A real-time thermal field theoretical analysis of Kubo-type shear viscosity: Numerical understanding with simple examples

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

Renormalization of fermion mixing

Precision measurements of phenomena related to fermion mixing require the inclusion of higher order corrections in the calculation of corresponding theoretical predictions. For this, a complete renormalization scheme for models that allow for fermion mixing is highly required. The correct treatment of unstable particles makes this task difficult and yet, no satisfactory and general solution can be found in the literature. In the present work, we study the renormalization of the fermion Lagrange density with Dirac and Majorana particles in models that involve mixing. The first part of the thesis provides a general renormalization prescription for the Lagrangian, while the second one is an application to specific models. In a general framework, using the on-shell renormalization scheme, we identify the physical mass and the decay width of a fermion from its full propagator. The so-called wave function renormalization constants are determined such that the subtracted propagator is diagonal on-shell. As a consequence of absorptive parts in the self-energy, the constants that are supposed to renormalize the incoming fermion and the outgoing antifermion are different from the ones that should renormalize the outgoing fermion and the incoming antifermion and not related by hermiticity, as desired. Instead of defining field renormalization constants identical to the wave function renormalization ones, we differentiate the two by a set of finite constants. Using the additional freedom offered by this finite difference, we investigate the possibility of defining field renormalization constants related by hermiticity. We show that for Dirac fermions, unless the model has very special features, the hermiticity condition leads to ill-defined matrix elements due to self-energy corrections of external legs. In the case of Majorana fermions, the constraints for the model are less restrictive. Here one might have a better chance to define field renormalization constants related by hermiticity. After analysing the complete renormalized Lagrangian in a general theory including vector and scalar bosons with arbitrary renormalizable interactions, we consider two specific models: quark mixing in the electroweak Standard Model and mixing of Majorana neutrinos in the seesaw mechanism. A counter term for fermion mixing matrices can not be fixed by only taking into account self-energy corrections or fermion field renormalization constants. The presence of unstable particles in the theory can lead to a non-unitary renormalized mixing matrix or to a gauge parameter dependence in its counter term. Therefore, we propose to determine the mixing matrix counter term by fixing the complete correction terms for a physical process to experimental measurements. As an example, we calculate the decay rate of a top quark and of a heavy neutrino. We provide in each of the chosen models sample calculations that can be easily extended to other theories.

HIGHER-DERIVATIVE SCHWINGER MODEL

Using the operator formalism, we obtain the bosonic representation for the free fermion field satisfying an equation of motion with higher-order derivatives. Then, we consider the operator solution of a generalized Schwinger model with higher-derivative coupling. Since the increasing of the derivative order implies the introduction of an equivalent number of extra fermionic degrees of freedom, the mass acquired by the gauge field is bigger than the one for the standard two-dimensional QED. An analysis of the problem from the functional integration point of view corroborates the findings of canonical quantization, and corrects certain results previously announced in the literature on the basis of Fujikawa's technique.

The Schwinger model on the null-plane

We study the Schwinger Model on the null-plane using the Dirac method for constrained systems. The fermion field is analyzed using the natural null-plane projections coming from the γ-algebra and it is shown that the fermionic sector of the Schwinger Model has only second class constraints. However, the first class constraints are exclusively of the bosonic sector. Finally, we establish the graded Lie algebra between the dynamical variables, via generalized Dirac bracket in the null-plane gauge, which is consistent with every constraint of the theory. © World Scientific Publishing Company.

O operador espalhamento para férmions num campo externo em Thermofield Dynamics

Pós-graduação em Física - IFT

Mean-field description of a dynamical collapse of a fermionic condensate in a trapped boson-fermion mixture

We suggest a time-dependent dynamical mean-field-hydrodynamic model for the collapse of a trapped boson-fermion condensate and perform numerical simulation based on it to understand some aspects of the experiment by Modugno et al. [Science 297, 2240 (2002)] on the collapse of the fermionic condensate in the K-40-Rb-87 mixture. We show that the mean-field model explains the formation of a stationary boson-fermion condensate at zero temperature with relative sizes compatible with experiment. This model is also found to yield a faithful representation of the collapse dynamics in qualitative agreement with experiment. In particular we consider the collapse of the fermionic condensate associated with (a) an increase of the number of bosonic atoms as in the experiment and (b) an increase of the attractive boson-fermion interaction using a Feshbach resonance. Suggestion for experiments of fermionic collapse using a Feshbach resonance is made.

Fermion localization on two-field thick branes

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Dynamical Lorentz and CPT symmetry breaking in a 4D four-fermion model

In a 4D chiral Thirring model we analyze the possibility that radiative corrections may produce spontaneous breaking of Lorentz and CPT symmetry. By studying the effective potential, we verified that the chiral current (psi) over bar gamma(mu)gamma(5)psi may assume a nonzero vacuum expectation value which triggers Lorentz and CPT violations. Furthermore, by making fluctuations on the minimum of the potential we dynamically induce a bumblebee-like model containing a Chem-Simons term.

