A State-Space Symmetry in the Electroweak Interaction Hamiltonian

Practical computations in the field of elementary particle physics usually employ a form of the $\gamma^\mu$ matrices, which possesses a symmetric property stronger than that required by the Lorentz symmetry; that is, the matrices are invariant (not just covariant) under Lorentz transformations for both the vector and spinor indices. In their chiral representation, the $\gamma^\mu$ matrices are constructible from the so-called Enfeld-van der Waerden (EvdW) symbols, which also possess the above property. In this paper, it is shown that the operator form of the EvdW symbols plays a central role in a major part of the Glashow-Weinberg-Salam electroweak interaction Hamiltonian, which describes interactions between leptons and vector bosons. This suggests that the symmetric property may be regarded as a symmetry of fundamental relevance, not just for the sake of convenience in practical computations.