18 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 extended¹ 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

[ Qⁱ, H ] = cⁱ _k Q^k.