficients are unchanged, hence the number density of the produced particle is the same as for the commutative case. What changes though is the associated energy density, and this offers a simple solution to the transplanckian problem.