Special Issue: In Memory of Abdus Salam’s 90th Birthday (Part II)No Access

Lorentz invariant CPT breaking in the Dirac equation

Kazuo Fujikawa

Quantum Hadron Physics Laboratory, RIKEN Nishina Center, Wako 351-0198, Japan

E-mail Address: k-fujikawa@riken.jp

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and

Anca Tureanu

Department of Physics, University of Helsinki, P. O. Box 64, FIN-00014 Helsinki, Finland

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https://doi.org/10.1142/S0217751X17410147Cited by:4 (Source: Crossref)

Abstract

If one modifies the Dirac equation in momentum space to $[γ^{μ} p_{μ} - m - Δ m (𝜃 (p_{0}) - 𝜃 (- p_{0})) 𝜃 (p_{μ}^{2})] ψ (p) = 0$ , the symmetry of positive and negative energy eigenvalues is lifted by $m \pm Δ m$ for a small $Δ m$ . The mass degeneracy of the particle and antiparticle is thus lifted in a Lorentz invariant manner since the combinations $𝜃 (\pm p_{0}) 𝜃 (p_{μ}^{2})$ with step functions are manifestly Lorentz invariant. We explain an explicit construction of this CPT breaking term in coordinate space, which is Lorentz invariant but nonlocal at the distance scale of the Planck length. The application of this Lorentz invariant CPT breaking mechanism to the possible mass splitting of the neutrino and antineutrino in the Standard Model is briefly discussed.

Based on a talk given by one of the authors (KF) at Memorial Meeting for Abdus Salam’s 90th Birthday, Nanyang Technological University, Singapore, January 25-28, 2016.

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