Higher-derivative non-Abelian gauge fields via the Faddeev-Jackiw formalism

In this paper we analyze two higher-derivative theories, the generalized electrodynamics and the Alekseev-Arbuzov-Baikov's effective Lagrangian from the point of view of Faddeev-Jackiw sympletic approach. It is shown that the full set of constraint is obtained directly from the zero-mode eigenvectors, and that they are in accordance with known results from Dirac's theory, a remnant and recurrent issue in the literature. The method shows to be rather economical in relation to the Dirac's one, obviating thus unnecessary classification and calculations. Afterwards, to conclude we construct the transition-amplitude of the non-Abelian theory following a constrained BRST-method.Comment: 17 page

Nonperturbative Aspects of the two-dimensional Massive Gauged Thirring Model

In this paper we present a study based on the use of functional techniques on the issue of insertions of massive fermionic fields in the two-dimensional massless Gauged Thirring Model. As it will be shown, the fermionic mass contributes to the Green's functions in a surprisingly simple way, leaving therefore the original nonperturbative nature of the massless results still intact in the massive theory. Also, by means of complementarity, we present a second discussion of the massive model, now at its bosonic representation.Comment: 18 pages, to appear at Int. J. Mod. Phys.

Spin Glass Field Theory with Replica Fourier Transforms

We develop a field theory for spin glasses using Replica Fourier Transforms (RFT). We present the formalism for the case of replica symmetry and the case of replica symmetry breaking on an ultrametric tree, with the number of replicas $n$ and the number of replica symmetry breaking steps $R$ generic integers. We show how the RFT applied to the two-replica fields allows to construct a new basis which block-diagonalizes the four-replica mass-matrix, into the replicon, anomalous and longitudinal modes. The eigenvalues are given in terms of the mass RFT and the propagators in the RFT space are obtained by inversion of the block-diagonal matrix. The formalism allows to express any $i$-replica vertex in the new RFT basis and hence enables to perform a standard perturbation expansion. We apply the formalism to calculate the contribution of the Gaussian fluctuations around the Parisi solution for the free-energy of an Ising spin glass.Comment: 39 pages, 3 figure