Variational method for nonconservative field theories: Formulation and twoPT-symmetric case examples

Abstract

In a recent publication [Galley, Phys. Rev. Lett. 110, 174301 (2013)], Galley proposed an initial value problem formulation of Hamilton's principle that enables consideration of dissipative systems. Here we explore this formulation at the level of field theories with infinite degrees of freedom. In particular, we illustrate that it affords a previously unwarranted and appealing as well as broadly relevant possibility, namely, to generalize the popular collective coordinate or variational method to open systems, i.e., nonconservative ones. To showcase the relevance or validity of the method we explore two case examples from the timely area of $\mathcal{PT}$-symmetric variants of field theories, in this case for a sine-Gordon and for a ${\ensuremath{\phi}}^{4}$ model.