An Extension of Goldstone Theorem to Non-symmetric Hamiltonians

Abstract

The Goldstone theorem and its rigorous predictions on the energy spectrum at zero momentum can be extended¹⁸⁴ to the case in which the Hamiltonian H is not symmetric, but it has simple transformation properties, in the sense that the multiple commutators of H and the charge Q generate a finite dimensional Lie algebra, briefly

$$ \left[ {Q^i ,H} \right] = c_k^i Q^k . $$