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arXiv · 1801.02582

Continuum Modes of Nonlocal Field Theories

Mehdi Saravani
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Abstract

A class of nonlocal Lorentzian quantum field theories is introduced in arXiv:1502.01655 and arXiv:1411.6513, where the d'Alembertian operator $\Box$ is replaced by a non-analytic function of the d'Alembertian, $f(\Box)$. This is inspired by the Causal Set program where such an evolution arises as the continuum limit of a wave equation on causal sets. The spectrum of these theories contains a continuum of massive excitations. This is perhaps the most important feature which leads to distinct/interesting phenomenology. In this paper, we study properties of the continuum massive modes in depth. We derive the path integral formulation of these theories. Meanwhile, this derivation introduces a dual picture in terms of local fields which clearly shows how continuum massive modes of the nonlocal field interact. The dual picture, in principle, provides a path to extension beyond scalar fields and addressing the issue of renormalization.

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Mehdi Saravani. 2018-01-08. Continuum Modes of Nonlocal Field Theories. https://doi.org/10.1088/1361-6382%2Faaaea8

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