We study the equivalence between the self-dual and the Maxwell-Chern-Simons (MCS) models coupled to dynamical, U(1) charged matter, both fermionic and bosonic. This is done through an iterative procedure of gauge embedding that produces the dual mapping of the self-dual vector field theory into a Maxwell-Chern-Simons version. In both cases, to establish this equivalence a current-current interaction term is needed to render the matter sector unchanged. Moreover, the minimal coupling of the original self-dual model is replaced by a non-minimal magnetic like coupling in the MCS side. Unlike the fermionic instance however, in the bosonic example the dual mapping proposed here leads to a Maxwell-Chern-Simons theory immersed in a field dependent medium.
The non-abelian version of the self-dual model proposed by Townsend, Pilch and van Nieuwenhuizen presents some well known difficulties not found in the abelian case, such as well defined duality operation leading to self-duality and dual equivalence with the Yang-Mills-Chern-Simons theory, for the full range of the coupling constant. These questions are tackled in this work using a distinct gauge lifting technique that is alternative to the master action approach first proposed by Deser and Jackiw. The master action, which has proved useful in exhibiting the dual equivalence between theories in diverse dimensions, runs into trouble when dealing with the non-abelian case apart from the weak coupling regime. This new dualization technique on the other hand, is insensitive of the non-abelian character of the theory and generalize straightforwardly from the abelian case. It also leads, in a simple manner, to the dual equivalence for the case of couplings with dynamical fermionic matter fields. As an application, we discuss the consequences of this dual equivalence in the context of 3D non-abelian bosonization.
In this work we give an alternative way which generalizes the recently implemented Neves-Wotzasek method of conversion from second to first-class systems. We have proved that this generalization is correct reproducing the results given in the literature using the case of a sphere with an antisymmetric generator as an example.
The Boltzmann equation with the Bhatnagar-Gross-Krook collision operator is considered for the Bose-Einstein and Fermi-Dirac equilibrium distribution functions. We show that the expansion of the microscopic velocity in terms of Hermite polynomials must be carried until the fourth order to correctly describe the energy equation. The viscosity and thermal coefficients, previously obtained by J.Y. Yang et al 1,2 through the Uehling-Uhlenbeck approach, are also derived here. Thus the construction of a lattice Boltzmann method for the quantum fluid is possible provided that the Bose-Einstein and Fermi-Dirac equilibrium distribution functions are expanded until fourth order in the Hermite polynomials.
The extension of the general relativity theory to higher dimensions, so that the field equations for the metric remain of second order, is done through the Lovelock action. This action can also be interpreted as the dimensionally continued Euler characteristics of lower dimensions. The theory has many constant coefficients apparently without any physical meaning. However, it is possible, in a natural way, to reduce to two (the cosmological and Newton's constant) these several arbitrary coefficients, yielding a restricted Lovelock gravity. In this process one separates theories in even dimensions from theories in odd dimensions. These theories have static black hole solutions. In general relativity, black holes appear as the final state of gravitational collapse. In this work, gravitational collapse of a regular dust fluid in even dimensional restricted Lovelock gravity is studied. It is found that black holes emerge as the final state for these regular initial conditions.
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