State space as projective space. The case of massless particles

Everett G. Larson, Orville W. Day

The relation between the 2-particle Green function and the projections of the excited states onto the particle-hole space of the ground state of a fermion system is derived for the case in which the spectrum of the Green function is totally discrete. From this relation, the conditions for the N-representability of the 2-particle Green function are obtained, as is an explicit representation of the projection operator for the particle-hole space. The projection operator for the 2-particle-2-hole space is also presented.

Suzanne Lanéry, Thomas Thiemann

Riccardo Falcone, Simon Fuchs

We investigate whether relativistic massless classical particles may emerge as the classical limit of massless quanta. To address this question independently of any specific dynamics, environment, or pointer basis, we develop an axiomatic and purely kinematical framework for the coarse-graining approach. In this formulation, a candidate classical phase space is taken as the outcome space of a POVM subject only to minimal classicality and covariance under the relevant spacetime symmetry group. Applying this framework to the Poincaré group, we prove a no-go theorem for massless particles: the covariance requirement is incompatible with the operational conditions for classicality. The theorem leaves open field-like limits of massless quanta, for example the emergence of electromagnetic or gravitational fields, while ruling out classical massless particles, such as classical photons or gravitons.

Xiao-Gang Wen

Recently, it was pointed out that quantum orders and the associated projective symmetry groups can produce and protect massless gauge bosons and massless fermions in local bosonic models. In this paper, we demonstrate that a state with such kinds of quantum order can be viewed as a condensed state of nets of strings. The emergent gauge bosons and fermions in local bosonic models can be regarded as a direct consequence of string-net condensation. The gauge bosons are fluctuations of large closed string nets. The ends of open strings are the charged particles of the corresponding gauge field. For certain types of strings, the ends of open strings can even be fermions. According to the string-net picture, fermions always carry gauge charges. This suggests the existence of a new discrete gauge field that couples to neutrinos and neutrons. We also discuss how chiral symmetry that protects massless Dirac fermions can emerge from the projective symmetry of quantum order.