Abstract
We revisit the CPT theorem for the Dirac equation and its extended version based on the vector representation of the Lorentz group. Then it is proposed that CPTM may apply to this fundamental equation for a massive fermion a s a singlet or a doublet with isospin. The symbol M stands here for reversing the sign of the mass in the Dirac equation, which can be accomplished by operation on it with the so-called gamma-five matrix that plays an essential role for the chirality in the Standard Model. We define the CPTM symmetry for the standard and extended Dirac equation and discuss its physical implications and some possible consequences for general relativity.
Highlights
The famous CPT invariance of quantum field theory means that the reversal of the sign of the charge, and of the space-time coordinates are fundamental physical symmetries [1,2,3,4,5,6] of any field equations, and the related Lagrangians should be invariant under these transformations
In his conclusion “CPT symmetry has been violated in relation to beta decay of mesons and for the three inverted CPT operations of antimatter that result in odd parity, and so it cannot be a fundamental symmetry of Nature
In the context of modern cosmology and general relativity, an extension of the CPT theorem has been considered by Bondarenko [15], which addresses the possibility of a negative sign of the particle mass, and related with it the mass signinversion symmetry
Summary
The famous CPT invariance of quantum field theory means that the reversal of the sign of the charge (charge conjugation, C), and of the space-time coordinates (parity reflection P and time reversal T) are fundamental physical symmetries [1,2,3,4,5,6] of any field equations, and the related Lagrangians should be invariant under these transformations. Larin [9] argued that there is a possibility of violation of CPT symmetry in the SM, yet consistent with the CPT theorem, by choosing non-standard phases of the quark fields To check this experimentally requires by an order of magnitude higher precision of measurements of the proton and antiproton mass difference than possible presently. By allowing the mass sign inversion to extend the CPT transformation into CPTM, the maximal symmetry of the Dirac equation based on the five gamma matrices is achieved. In the context of modern cosmology and general relativity, an extension of the CPT theorem has been considered by Bondarenko [15], which addresses the possibility of a negative sign of the particle mass, and related with it the mass signinversion symmetry.
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