Natural Higher-Derivatives Generalization for the Klein-Gordon Equation

Abstract

We propose a natural family of higher-order partial differential equations generalizing the second-order Klein-Gordon equation. We characterize the associated model by means of a generalized action for a scalar field, containing higher-derivative terms. The limit obtained by considering arbitrarily higher-order powers of the d'Alembertian operator leading to a formal infinite-order partial differential equation is discussed. The general model is constructed using the exponential of the d'Alembertian differential operator. The canonical energymomentum tensor densities and field propagators are explicitly computed. We consider both homogeneous and non-homogeneous situations. The classical solutions are obtained for all cases.

BFFT Nonlinear Constraints Abelianization of a Prototypical Second-Class System

“…where we have used w = m −1 , as can be checked from ( 14) to be the case for the current example. In equation ( 58) above we have of course Q rr = 0 while Q θθ and Q φφ are given by the two non-null entries in (56). In passing, we notice that w = m −1 fulfills the condition (15) for a genuine second-class system.…”

“…We are using here the compact notation introduced in reference [56], by which equation ( 29) above more explicitly means…”

“…In this way, using the compact notation of [56], we may expand F in Taylor series in the BFFT variable η…”

“…The functions T , f rr , f θθ , Q rr , and Q θθ obtainted from equations ( 53), ( 55) and (56), can be extended to fulfill condition (44) by solving the relations (45) as in (47). Specifically, using the recursive relations (47) and the expansion (42), we compute…”