Modelo de Thirring com simetria de Gauge: uma análise funcional

Pós-graduação em Física - IFT

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.

Duality in noncommutative topologically massive gauge field theory revisited

We introduce a master action in non-commutative space, out of which we obtain the action of the non-commutative Maxwell-Chern-Simons theory. Then, we look for the corresponding dual theory at both first and second order in the non-commutative parameter. At the first order, the dual theory happens to be, precisely, the action obtained from the usual commutative self-dual model by generalizing the Chern-Simons term to its non-commutative version, including a cubic term. Since this resulting theory is also equivalent to the non-commutative massive Thirring model in the large fermion mass limit, we remove, as a byproduct, the obstacles arising in the generalization to non-commutative space, and to the first non-trivial order in the non-commutative parameter, of the bosonization in three dimensions. Then, performing calculations at the second order in the non-commutative parameter, we explicitly compute a new dual theory which differs from the non-commutative self-dual model and, further, differs also from other previous results and involves a very simple expression in terms of ordinary fields. In addition, a remarkable feature of our results is that the dual theory is local, unlike what happens in the non-Abelian, but commutative case. We also conclude that the generalization to non-commutative space of bosonization in three dimensions is possible only when considering the first non-trivial corrections over ordinary space.

Remarks on fermion-boson equivalence in three dimensions

Starting from a decomposition of the self-dual field in (2 + 1) dimensions, we build up an alternative quantum theory which consists of a self-dual model coupled to a Maxwell-generalized Chern-Simons theory. We discuss the fermion-boson equivalence of this quantum theory by comparing it with the Thirring model. Using these results we were able to compute the mass of the bosonized fermions up to third order in 1/m. Some problems related to the number of poles of the effective propagator are also addressed.

Chaotic thermalization in classical gauge theories

We explore the idea that chaos concepts might be useful for understanding the thermalization in gauge theories. The SU(2) Higgs model is discussed as a prototype of system with gauge fields coupled to matter fields. Through the numerical solution of the equations of motion, we are able to characterize chaotic behavior via the corresponding Lyapunov exponent. Then it is demonstrated that the system's approach to equilibrium can be understood through direct application of the principles of Statistical Mechanics. © 2013 AIP Publishing LLC.

The algebraic structure behind the derivative nonlinear Schrödinger equation

The Kaup-Newell (KN) hierarchy contains the derivative nonlinear Schrödinger equation (DNLSE) amongst others interesting and important nonlinear integrable equations. In this paper, a general higher grading affine algebraic construction of integrable hierarchies is proposed and the KN hierarchy is established in terms of an Ŝℓ2Kac-Moody algebra and principal gradation. In this form, our spectral problem is linear in the spectral parameter. The positive and negative flows are derived, showing that some interesting physical models arise from the same algebraic structure. For instance, the DNLSE is obtained as the second positive, while the Mikhailov model as the first negative flows. The equivalence between the latter and the massive Thirring model is also explicitly demonstrated. The algebraic dressing method is employed to construct soliton solutions in a systematic manner for all members of the hierarchy. Finally, the equivalence of the spectral problem introduced in this paper with the usual one, which is quadratic in the spectral parameter, is achieved by setting a particular automorphism of the affine algebra, which maps the homogeneous into principal gradation. © 2013 IOP Publishing Ltd.

Signatures of doubly charged Higgs in the SU(3)(L) circle times U(1)(N) model at the CERN LHC

The scalar sector of the simplest version of the 3-3-1 electroweak model is constructed with three Higgs triplets only. We show that a relation involving two of the constants of the model, two vacuum expectation values of the neutral scalars, and the mass of the doubly charged Higgs boson leads to important information concerning the signals of this scalar particle.

Neutral Higgs bosons in the SU(3)(L)circle times U(1)(N) model

The SU(3)(L)circle times U(1)(N) electroweak model predicts new Higgs bosons beyond the one of the standard model. In this work we investigate the signature and production of neutral SU(3)(L)circle times U(1)(N) Higgs bosons in the e(-)e(+) Next Linear Collider and in the CERN Linear Collider . We compute the branching ratios of two of the SU(3)(L)circle times U(1)(N) neutral Higgs bosons and study the possibility to detect them and the Z' extra neutral boson of the model.

SU(5)circle times Z(13) grand unification model

We propose an SU(5) grand unified model with an invisible axion and the unification of the three coupling constants which is in agreement with the values, at M(Z), of alpha, alpha(s), and sin(2)theta(W). A discrete, anomalous, Z(13) symmetry implies that the Peccei-Quinn symmetry is an automatic symmetry of the classical Lagrangian protecting, at the same time, the invisible axion against possible semiclassical gravity effects. Although the unification scale is of the order of the Peccei-Quinn scale the proton is stabilized by the fact that in this model the standard model fields form the SU(5) multiplets completed by new exotic fields and, also, because it is protected by the Z(13) symmetry.

LEPTON MASSES IN AN SU(3)L-CIRCLE-TIMES-U(1)N GAUGE-MODEL

The SU(3)cxSU(3)LxU(1)N model of Pisano and Pleitez extends the standard model in a particularly nice way, so that, for example, the anomalies cancel only when the number of generations is divisible by 3. The original version of the model has some problems accounting for the lepton masses. We resolve this problem by modifying the details of the symmetry-breaking sector in the model.

NEUTRINOLESS DOUBLE-BETA DECAY IN AN SU(3)(L)CIRCLE-TIMES-U(1)(N) MODEL

We consider a model for the electroweak interactions with the SU(3)(L) circle times U(1)(N) gauge symmetry. We show that the conservation of the quantum number F = L+B forbids the appearance of massive neutrinos and the neutrinoless double-beta decay (beta beta)(0 nu). Explicit or/and spontaneous breaking of F implies that the neutrinos have an arbitrary mass. In addition the (beta beta)(0 nu) decay also has some channels that do not depend explicitly on the neutrino mass.

HEAVY CHARGED LEPTONS IN AN SU(3)L-CIRCLE-TIMES-U(1)N MODEL

We consider an SU(3)L x U(1)N model for the electroweak interactions which includes extra charged leptons which do not mix with the known leptons. These new leptons couple to Z0 only through vector currents. We consider constraints on the mass of one of these leptons coming from the Z0 width and from the muon (g - 2) factor. The last one is less restrictive than the former.

SU(3)CIRCLE-TIMES-U(1) MODEL FOR ELECTROWEAK INTERACTIONS

We consider a gauge model based on a SU(3)XU(1) symmetry in which the lepton number is violated explicitly by charged scalar and gauge bosons, including a vector field with double electric