Complete factorization of equations of motion for generalized scalar field theories

Abstract

-We demonstrate that the complete factorization of equations of motion into first-order differential equations can be obtained for real and complex scalar field theories with non-canonical dynamics.Introduction. -In 1934, Born and Infeld (BI) proposed a nonlinear generalization of electrodynamics [1] to avoid the divergence problem with the electron self-energy. It is an important example where nonlinear dynamics may play a role and it was later shown that such action, now called DBI action [1,2], arises naturally in the context of string theory [3]. Some examples of its usage can be seen as, for instance: an effective action for the tachyon condensation [4]; a string theory model to describe the early inflationary period of the universe [5]; in cosmology a scalar DBI action can be used to describe the acceleration of the universe [6], as well as the inflationary period in the early universe [7]; models with the presence of instanton solutions [8], the description of global strings [9]; vortex solutions [10,11]; formulation of twinlike models [12] and so on. More recently, several analytical models described within the DBI context admitting kinks solutions were explored in Ref. [13]. The DBI model opened up a new road to consider non-canonical dynamics and to deal with more general forms of the kinetic term.Domain walls and branes have drawn a lot of attention to the physics community [14] and may appear when the scalar field has nonlinear dynamics as well. Some examples include: in [15] one investigates specific features of kinks and vortices; in [16][17][18][19] one studies how the modifications on the kinetic part of the Lagrangian introduce new nonlinear terms to the equations of motion, which can permit the appearance of compact solutions [16][17][18], also known as compactons [20]; in [21] the defect structure within a scalar generalized profile is studied; and in [22,23] the braneworld scenario is also investigated.

Multi-component scalar fields and the complete factorization of its equations of motion

“…In the Ref. [11], the authors show that this demonstration is valid in a scalar field model with non-canonical dynamics. In our work we demonstrate that this equivalence is valid for the most general scalar field model by treating the single and multi-component scalar field cases.…”

“…In [9,10], the authors demonstrate the equivalence between the second-order differential equation of motion and a family of first-order differential equations of BogomolâĂŹnyi type in the bosonic sectors of supersymmetric theories. This result was extended in [11] to the cases of single real and complex scalar fields theories with a non-standard kinetic term.…”

“…This result is a extension of what was introduced in Refs. [9][10][11] to the case of a single real scalar with the general first-order framework introduced in Ref. [2].…”

“…The main goal of this paper is to extend the demonstration found in [9-11] to a system described by multi-component real scalar fields. This paper is organized as follows: in the section II we extend the demonstration presented in [9][10][11] for the single real scalar field case to a case where the Lagrangian can develop a more general dependence on the kinetic and potential terms; in the section III, we treat the multi-component scalar field case. We work in (1 + 1)dimensional spacetime with metric (+, −) and for simplicity we adopt dimensionless field, spacetime coordinates and coupling constants.…”

Kinklike structures in an arcsin real scalar dynamics

“…where the implementation of the first-order formalism for the Lagrangian ( 16) can be found in [19]. For F (X) = X, the standard dynamics is recover.…”