Effect of disorder on quantum phase transitions in anisotropic XY spin chains in a transverse field

We present some exact results for the effect of disorder on the critical properties of an anisotropic XY spin chain in a transverse held. The continuum limit of the corresponding fermion model is taken and in various cases results in a Dirac equation with a random mass. Exact analytic techniques can then be used to evaluate the density of states and the localization length. In the presence of disorder the ferromagnetic-paramagnetic or Ising transition of the model is in the same universality class as the random transverse field Ising model solved by Fisher using a real-space renormalization-group decimation technique (RSRGDT). If there is only randomness in the anisotropy of the magnetic exchange then the anisotropy transition (from a ferromagnet in the x direction to a ferromagnet in the y direction) is also in this universality class. However, if there is randomness in the isotropic part of the exchange or in the transverse held then in a nonzero transverse field the anisotropy transition is destroyed by the disorder. We show that in the Griffiths' phase near the Ising transition that the ground-state energy has an essential singularity. The results obtained for the dynamical critical exponent, typical correlation length, and for the temperature dependence of the specific heat near the Ising transition agree with the results of the RSRODT and numerical work. [S0163-1829(99)07125-8].

Transport properties of strongly correlated metals: A dynamical mean-field approach

The temperature dependence of the transport properties of the metallic phase of a frustrated Hubbard model on the hypercubic lattice at half-filling is calculated. Dynamical mean-held theory, which maps the Hubbard model onto a single impurity,Anderson model that is solved self-consistently, and becomes exact in the limit of large dimensionality, is used. As the temperature increases there is a smooth crossover from coherent Fermi liquid excitations at low temperatures to incoherent excitations at high temperatures. This crossover leads to a nonmonotonic temperature dependence for the resistance, thermopower, and Hall coefficient, unlike in conventional metals. The resistance smoothly increases from a quadratic temperature dependence at low temperatures to large values which can exceed the Mott-Ioffe-Regel value ha/e(2) (where a is a lattice constant) associated with mean free paths less than a lattice constant. Further signatures of the thermal destruction of quasiparticle excitations are a peak in the thermopower and the absence of a Drude peak in the optical conductivity. The results presented here are relevant to a wide range of strongly correlated metals, including transition metal oxides, strontium ruthenates, and organic metals.

Fermion perturbations in string theory black holes

In this paper we study fermion perturbations in four-dimensional black holes of string theory, obtained either from a non-extreme configuration of three intersecting five-branes with a boost along the common string or from a non-extreme intersecting system of two two-branes and two five-branes. The Dirac equation for the massless neutrino field, after conformal re-scaling of the metric, is written as a wave equation suitable to study the time evolution of the perturbation. We perform a numerical integration of the evolution equation, and with the aid of Prony fitting of the time-domain profile, we calculate the complex frequencies that dominate the quasinormal ringing stage, and also determine these quantities by the semi-analytical sixth-order WKB method. We also find numerically the decay factor of fermion fields at very late times, and show that the falloff is identical to those showing for massless fields in other four-dimensional black hole spacetimes.

Fock space for fermion-like lattices and the linear Glauber model

The concept of Fock space representation is developed to deal with stochastic spin lattices written in terms of fermion operators. A density operator is introduced in order to follow in parallel the developments of the case of bosons in the literature. Some general conceptual quantities for spin lattices are then derived, including the notion of generating function and path integral via Grassmann variables. The formalism is used to derive the Liouvillian of the d-dimensional Linear Glauber dynamics in the Fock-space representation. Then the time evolution equations for the magnetization and the two-point correlation function are derived in terms of the number operator. (C) 2008 Elsevier B.V. All rights reserved.

Structural aspects of the fermion-boson mapping in two-dimensional gauge and anomalous gauge theories with massive fermions

Using a synthesis of the functional integral and operator approaches we discuss the fermion-buson mapping and the role played by the Bose field algebra in the Hilbert space of two-dimensional gauge and anomalous gauge field theories with massive fermions. In QED, with quartic self-interaction among massive fermions, the use of an auxiliary vector field introduces a redundant Bose field algebra that should not be considered as an element of the intrinsic algebraic structure defining the model. In anomalous chiral QED, with massive fermions the effect of the chiral anomaly leads to the appearance in the mass operator of a spurious Bose field combination. This phase factor carries no fermion selection rule and the expected absence of Theta-vacuum in the anomalous model is displayed from the operator solution. Even in the anomalous model with massive Fermi fields, the introduction of the Wess-Zumino field replicates the theory, changing neither its algebraic content nor its physical content. (C) 2002 Elsevier B.V. (USA).

Effective action for QED with fermion self-interaction in D=2 and D=3 dimensions

In this work we discuss the effect of the quartic fermion self-interaction of Thirring type in QED in D=2 and D=3 dimensions. This is done through the computation of the effective action up to quadratic terms in the photon field. We analyze the corresponding nonlocal photon propagators nonperturbatively in k/m, where k is the photon momentum and m the fermion mass. The poles of the propagators were determined numerically by using the MATHEMATICA software. In D=2 there is always a massless pole whereas for strong enough Thirring coupling a massive pole may appear. For D=3 there are three regions in parameter space. We may have one or two massive poles or even no pole at all. The interquark static potential is computed analytically in D=2. We notice that the Thirring interaction contributes with a screening term to the confining linear potential of massive two-dimensional QED (QED(2)). In D=3 the static potential must be calculated numerically. The screening nature of the massive QED(3) prevails at any distance, indicating that this is a universal feature of D=3 electromagnetic interaction. Our results become exact for an infinite number of fermion flavors.

Fermion localization on a split brane

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)