Perturbative Approach to Higher Derivative and Nonlocal Theories

Abstract

We review a perturbative approach to deal with Lagrangians with higher or infinite order time derivatives. It enables us to construct a consistent Poisson structure and Hamiltonian with only first time derivatives order by order in coupling. To the lowest order, the Hamiltonian is bounded from below whenever the potential is. We consider spacetime noncommutative field theory as an example.

19 pages, Latex, reference added

References in corpus (5)

• Remarks on Time-Space Noncommutative Field Theories
• On the unitarity of quantum gauge theories on non-commutative spaces
• Remarks on the canonical quantization of noncommutative theories
• Dimensional Reduction via Noncommutative Spacetime: Bootstrap and Holography
• A Note on Unitarity of Non-Relativistic Non-Commutative Theories

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