What is a field, what is a particle?...what about algebras?

relativity;localizability;vacuum entanglement

Papageorgiou, Maria-Eftychiaadvisor:Kempf, Achim ; advisor:Martin-Martinez, Eduardo ; affiliation1:Faculty of Mathematics ; Martin-Martinez, Eduardo ; Kempf, Achim ;

University of Waterloo

关键词: vacuum entanglement;    Master Thesis;    relativity;    localizability;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/14421/3/Papageorgiou_Maria.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

Much of the structure of quantum field theory (QFT) is predicated on the principleof locality. Adherence to locality is achieved in Algebraic QFT (AQFT) by the associationof algebras of observables with regions of spacetime. Although, by construction, theobservables of QFT are local objects, one may consider characterizing the spatial or spacetimefeatures of a state. For example, if we have a single-particle state in QFT, how canwe say that the particle is localized in a certain region of space? It turns out that sucha characterization is obstructed by a collection of no-go theorems that we will review inthefirst two chapters, which imply the absence of any suitable position operator or localnumber operator in the local algebra of observables. These difficulties, along with otherconsiderations that involve acceleration, gravity and interactions, suggest that relativisticQFT cannot support a particle ontology. The common factor of all these reasons is thetheory of relativity, which is commonly blamed for the inappropriateness of the particlenotion in relativistic quantum theories.Looking towards low energies, onefinds the widespread applicability of non-relativisticquantum mechanics (NRQM), a theory in which particle states are localizable by means oftheir wavefunction. This seems to imply that NRQM can support a particle ontology, so itis natural to ask whether one can make contact between the NRQM description of particlesand some appropriate notion in the latent QFT. Admittedly QFT and NRQM are verydifferent theories, both at the dynamical and kinematical level, and recovering one from theother cannot come with no cost. The main undertaking of this thesis will be to illuminatethis connection, by starting with a relativistic QFT and making suitable approximationsto recover features of NRQM. Furthermore, it has been suggested that the existence ofvacuum entanglement in a relativistic QFT is further obscuring the localizability of states.This is why we are investigating the behavior of vacuum entanglement under the nonrelativistic approximation to ask whether vacuum entanglement is a relativistic effect.