Waves in Bopp-Landé-Thomas-Podolsky generalized electrodynamics

TL;DR

BLTP electrodynamics modifies vacuum by a length scale $l$ that introduces a massive-photon–like BLTP mode in addition to standard Maxwell waves. The paper derives complete dispersion relations for both vacuum and a cold, non-magnetized plasma, revealing notable features such as longitudinal BLTP_- modes with negative group velocity while preserving forward energy flux and a causal signal velocity $c$. Practical detection of BLTP effects in the lab is hindered by the stringent bound $l\lesssim 10^{-18}$ m, which pushes propagating BLTP modes to Gamma-ray frequencies and yields minuscule deviations in plasma dispersion. Despite these challenges, the findings highlight distinctive BLTP signatures, including negative-group-velocity longitudinal modes and density-dependent transverse branches, that conceptually distinguish BLTP from standard Maxwell theory.

Abstract

We investigate the feasibility of probing Bopp-Landé-Thomas-Podolsky generalized electrodynamics with traveling and standing wave experiments. We consider wave propagation in vacuum and in a cold and non-magnetized plasma. Dispersion relations are found for all possible transverse and longitudinal modes. Longitudinal traveling waves are found which exhibit negative group velocities.

Figures (6)

• Figure 1: Group and phase velocities for the (transverse and longitudinal) BLTP modes in vacuum. In the case of the Maxwell modes only the transverse modes exist.
• Figure 2: Dispersion relations of the longitudinal BLTP$_+$ and BLTP$_-$ modes for a plasma frequency that is subcritical (solid blue and black lines) $\omega_p = 0.45 \frac{c}{l}$, critical (dash dotted) $\omega_p = 0.5 \frac{c}{l}$ and supercritical (dashed) $\omega_p = 0.55 \frac{c}{l}$. For comparison the dispersion relation of the analogous Maxwell plasma using the respective plasma frequency is given in green and the vacuum BLTP is given in red.
• Figure 3: Group and phase velocities for longitudinal modes in a plasma for subcritical, critical (top panel) and supercritical (bottom panel) densities. In each panel we combine the plots for the BLTP$_+$ modes (solid line) and for the BLTP$_-$ (dashed line) in one diagram. For the BLTP$_+$ modes the group velocity is always positive and defined above a minimum frequency, for the BLTP$_-$ the group velocity is always negative and defined below a maximum frequency.
• Figure 4: Dispersion relations of transverse waves. The lines describing plasma dispersion relations use $\omega_p = 0.45 \frac{c}{l}$.
• Figure 5: Deviation from the Maxwell case of the minimum frequency for transverse modes, as a function of the plasma frequency