PIRSA:14050117 Scientific Series Quantum Foundations

DOI10.48660/14050117

Series: Quantum Foundations

Westman, H. (2014). Local quanta, unitary inequivalence, and vacuum entanglement. Perimeter Institute. https://pirsa.org/14050117

Westman, Hans. Local quanta, unitary inequivalence, and vacuum entanglement. Perimeter Institute, May. 20, 2014, https://pirsa.org/14050117 

@misc{ pirsa_PIRSA:14050117,
  doi = {10.48660/14050117},
  url = {https://pirsa.org/14050117},
  author = {Westman, Hans},
  keywords = {Quantum Foundations},
  language = {en},
  title = {Local quanta, unitary inequivalence, and vacuum entanglement},
  publisher = {Perimeter Institute},
  year = {2014},
  month = {may},
  note = {PIRSA:14050117 see, \url{https://pirsa.org}}
}

Abstract

In this work we develop a formalism for describing localised quanta for a real-valued Klein-Gordon field in a one-dimensional box [0, R]. We quantise the field using non-stationary local modes which, at some arbitrarily chosen initial time, are completely localised within the left or the right side of the box. In this concrete set-up we directly face the problems inherent to a notion of local field excitations, usually thought of as elementary particles. Specifically, by computing the Bogoliubov coefficients relating local and standard (global) quantizations, we show that the local quantisation yields a Fock space F^L which is unitarily inequivalent to the standard one F^G. In spite of this, we find that the local creators and annihilators remain well defined in the global Fock space F^G, and so do the local number operators associated to the left and right partitions of the box. We end up with a useful mathematical toolbox to analyse and characterise local features of quantum states in F^G . Specifically, an analysis of the global vacuum state |0_G> ∈ F^G in terms of local number operators shows, as expected, the existence of entanglement between the left and right regions of the box. The local vacuum |0_L> ∈ F^L , on the contrary, has a very different character. It is neither cyclic nor separating and displays no entanglement. Further analysis shows that the global vacuum also exhibits a distribution of local excitations reminiscent, in some respects, of a thermal bath. We discuss how the mathematical tools developed herein may open new ways for the analysis of fundamental problems in local quantum field theory.

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