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

Abstract

In this paper we analyze two higher-derivative theories, the generalized electrodynamics and the AlekseevArbuzov-Baikov effective Lagrangian from the point of view of the Faddeev-Jackiw symplectic approach. It is shown that the full set of constraints is obtained directly from the zeromode eigenvectors, and that they are in accordance with wellknown results from Dirac's theory, a recurrent issue in the literature. The method shows to be rather economical in relation to the Dirac 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.

Faddeev–Jackiw approach of noncommutative space–time electromagnetic theories

“…which are the equations of motion. However, if det(f αβ ) = 0 we have that f αβ is singular and we cannot write the velocities as in (9). In order to describe the symplectic formalism with constraints [6], let us denote f αβ as f…”

Reduction of order and Fadeev–Jackiw formalism in generalized electrodynamics

“…The neat separation between the Maxwell and Proca sectors is a distinctive feature of the (FJ) formalism applied to the reduced order Podolsky electrodynamics, which does not happen within the Ortogradsky formalism [39].…”

Thermal effective Lagrangian of generalized electrodynamics in static gravitational fields

“…Therefore, from the result (20) and subsequent manipulation on the change of variables (21), we can deal properly with the metric dependence, and the expressions (13) and (14) are written simply as…”

“…As it has been pointed out in several works [15][16][17][18][19][20] along the years, it is long clear that Maxwell's theory is not the only one to describe the electromagnetic field. One of the most successful generalizations is the generalized electrodynamics [15].…”