CP-violating non-linear electrodynamics and corrections to blackbody radiation thermal laws

TL;DR

This work analyzes CP-violating non-linear electrodynamics (NLED) within an effective-field-theory framework, focusing on photon propagation in a uniform magnetic background and the resulting bi-anisotropic vacuum when a CP-violating term is present. The authors derive modified field equations, perform a plane-wave analysis to obtain the CP-violating dispersion relations $w_{(\pm)}$, and define the group velocities, illustrating how a nonzero $d_3$ couples electric and magnetic perturbations. In the low-temperature regime $k_B T \ll m_e c^2$, they compute the photon partition function and show that the energy density $u$ remains proportional to $T^4$ but with a corrected coefficient $a$ through $\Phi_{(\pm)}$, which also modifies the Planck spectrum and the Stefan–Boltzmann law to $R(T) = \sigma_{\text{eff}} T^4$. The paper connects these corrections to Euler–Heisenberg and Born–Infeld models, discusses experimental bounds on the CP-violating parameters, and highlights potential observables in strong magnetic-field environments such as neutron stars, offering avenues for future astrophysical and string-theoretic investigations.

Abstract

Motivated by ideas from effective field theories, we conduct a twofold investigation in CP-violating non-linear electrodynamics models. On the one hand, features related to field equations and wave propagation in the presence of a magnetic background field are evaluated. Interestingly, we show that the CP-violating term in our framework induces a bi-anisotropic behavior of the vacuum. On the other hand, blackbody radiation thermal laws in this situation are studied. Here, we provide a general formalism for photons at low temperature, namely, with $k_{B}T\ll{m_{e}c^{2}}$. The deviations from standard values of the thermodynamic quantities, such as energy, pressure, entropy, and specific heat, are discussed. In addition, we investigate the modifications in the Planck distribution and the Stefan-Boltzmann law induced by a non-trivial CP-violating parameter.

Figures (3)

• Figure 1: Relative deviations in Eq. \ref{['rel_dev']} of Euler-Heisenberg (blue line) and Born-Infeld (dashed green line) models from Planck's blackbody radiation law (red line). We have assumed a temperature of $T=6 \times 10^5 \,K$ and a magnetic background field $B_0=10^{7} \, T$.
• Figure 2: Graph of the spectral energy density distribution for a surface temperature $T=6 \times 10^5 \,K$ and a magnetic background field $B_0= 4 \times 10^{11} \, T$. The red line corresponds to the Planck spectrum, while the blue and green are associated with CP-preserving and CP-violating non-linear electrodynamics, respectively.
• Figure 3: Relative deviations in Eq. \ref{['rel_dev']} of CP-preserving (blue line) and CP-violating (green line) models from Planck's blackbody radiation law (red line).