Non-Locality and Ellipticity in a Gauge-Invariant Quantization

The quantum theory of a free particle in two dimensions with non-local boundary conditions on a circle is known to lead to surface and bulk states. Such a scheme is here generalized to the quantized Maxwell field, subject to mixed boundary conditions. If the Robin sector is modified by the addition of a pseudo-differential boundary operator, gauge-invariant boundary conditions are obtained at the price of dealing with gauge-field and ghost operators which become pseudo-differential. A good elliptic theory is then obtained if the kernel occurring in the boundary operator obeys certain summability conditions, and it leads to a peculiar form of the asymptotic expansion of the symbol. The cases of ghost operator of negative and positive order are studied within this framework.Comment: 17 pages, plain Te

Boundary Operators in Quantum Field Theory

The fundamental laws of physics can be derived from the requirement of invariance under suitable classes of transformations on the one hand, and from the need for a well-posed mathematical theory on the other hand. As a part of this programme, the present paper shows under which conditions the introduction of pseudo-differential boundary operators in one-loop Euclidean quantum gravity is compatible both with their invariance under infinitesimal diffeomorphisms and with the requirement of a strongly elliptic theory. Suitable assumptions on the kernel of the boundary operator make it therefore possible to overcome problems resulting from the choice of purely local boundary conditions.Comment: 23 pages, plain Tex. The revised version contains a new section, and the presentation has been improve

UV-finite scalar field theory with unitarity

In this paper we show how to define the UV completion of a scalar field theory such that it is both UV-finite and perturbatively unitary. In the UV completed theory, the propagator is an infinite sum of ordinary propagators. To eliminate the UV divergences, we choose the coefficients and masses in the propagator to satisfy certain algebraic relations, and define the infinite sums involved in Feynman diagram calculation by analytic continuation. Unitarity can be proved relatively easily by Cutkosky's rules. The theory is equivalent to infinitely many particles with specific masses and interactions. We take the $\phi^4$ theory as an example and demonstrate our idea through explicit Feynman diagram computation.Comment: 14 pages, references adde

Relativistically Covariant Symmetry in QED

We construct a relativistically covariant symmetry of QED. Previous local and nonlocal symmetries are special cases. This generalized symmetry need not be nilpotent, but nilpotency can be arranged with an auxiliary field and a certain condition. The Noether charge generating the symmetry transformation is obtained, and it imposes a constraint on the physical states.Comment: Latex file, 9 page

The Next Big Match: Convergence, Competition and Sports Media Rights

Using examples from a number of different European countries, this article analyses the increasingly prominent position of traditional telecommunications companies, such as British Telecom (UK), Deutsche Telekom (Germany), France Telecom/Orange (France) and Telefonica (Spain), in the contemporary sports media rights market. The first part of the article examines the commercial strategies of telecommunications operators and highlights how their acquisition of sports rights has been driven by the need to ensure a competitive position within an increasingly converged communications market. The second part of the article then moves on to consider the regulation of the sports media rights market. Most significantly, this section emphasises the need for further regulatory intervention to ensure that increased competition for sports rights leads to improved services and lower prices for consumers, rather than merely endlessly spiralling fees for the exclusive ownership of premium rights that are then passed on to sports channel and/or broadband subscribers

Hamilton-Jacobi formalism for Linearized Gravity

In this work we study the theory of linearized gravity via the Hamilton-Jacobi formalism. We make a brief review of this theory and its Lagrangian description, as well as a review of the Hamilton-Jacobi approach for singular systems. Then we apply this formalism to analyze the constraint structure of the linearized gravity in instant and front-form dynamics.Comment: To be published in Classical and Quantum Gravit

Ultraviolet Complete Electroweak Model Without a Higgs Particle

An electroweak model with running coupling constants described by an energy dependent entire function is utraviolet complete and avoids unitarity violations for energies above 1 TeV. The action contains no physical scalar fields and no Higgs particle and the physical electroweak model fields are local and satisfy microcausality. The $W$ and $Z$ masses are compatible with a symmetry breaking $SU(2)_L\times U(1)_Y \rightarrow U(1)_{\rm em}$, which retains a massless photon. The vertex couplings possess an energy scale $\Lambda_W > 1$ TeV predicting scattering amplitudes that can be tested at the LHC.Comment: 19 pages, no figures, LaTex file. Equation and text corrected. Reference added. Results remain the same. Final version published in European Physics Journal Plus, 126 (2011

Workmen\u27s Compensation at Sea

At the present time there are three possible remedies available to seamen who are injured in the course of their employment. In order to maintain any of these actions, the injured party must of course qualify as a seaman. The traditional tests used to determine whether a maritime worker is a seaman are as follows: 1) the vessel must be in navigation, 2) the worker must have a more or less permanent connection with the vessel, and 3) the worker must be aboard the vessel primarily to aid in navigation. These standards have been somewhat modified by Offshore Company v. Robinson. In that case, the court stated that there is an evidentiary basis for holding a person to be a seaman if: 1) there is evidence that the worker was assigned permanently to a vessel, or performed a substantial part of his work aboard a vessel, and 2) his duties contributed to the function of the vessel or to the accomplishment of its mission. Therefore, it seems that it does not matter whether the vessel is actually in navigation or if the maritime worker is aboard primarily in aid of navigation so long as he performs a substantial part of his work on the vessel. Furthermore, the definition of vessel has been extended to cover almost any floating object that is capable of being moved from one place to another

Modular classes of skew algebroid relations

Skew algebroid is a natural generalization of the concept of Lie algebroid. In this paper, for a skew algebroid E, its modular class mod(E) is defined in the classical as well as in the supergeometric formulation. It is proved that there is a homogeneous nowhere-vanishing 1-density on E* which is invariant with respect to all Hamiltonian vector fields if and only if E is modular, i.e. mod(E)=0. Further, relative modular class of a subalgebroid is introduced and studied together with its application to holonomy, as well as modular class of a skew algebroid relation. These notions provide, in particular, a unified approach to the concepts of a modular class of a Lie algebroid morphism and that of a Poisson map.Comment: 20 page

Integral Grothendieck-Riemann-Roch theorem

We show that, in characteristic zero, the obvious integral version of the Grothendieck-Riemann-Roch formula obtained by clearing the denominators of the Todd and Chern characters is true (without having to divide the Chow groups by their torsion subgroups). The proof introduces an alternative to Grothendieck's strategy: we use resolution of singularities and the weak factorization theorem for birational maps.Comment: 24 page