A class of QFTs with higher derivative field equations leading to standard dispersion relation for the particle excitations

Abstract

Given any (Feynman) propagator which is Lorentz and translation invariant, it is possible to construct an action functional for a scalar field such that the quantum field theory, obtained by path integral quantization, leads to this propagator. In general, such a theory will involve derivatives of the field higher than two and can even involve derivatives of infinite order. The poles of the given propagator determine the dispersion relation for the excitations of this field. I show that it is possible to construct field theories in which the dispersion relation is the same as that of standard Klein-Gordan field, even though the Lagrangian contains derivatives of infinite order. I provide a concrete example of this situation starting from a propagator which incorporates the effects of the zero-point-length of the spacetime. I compare the path integral approach with an alternative, operator-based approach, and highlight the advantages of using the former.

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• Thermodynamic structure of Lanczos-Lovelock field equations from near-horizon symmetries
• Grin of the Cheshire cat: Entropy density of spacetime as a relic from quantum gravity
• Path integral duality modified propagators in spacetimes with constant curvature
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Cited by in corpus (4)

• Covariant formulation of Generalised Uncertainty Principle
• Ultraviolet dimensional reduction of spacetime with zero-point length
• World-line Path integral for the Propagator expressed as an ordinary integral: Concept and Applications
• Discrete time heat kernel and UV modified propagators with Dimensional Deconstruction