States, Symmetries and Superselection

Domenico Giulini

Domenico Giulini

D. Giulini, Claus Kiefer, H.D. Zeh

Nikolay Leonidovich Chuprikov

It is shown that spontaneous symmetry breaking occurs in this scattering problem. As a result, the unitary, asymptotically free quantum dynamics of this process is unstable. It transforms into dynamics associated with the violation of $P$- and $T$-symmetries and the appearance of a superselection rule. Here, the non-unitary scattering state is a mixed vector state, which is a coherent superposition of transmission and reflection states related to different Hamiltonians. Superselection operators for the transmission and reflection subprocesses are defined.

Horacio Casini, Marina Huerta, Javier M. Magán +1 more

Abstract Some quantum field theories show, in a fundamental or an effective manner, an alternative between a loss of duality for algebras of operators corresponding to complementary regions, or a loss of additivity. In this latter case, the algebra contains some operator that is not generated locally, in the former, the entropies of complementary regions do not coincide. Typically, these features are related to the incompleteness of the operator content of the theory, or, in other words, to the existence of superselection sectors. We review some aspects of the mathematical literature on superselection sectors aiming attention to the physical picture and focusing on the consequences for entanglement entropy (EE). For purposes of clarity, the whole discussion is divided into two parts according to the superselection sectors classification: the present part I is devoted to superselection sectors arising from global symmetries, and the forthcoming part II will consider those arising from local symmetries. Under this perspective, here restricted to global symmetries, we study in detail different cases such as models with finite and Lie group symmetry as well as with spontaneous symmetry breaking or excited states. We illustrate the general results with simple examples. As an important application, we argue the features of holographic entanglement entropy correspond to a picture of an sub-theory with a large number of superselection sectors and suggest some ways in which this identification could be made more precise.

Nikolay Leonidovich Chuprikov

It is shown that spontaneous symmetry breaking occurs in this scattering problem. As a result, the unitary, asymptotically free quantum dynamics of this process is unstable. It transforms into dynamics associated with the violation of $P$- and $T$-symmetries and the appearance of a superselection rule. Here, the non-unitary scattering state is a mixed vector state, which is a coherent superposition of transmission and reflection states related to different Hamiltonians. Superselection operators for the transmission and reflection subprocesses are defined.