arXiv subjects
Publications and source records attributed to J. Barcelos-Neto.
We study the 0+1 dimensional Chern-Simons theory at finite temperature within the framework of derivative expansion. We obtain various interesting relations, solve the theory within this framework and argue that the derivative expansion is not a suitable formalism for a study of the question of large gauge invariance.
We study the problem of axial and gauge anomalies in a reducible theory involving vector and tensor gauge fields coupled in a topological way. We consider that vector and axial fermionic currents couple with the tensor field in the same topological manner as the vector gauge one. This kind of coupling leads to an anomalous axial current, contrarily to the results found in literature involving other tensor couplings, where no anomaly is obtained.
We propose a systematic method of dealing with the canonical constrained structure of reducible systems in the Dirac and symplectic approaches which involves an enlargement of phase and configuration spaces, respectively. It is not necessary, as in the Dirac approach, to isolate the independent subset of constraints or to introduce, as in the symplectic analysis, a series of lagrange multipliers-for-lagrange multipiers. This analysis illuminates the close connection between the Dirac and symplectic approaches of treating reducible theories, which is otherwise lacking. The example of p-form gauge fields (p=2,3) is analyzed in details.
We use an extension of the method due to Batalin, Fradkin, Fradkina, and Tyutin (BFFT) for transforming the nonlinear $σ$ model in a non-Abelian gauge theory. We deal with both supersymmetric and nonsupersymmetric cases. The bosonic case was already considered in literature but just gauged with an Abelian algebra. We show that the supersymmetric version is only compatible with a non-Abelian gauge theory. The usual BFFT method for this case leads to a nonlocal algebra.
Using the general notions of Batalin, Fradkin, Fradkina and Tyutin to convert second class systems into first class ones, we present a gauge invariant formulation of the massive Yang-Mills theory by embedding it in an extended phase space. The infinite set of correction terms necessary for obtaining the involutive constraints and Hamiltonian is explicitly computed and expressed in a closed form. It is also shown that the extra fields introduced in the correction terms are exactly identified with the auxiliary scalars used in the generalized Stückelberg formalism for converting a gauge noninvariant Lagrangian into a gauge invariant form.
We consider the method due to Batalin, Fradkin, Fradkina, and Tyutin (BFFT) that makes the conversion of second-class constraints into first-class ones for the case of nonlinear theories. We first present a general analysis of an attempt to simplify the method, showing the conditions that must be fulfilled in order to have first-class constraints for nonlinear theories but that are linear in the auxiliary variables. There are cases where this simplification cannot be done and the full BFFT method has to be used. However, in the way the method is formulated, we show with details that it is not practicable to be done. Finally, we speculate on a solution for these problems.
We use the method due to Batalin, Fradkin, Fradkina, and Tyutin (BFFT) in order to convert second-class into first-class constraints for some quantum mechanics supersymmetric theories. The main point to be considered is that the extended theory, where new auxiliary variables are introduced, has to be supersymmetric too. This leads to some additional restrictions with respect the conventional use of the BFFT formalism.
We consider the Salam-Weinberg theory by introducing tensor gauge fields. When these fields are coupled in a topological way with the vector ones, the resulting system constitutes an alternative mechanism of mass generation for vector fields without the presence of Higgs bosons. We show that these masses are in agreement with the ones obtained by means of the spontaneous symmetry breaking.
We make a comparative study of chiral-boson theories in the Florenani-Jackiw (FJ) and linear constraint formulations. A special attention is given to the case with an improved way of implementing the linear constraint. We show that it has the same spectrum of the FJ formulation.
We use the BV quantization method for a theory with coupled tensor and vector gauge fields through a topological term. We consider in details the reducibility of the tensorial sector as well as the appearance of a mass term in the effective vectorial theory .
The field-antifield quantization method is used to calculate the trace anomaly for a massless scalar field in a curved background, by means of the zeta function regularization procedure.
We study an extension of the axial model where local gauge symmetries are taken into account. The anomaly of the axial current is calculated by the Fujikawa formalism and the model is also solved. Besides the well known features of the particular models (axial and Schwinger) it was obtained an effective interaction of scalar and gauge fields via a topological current.
We quantize the Einstein gravity in the formalism of weak gravitational fields by using the constrained Hamiltonian method. Special emphasis is given to the 2+1 spacetime dimensional case where a (topological) Chern-Simons term is added to the Lagrangian.
We study an extension of the symplectic formalism in order to quantize reducible systems. We show that a procedure like {\it ghost-of-ghost} of the BFV method can be applied in terms of Lagrange multipliers. We use the developed formalism to quantize the antisymmetric Abelian gauge fields.
We use the method due to Batalin, Fradkin and Tyutin (BFT) for the quantization of chiral boson theories. We consider the Floreanini-Jackiw (FJ) formulation as well as others with linear constraints.
We study the Chern-Simons theory coupled to matter field by means of an effective Lagrangian obtained from the Batalin-Fradkin-Vilkovisky formalism. We show that there is no rotational anomaly for any proper gauge we choose.
We study the symplectic quantization of Abelian gauge theories in $2+1$ space-time dimensions with the introduction of a topological Chern-Simons term.
We consider the even parity superLax operator for the supersymmetric KP hierarchy of the form $L~=~D^2 + \sum_{i=0}^\infty u_{i-2} D^{-i+1}$ and obtain the two Hamiltonian structures following the standard method of Gelfand and Dikii. We observe that the first Hamiltonian structure is local and linear whereas the second Hamiltonian structure is non-local and nonlinear among the superfields appearing in the Lax operator. We discuss briefly on their connections with the super $w_{\infty}$ algebra.