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Theories with an infinite number of derivatives are described by non-localLagrangians for which the standard Hamiltonian formalism cannot be applied.Hamiltonians of special types of non-local theories can be constructed by meansof the (1+1)-dimensional Hamiltonian formalism. In this paper, we consider asimple scalar field model inspired by the infinite derivative gravity and studyits reduced phase space by using this formalism. Assuming the expansion of thesolutions in the coupling constant, we compute the perturbative Hamiltonian andthe symplectic 2-form. We also discuss an example of a theory leading to aninfinite-dimensional reduced phase space for a different choice of the formfactor.

Hamiltonian for scalar field model of infinite derivative gravity