Charges and fluxes in Maxwell theory on compact manifolds with boundary

We investigate the charges and fluxes that can occur in higher-order Abelian gauge theories defined on compact space-time manifolds with boundary. The boundary is necessary to supply a destination to the electric lines of force emanating from brane sources, thus allowing non-zero net electric charges, but it also introduces new types of electric and magnetic flux. The resulting structure of currents, charges, and fluxes is studied and expressed in the language of relative homology and de Rham cohomology and the corresponding abelian groups. These can be organised in terms of a pair of exact sequences related by the Poincare-Lefschetz isomorphism and by a weaker flip symmetry exchanging the ends of the sequences. It is shown how all this structure is brought into play by the imposition of the appropriately generalised Maxwell's equations. The requirement that these equations be integrable restricts the world-volume of a permitted brane (assumed closed) to be homologous to a cycle on the boundary of space-time. All electric charges and magnetic fluxes are quantised and satisfy the Dirac quantisation condition. But through some boundary cycles there may be unquantised electric fluxes associated with quantised magnetic fluxes and so dyonic in nature.

On Clifford subalgebras, spacetime splittings and applications

Z(2)-gradings of Clifford algebras are reviewed and we shall be concerned with an alpha-grading based on the structure of inner automorphisms, which is closely related to the spacetime splitting, if we consider the standard conjugation map automorphism by an arbitrary, but fixed, splitting vector. After briefly sketching the orthogonal and parallel components of products of differential forms, where we introduce the parallel [orthogonal] part as the space [time] component, we provide a detailed exposition of the Dirac operator splitting and we show how the differential operator parallel and orthogonal components are related to the Lie derivative along the splitting vector and the angular momentum splitting bivector. We also introduce multivectorial-induced alpha-gradings and present the Dirac equation in terms of the spacetime splitting, where the Dirac spinor field is shown to be a direct sum of two quaternions. We point out some possible physical applications of the formalism developed.

Spinning Hopf solitons on S-3 x R

We consider a field theory with target space being the two dimensional sphere S-2 and defined on the space-time S-3 x R. The Lagrangean is the square of the pull-back of the area form on S-2. It is invariant under the conformal group SO(4, 2) and the infinite dimensional group of area preserving diffeomorphisms of S-2. We construct an infinite number of exact soliton solutions with non-trivial Hopf topological charges. The solutions spin with a frequency which is bounded above by a quantity proportional to the inverse of the radius of S-3. The construction of the solutions is made possible by an ansatz which explores the conformal symmetry and a U(1) subgroup of the area preserving diffeomorphism group.

Duality between coordinates and Dirac field

The duality between the Cartesian coordinates on the Minkowski space-time and the Dirac field is investigated. Two distinct possibilities to define this duality are shown to exist. In both cases, the equations satisfied by prepotentials are of second order. (C) 2000 Elsevier B.V. B.V. All rights reserved.

PT-invariant point interactions in one dimension

By using Wu and Yu's pseudo-potential, we construct point interactions in one dimension that are complex but conform to space-time reflection (PT) invariance. The resulting point interactions are equivalent to those obtained by Albeverio, Fei and Kurasov as self-adjoint extensions of the kinetic energy operator.

Scalar field theory at finite temperature in D=2+1

We discuss the phi(6) theory defined in D=2+1-dimensional space-time and assume that the system is in equilibrium with a thermal bath at temperature beta(-1). We use the 1/N expansion and the method of the composite operator (Cornwall, Jackiw, and Tomboulis) for summing a large set of Feynman graphs. We demonstrate explicitly the Coleman-Mermin-Wagner theorem at finite temperature.

Spinorial field and Lyra geometry

The Dirac field is studied in a Lyra space-time background by means of the classical Schwinger Variational Principle. We obtain the equations of motion, establish the conservation laws, and get a scale relation relating the energy-momentum and spin tensors. Such scale relation is an intrinsic property for matter fields in Lyra background.

