Pauli–Villars regularization elucidated in Bopp–Podolsky’s generalized electrodynamics

Abstract

We discuss an inherent Pauli-Villars regularization in Bopp-Podolsky's generalized electrodynamics. Introducing gauge-fixing terms for Bopp-Podolsky's generalized electrodynamic action, we realize a unique feature for the corresponding photon propagator with a built-in Pauli-Villars regularization independent of the gauge choice made in Maxwell's usual electromagnetism. According to our realization, the length dimensional parameter a associated with Bopp-Podolsky's higher order derivatives corresponds to the inverse of the Pauli-Villars regularization mass scale Λ, i.e. a = 1/Λ. Solving explicitly the classical static Bopp-Podolsky's equations of motion for a specific charge distribution, we explore the physical meaning of the parameter a in terms of the size of the charge distribution. As an offspring of the generalized photon propagator analysis, we also discuss our findings regarding on the issue of the two-term vs. three-term photon propagator in light-front dynamics. arXiv:1902.07632v1 [hep-th]

Special relativity on the light-front

“…In this senseat least in principle -the quantum field formulation would be simpler. This is the very fact that have encouraged many to apply this formulation in the light front for more complex cases like gauge fields in quantum electrodynamics [17,18] and quantum chromodynamics.…”

Green functions and propagation in the Bopp–Podolsky electrodynamics

“…where G is the Green function of the d'Alembert equation (24) and G KG is the Green function of the Klein-Gordon equation (25). It can be seen that the Bopp-Podolsky equation (20) [35])…”

“…The Bopp-Podolsky electrodynamics is akin to the Pauli-Villars regularization procedure used in quantum electrodynamics (see, e.g., [21,23,13,24]). Therefore, the Bopp-Podolsky electrodynamics provides a regularization of the Maxwell electrodynamics based on higher order partial differential equations.…”

“…The two-dimensional Green functions (fundamental solutions) of the wave (d'Alembert) operator(24), the Klein-Gordon operator(25) and the Bopp-Podolsky (Klein-Gordon-Plots of the two-dimensional Bopp-Podolsky Green function for c =…”

Dirichlet boundary condition for the Lee–Wick-like scalar model

“…Some aspects of Lee-Wick models have been investigated, for example, in interactions between external sources [11], issues related with the ghosts problems [12][13][14], radiative corrections [15], propagation of waves [16], dual symmetry [17], phenomenological and cosmological implications [18][19][20][21][22][23][24][25][26], the connection with Pauli-Villars regularization [27], and so on. In fact, there is a vast literature concerning Lee-Wick models.…”