Extensão supersimétrica do problema de Gribov no formalismo de supercampos

Nesta tese estudamos uma extensão supersimétrica do mecanismo de Gribov no caso N = 1 em supercampos. Abordamos as teorias de super Yang-Mills em D = 4 e super Yang-Mills-Chern-Simons em D = 3. E verificamos como nestes casos o princípio de calibre leva ao cenário de confinamento de Gribov.

Jackiw-Pi模型的新涡旋解

运用映射拓扑流理论研究了Jackiw-Pi模型中的自对偶方程,得到一个静态的自对偶解满足带有δ函数项的刘维尔方程,从而得到了一个完整的带有拓扑信息的涡旋解,自然给出了磁通量子化.

Topological structure of the many vortices solution in Jackiw-Pi model

By using the gauge potential decomposition, we discuss the self-dual equation and its solution in Jackiw-Pi model. We obtain a new concrete self-dual equation and find relationship between Chern-Simons vortices solution and topological number which is determined by Hopf indices and Brouwer degrees of Psi-mapping. To show the meaning of topological number we give several figures with different topological numbers. In order to investigate the topological properties of many vortices, we use five parameters (two positions, one scale, one phase per vortex and one charge of each vortex) to describe each vortex in many vortices solutions in Jackiw-Pi model. For many vortices, we give three figures with different topological numbers to show the effect of the charge on the many vortices solutions. We also study the quantization of flux of those vortices related to the topological numbers in this case.

New vortex solutions of Jackiw-Pi model

Based on current phi-mapping topological theory, a kind of self-dual equations in Jackiw-Pi model are studied. We first obtain explicit, self-dual solutions that satisfy Liouville equation which contains delta-function. Then we get perfect vortex solutions which reflect the system's internal topological structure, and consequently the quantization of flux.

Topological structure of vortex solution in Jackiw-Pi model

By using phi-mapping method, we discuss the topological structure of the self-duality solution in Jackiw-Pi model in terms of gauge potential decomposition. We set up relationship between Chern-Simons vortex solution and topological number, which is determined by Hopf index and Brouwer degree. We also give the quantization of flux in this case. Then, we study the angular momentum of the vortex, which can be expressed in terms of the flux.

Topological structure of the solitons solution in SU(3) Dunne-Jackiw-Pi-Trugenberger model

By using phi-mapping topological current theory and gauge potential decomposition, we discuss the self-dual equation and its solution in the SU(N) Dunne-Jackiw-Pi-Trugenberger model and obtain a new concrete self-dual equation with a 6 function. For the SU(3) case, we obtain a new self-duality solution and find the relationship between the soliton solution and topological number which is determined by the Hopf index and Brouwer degree of phi-mapping. In our solution, the flux of this soliton is naturally quantized.

Consistent couplings between fields with a gauge freedom and deformations of the master equation

The antibracket in the antifield-BRST formalism is known to define a map Hp × Hq → Hp + q + 1 associating with two equivalence classes of BRST invariant observables of respective ghost number p and q an equivalence class of BRST invariant observables of ghost number p + q + 1. It is shown that this map is trivial in the space of all functionals, i.e. that its image contains only the zeroth class. However, it is generically non-trivial in the space of local functionals. Implications of this result for the problem of consistent interactions among fields with a gauge freedom are then drawn. It is shown that the obstructions to constructing non-trivial such interactions lie precisely in the image of the antibracket map and are accordingly non-existent if one does not insist on locality. However consistent local interactions are severely constrained. The example of the Chern-Simons theory is considered. It is proved that the only consistent, local, Lorentz covariant interactions for the abelian models are exhausted by the non-abelian Chern-Simons extensions. © 1993.

Géométrie noncommunicative et effet Hall quantique

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

Lorentz violation and the proper-time method

In this Letter, we apply the proper-time method to generate the Lorentz-violating Chern-Simons terms in the four-dimensional Yang-Mills and non-linearized gravity theories. It is shown that the coefficient of the induced Chern-Simons term is finite but regularization dependent. (C) 2008 Elsevier B.V. All rights reserved.

Coherent and semiclassical states in a magnetic field in the presence of the Aharonov-Bohm solenoid

A new approach to constructing coherent states (CS) and semiclassical states (SS) in a magnetic-solenoid field is proposed. The main idea is based on the fact that the AB solenoid breaks the translational symmetry in the xy-plane; this has a topological effect such that there appear two types of trajectories which embrace and do not embrace the solenoid. Due to this fact, one has to construct two different kinds of CS/SS which correspond to such trajectories in the semiclassical limit. Following this idea, we construct CS in two steps, first the instantaneous CS (ICS) and then the time-dependent CS/SS as an evolution of the ICS. The construction is realized for nonrelativistic and relativistic spinning particles both in (2 + 1) and (3 + 1) dimensions and gives a non-trivial example of SS/CS for systems with a nonquadratic Hamiltonian. It is stressed that CS depending on their parameters (quantum numbers) describe both pure quantum and semiclassical states. An analysis is represented that classifies parameters of the CS in such respect. Such a classification is used for the semiclassical decompositions of various physical quantities.

