Localizing Dirac field states

Abstract

Non-locality and quantum appear together entitling scientific projects and papers quite usually. These are two hardly detachable concepts and modern quantum theories are built up taking into account this aspect explicitly. However, that characteristic turns challenging from a fundamental point of view and can be unhelpful for practical purposes. Here, we construct quantum field theory with deliberately local aspects for a 1+1 dimensional Dirac field in flat spacetime generalizing a recently developed formalism for scalar fields. That purpose is achieved exploiting the non-uniqueness of quantization process. This local construction leads to a natural notion of local quanta and provides a local algebra of operators. As an application, it is shown that the standard vacuum state is a boiling soup of local particles and this fact is connected with a still Gedankenexperiment consisting in slamming down and removing a mirror in an empty cavity.