Type: Article

Towards state locality in quantum field theory: free fermions

Robert Oeckl;

Abstract:

We provide a restricted solution to the state locality problem in quantum field theory for the case of free fermions. Concretely, we present a functorial quantization scheme that takes as input a classical free fermionic field theory. Crucially, no data is needed beyond the classical structures evident from a Lagrangian setting. The output is a quantum field theory encoded in a weakened version of the positive formalism of the general boundary formulation. When the classical data is augmented with complex structures on hypersurfaces, the quantum data correspondingly augment to the full positive formalism and the standard quantization of free fermionic field theory is recovered. This augmentation can be performed selectively, i.e., it may be limited to a subcollection of hypersurfaces. The state locality problem arises from the fact that suitable complex structures only exist on a very restricted class of unbounded hypersurfaces. But standard quantization requires them on all hypersurfaces and is thus only able to include very restricted classes of hypersurfaces and regions. The latter are typically non-compact, thereby precluding a completely local description of physics. Since the presented quantization scheme works (selectively) without the need for complex structures this problem is avoided. In this way spaces of generalized mixed states are well defined even on compact hypersurfaces with boundary and compact regions are admissible.