Static potential in QED(3) with nonminimal coupling

Here we study the effect of the nonminimal coupling j(mu)epsilon(munualpha)partial derivative(nu)A(alpha) on the static potential in multiflavor QED(3). Both cases of four and two components fermions are studied separately at leading order in the 1/N expansion. Although a nonlocal Chern-Simons term appears, in the four components case the photon is still massless leading to a confining logarithmic potential similar to the classical one. In the two components case, as expected, the parity breaking fermion mass term generates a traditional Chern-Simons term which makes the photon massive and we have a screening potential which vanishes at large intercharge distance. The extra nonminimal couplings have no important influence on the static potential at large intercharge distances. However, interesting effects show up at finite distances. In particular, for strong enough nonminimal coupling we may have a new massive pole in the photon propagator, while in the opposite limit there may be no poles at all in the irreducible case. We also found that, in general, the nonminimal couplings lead to a finite range repulsive force between charges of opposite signs.

Dirac-like monopoles in three dimensions and their possible influences on the dynamics of particles

Dirac-like monopoles are studied in three-dimensional Abelian Maxwell and Maxwell-Chern-Simons models. Their scalar nature is highlighted and discussed through a dimensional reduction of four-dimensional electrodynamics with electric and magnetic sources. Some general properties and similarities whether considered in Minkowski or Euclidean space are mentioned. However, by virtue of the structure of the space-time in which they are studied, a number of differences among them occur. Furthermore, we pay attention to some consequences of these objects when they act upon the usual particles. Among other subjects, special attention is given to the study of a Lorentz-violating nonminimal coupling between neutral fermions and the field generated by a monopole alone. In addition, an analogue of the Aharonov-Casher effect is discussed in this framework.

Ghost free dual vector theories in 2+1 dimensions

We explore here the issue of duality versus spectrum equivalence in dual theories generated through the master action approach. Specifically we examine a generalized self-dual (GSD) model where a Maxwell term is added to the self-dual model. A gauge embedding procedure applied to the GSD model leads to a Maxwell-Chern-Simons (MCS) theory with higher derivatives. We show here that the latter contains a ghost mode contrary to the original GSD model. By figuring out the origin of the ghost we are able to suggest a new master action which interpolates between the local GSD model and a nonlocal MCS model. Those models share the same spectrum and are ghost free. Furthermore, there is a dual map between both theories at classical level which survives quantum correlation functions up to contact terms. The remarks made here may be relevant for other applications of the master action approach.

Multiflavor soldering

In two dimensions the simple addition of two chiral bosons of opposite chiralities does not lead to a full massless scalar field. Similarly, in three dimensions the addition of two Maxwell-Chern-Simons fields of opposite helicities +/- 1 will not produce a parity invariant Maxwell-Proca theory. An interference term between the opposite chiralities (helicities) states is required in order to obtain the expected result. The so-called soldering procedure provides the missing interference Lagrangian in both 2D and 3D cases. In two dimensions such interference term allows to fuse two chiral fermionic determinants into, a non-chiral one. In a recent work we have generalized this procedure by allowing the appearance of an extra parameter which takes two possible values and leads to two different soldered Lagrangians. Here we apply this generalized soldering in a bosonic theory which has appeared in a partial bosonization of the 3D gauged Thirring model with N flavors. The multiplicity of flavors allow new types of solderings and help us to understand the connection between different perturbative approaches to bosonization in 3D. In particular, we obtain an interference term which takes us from a multiflavor Niaxwell-Chern-Simons theory to a pair of self-dual and anti-self-dual theories when we combine together both fermionic determinants of +1/2 and -1/2 helicity fermions. An important role is played by a set of pure non-interacting Chern-Simons fields which amount to a normalization factor in the fermionic determinants and act like spectators in the original theory but play an active role in the soldering procedure. Our results suggest that the generalized soldering could be used to provide dual theories in both 2D and 3D cases. (c) 2007 Elsevier B.V. All rights reserved.

Generalized duality between local vector theories in D=2+1

The existence of an interpolating master action does not guarantee the same spectrum for the interpolated dual theories. In the specific case of a generalized self-dual (GSD) model defined as the addition of the Maxwell term to the self-dual model in D = 2 + 1, previous master actions have furnished a dual gauge theory which is either nonlocal or contains a ghost mode. Here we show that by reducing the Maxwell term to first order by means of an auxiliary field we are able to define a master action which interpolates between the GSD model and a couple of non-interacting Maxwell-Chern-Simons theories of opposite helicities. The presence of an auxiliary field explains the doubling of fields in the dual gauge theory. A generalized duality transformation is defined and both models can be interpreted as self-dual models. Furthermore, it is shown how to obtain the gauge invariant correlators of the non-interacting MCS theories from the correlators of the self-dual field in the GSD model and vice-versa. The derivation of the non-interacting MCS theories from the GSD model, as presented here, works in the opposite direction of the soldering approach.