Scalar field theory at finite temperature in D=2+1

We discuss the phi(6) theory defined in D = 2 + 1-dimensional space-time and assume that the system is in equilibrium with a thermal bath at temperature beta(-1). We use the 1/N expansion and the method of composite operator (CJT) for summing a large set of Feynman graphs. We demonstrate explicitly the Coleman-Mermin-Wagner theorem at finite temperature.

Light-front zero-mode contribution to the Ward Identity

In a covariant gauge we implicitly assume that the Green's function propagates information from one point of the space-time to another, so that the Green's function is responsible for the dynamics of the relativistic particle. In the light front form one would naively expect, that this feature would be preserved. In this manner, the fermionic field propagator can be split into a propagating piece and a non-propagating (contact) term. Since the latter (contact) one does not propagate information; and therefore, supposedly can be discarded with no harm to the field dynamics we wanted to know what would be the impact of dropping it off. To do that, we investigated its role in the Ward identity in the light front. Here we use the terminology Ward identity to identify the limiting case of photon's zero momentum transfer in the vertex from the more general Ward-Takahashi identity with nonzero momentum transfer.

Do tadpoles vanish in the light-front?

In covariant gauges (CG) regularized with dimensional regularization (DR) it is a standard procedure to set all tadpole Feynman integrals to zero, though; explicitly, they diverge quadratically as the space-time volume. on the other hand, in the notoriously subtle light-front gauge (LTG) some divergent tadpole integrals are said to be nonvanishing, i.e., cannot be set to zero as in the CC case. In this article we analyse the reasons behind this seemingly ambiguous results.

Cornering the unphysical vertex

In the classical pure spinor worldsheet theory of AdS(5) x S-5 there are some vertex operators which do not correspond to any physical excitations. We study their flat space limit. We find that the BRST operator of the worldsheet theory in flat space-time can be nontrivially deformed without deforming the worldsheet action. Some of these deformations describe the linear dilaton background. But the deformation corresponding to the nonphysical vertex differs from the linear dilaton in not being worldsheet parity even. The nonphysically deformed worldsheet theory has nonzero beta-function at one loop. This means that the classical Type IIB SUGRA backgrounds are not completely characterized by requiring the BRST symmetry of the classical worldsheet theory; it is also necessary to require the vanishing of the one-loop beta-function.

THERMAL RADIATION FROM A FLUCTUATING EVENT HORIZON

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Constantes de Movimento para um Potencial Dependente da Velocidade

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Phenomenology as a method to investigate the experience lived: a perspective from Husserl and Merleau Ponty's thought

Aim. By taking nursing as a human relationships activity, in spite of its strong technical-scientific features, this article reflects on the phenomenological method as one of the ways to develop ail investigation and acquire knowledge of the topic.Rationale. Based on Husserl's phenomenology, which is opposed to the way of doing science based on the laws that regulate the physics and mathematics, the article introduces Merleau Ponty's existential phenomenology as the theoretical foundation for the method it proposes. My existential conceptions-people as historic beings inserted in a world over which they act but which, in its turn, determines them; the human perception as reference for our way of being in the world; the space-time structure of perception-these are the key concepts that have led to the elaboration of ail approach to phenomenological research.Proposal of a methodology. Steps are proposed for such ail approach, namely phenomenological description, reduction and analysis. These lead to the building up of ideographic and nomothetic analyses, thus unveiling and describing general truths about the phenomenon studied. Finally, the possibilities for applying the methodology to nursing research are discussed, illustrated by my research into student nurses' perspectives on working oil an isolation ward.

Obtaining a light-like planar gauge

In the usual and current understanding of planar gauge choices for Abelian and non-Abelian gauge fields, the external defining vector n(mu), can either be space-like (n(2) < 0) or time-like (n(2) > 0) but not light-like (n(2) = 0). In this work we propose a light-like planar gauge that consists of defining a modified gauge-fixing term, L-GF, whose main characteristic is a two-degree violation of Lorentz covariance arising from the fact that four-dimensional space-time spanned entirely by null vectors as basis necessitates two light-like vectors, namely n(mu) and its dual m(mu), with n(2) = m(2) = 0, n . m not equal 0, say, e.g. normalized to n . m = 2.