R. L. P. G. Amaral

Quantum electrodynamics in two dimensions at a finite-temperature thermofield bosonization approach*

The Schwinger model at finite temperature is analyzed using the thermofield dynamics formalism. The operator solution due to Lowenstein and Swieca is generalized to the case of finite temperature within the thermofield bosonization approach. The general properties of the statistical–mechanical ensemble averages of observables in the Hilbert subspace of gauge invariant thermal states are discussed. The bare charge and chirality of the Fermi thermofields are screened, giving rise to an infinite number of mutually orthogonal thermal ground states. One consequence of the bare charge and chirality selection rule at finite temperature is that there are innumerably many thermal vacuum states with the same total charge and chirality of the doubled system. The fermion charge and chirality selection rules at finite temperature turn out to imply the existence of a family of thermal theta-vacua states parametrized with the same number of parameters as in the zero temperature case.

Thermofield quantum electrodynamics in (1 + 1) dimensions at a finite chemical potential: a bosonization approach

The recent generalization of the Lowenstein–Swieca operator solution of quantum electrodynamics in (1+1) dimensions to a finite temperature in thermofield dynamics is further generalized to include a non-vanishing chemical potential. The operator solution to the Euler–Lagrange equations respecting the Kubo–Martin–Schwinger condition is constructed. Two forms of this condition and their associated solutions are discussed. The correlation functions of an arbitrary number of chiral densities are computed in the thermal θ-vacuum.

On The Complete Seiberg-Witten Map For Theories With Topological Terms

The SW map problem is formulated and solved in the BRST cohomological approach. The well known ambiguities of the SW map are shown to be associated to distinct cohomological classes. This analysis is applied to the noncommutative Chern-Simons action resulting in the emergence of θ-dependent terms in the commutative action which come from the nontrivial ambiguities. It is also shown how a specific cohomological class can be choosen in order to map the noncommutative Maxwell-Chern-Simons theory into the commutative one.

A new picture on the (3+1)D topological mass mechanism

We present a class of mappings between the fields of the Cremmer–Sherk and pure BF models in 4D. These mappings are established by two distinct procedures. First, a mapping of their actions is produced iteratively resulting in an expansion of the fields of one model in terms of progressively higher derivatives of the other model fields. Second, an exact mapping is introduced by mapping their quantum correlation functions. The equivalence of both procedures is shown by resorting to the invariance under field scale transformations of the topological action. Related equivalences in 5D and 3D are discussed. The mapping in (2+1)D from the Maxwell–Chern–Simons to pure Chern–Simons models is investigated from a similar perspective.

The Seiberg-Witten map for the 4D noncommutative BF theory

We describe the Seiberg–Witten map taking the 4D noncommutative BF theory (NCBF) into its pure commutative version. The existence of this map is in agreement with the hypothesis that such maps are available for any noncommutative theory with Schwarz-type topological sectors, and represents a strong indication for the renormalizability of these theories in general.

Topological mass mechanism and exact fields mapping

We present a class of mappings between models with topological mass mechanism and purely topological models in arbitrary dimensions. These mappings are established by directly mapping the fields of one model in terms of the fields of the other model in closed expressions. These expressions provide the mappings of their actions as well as the mappings of their propagators. For a general class of models in which the topological model becomes the BF model the mappings present arbitrary functions which otherwise are absent for Chern–Simons like actions. This work generalizes the results of (Ventura O S, Amaral R L P G, Costa J V, Buffon L O and Lemes V E R 2004 J. Phys. A: Math. Gen. 37 11711–23) for arbitrary dimensions.

HIGHER-DERIVATIVE TWO-DIMENSIONAL MASSIVE FERMION THEORIES

We consider the canonical quantization of a generalized two-dimensional massive fermion theory containing higher odd-order derivatives. The requirements of Lorentz invariance, hermiticity of the Hamiltonian and absence of tachyon excitations suffice to fix the mass term, which contains a derivative coupling. We show that the basic quantum excitations of a higher-derivative theory of order 2N+1 consist of a physical usual massive fermion, quantized with positive metric, plus 2N unphysical massless fermions, quantized with opposite metrics. The positive-metric Hilbert subspace, which is isomorphic to the space of states of a massive free fermion theory, is selected by a subsidiary-like condition. Employing the standard bosonization scheme, the equivalent boson theory is derived. The results obtained are used as a guideline to discuss the solution of a theory including a current–current interaction.

Kelvin transformation and inverse multipoles in electrostatics

The inversion in the sphere or Kelvin transformation, which exchanges the radial coordinate for its inverse, is used as a guide to relate distinct electrostatic problems with dual features. The exact solution of some nontrivial problems are obtained through the mapping from simple highly symmetric systems. In particular, the concept of multipole expansion is revisited from a point of view opposed to the usual one: the sources are distributed in a region far from the origin while the electrostatic potential is described at points close to it.

CHARGE FLUCTUATIONS IN SOLITON–ANTISOLITON SYSTEMS WITHOUT CONJUGATION SYMMETRY

We analyze the fluctuations of charge of the (1+1)-dimensional Diracs fermion with charge conjugation breaking. This is done taking the separation between background soliton and antisoliton going to infinity.

Mappings From Models Presenting Topological Mass Mechanisms to Purely Topological Models

We duscuss a class of mappings between the fields of the Cremmer‐Sherk and pure BF model in 4D. These mappings are established both with an iterative procedure as well as with an exact mapping procedure. Related equivalences in 5D and 3D are discussed.