Matter relative to quantum hypersurfaces

Author:

Höhn Philipp A.12ORCID,Russo Andrea2ORCID,Smith Alexander R. H.34ORCID

Affiliation:

1. Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904 0495, Japan

2. Department of Physics and Astronomy, University College London, London, United Kingdom

3. Department of Physics, Saint Anselm College, Manchester, New Hampshire 03102, USA

4. Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire 03755, USA

Abstract

We explore the canonical description of a scalar field in 1+1 dimensional Minkowski space as a parametrized field theory on an extended phase space that includes additional embedding fields that characterize spacetime hypersurfaces X relative to which the scalar field is described. This theory is quantized via the Dirac prescription and physical states of the theory are used to define conditional wave functionals |ψϕ[X] interpreted as the state of the field relative to the hypersurface X, thereby extending the Page-Wootters formalism to quantum field theory. It is shown that this conditional wave functional satisfies the Tomonaga-Schwinger equation, thus demonstrating the formal equivalence between this extended Page-Wootters formalism and standard quantum field theory. We also construct relational Dirac observables and define a quantum deparametrization of the physical Hilbert space leading to a relational Heisenberg picture, which are both shown to be unitarily equivalent to the Page-Wootters formalism. Moreover, by treating hypersurfaces as quantum reference frames, we extend recently developed quantum frame transformations to changes between classical and nonclassical hypersurfaces. This allows us to exhibit the transformation properties of a quantum field under a larger class of transformations, which leads to a frame-dependent particle creation effect. Published by the American Physical Society 2024

Funder

Okinawa Institute of Science and Technology Graduate University

Simons Foundation

John Templeton Foundation

Publisher

American Physical Society (APS)

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