Discrete heat kernel, UV modified Green's function, and higher derivative theories
arXiv:2007.00220 · doi:10.1088/1361-6382/ac09cb
Abstract
We perform the UV deformation of the Green's function in free scalar field theory using a discrete heat kernel method. It is found that the simplest UV deformation based on the discretized diffusion equation leads to the well-known Pauli-Villars effective Lagrangian. Furthermore, by extending assumptions on the discretized equation, we find that the general higher derivative theory is derived from the present UV deformation. In some specific cases, we also calculate the vacuum expectation values of the scalar field squared in nontrivial background spaces and examine their dependence on the UV cutoff constant.
19 pages, 12 figures. final version
References in corpus (14)
- The Lee-Wick Standard Model
- A Higher-Derivative Lee-Wick Standard Model
- The quest for purely virtual quanta: fakeons versus Feynman-Wheeler particles
- The Lee-Wick Fields out of Gravity
- Nonlocal gravity with worldline inversion symmetry
- String-Inspired Infinite-Derivative Theories of Gravity: A Brief Overview
- TeV Scale Lee-Wick Fields out of Large Extra Dimensional Gravity
- Path integral duality modified propagators in spacetimes with constant curvature
- No Lee-Wick Fields out of Gravity
- Probing the Planck scale: The modification of the time evolution operator due to the quantum structure of spacetime
- Principle of Equivalence at Planck scales, QG in locally inertial frames and the zero-point-length of spacetime
- Vacuum expectation values in non-trivial background space from three types of UV improved Green's functions
- Worldline theories with towers of internal states
- A class of QFTs with higher derivative field equations leading to standard dispersion relation for the particle excitations