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Title: Hilbert space structure in quantum gravity: an algebraic perspective

Abstract

If quantum gravity respects the principles of quantum mechanics, suitably generalized, it may be that a more viable approach to the theory is through identifying the relevant quantum structures rather than by quantizing classical spacetime. Here, this viewpoint is supported by difficulties of such quantization, and by the apparent lack of a fundamental role for locality. In finite or discrete quantum systems, important structure is provided by tensor factorizations of the Hilbert space. However, even in local quantum field theory properties of the generic type III von Neumann algebras and of long range gauge fields indicate that factorization of the Hilbert space is problematic. Instead it is better to focus on the structure of the algebra of observables, and in particular on its subalgebras corresponding to regions. This paper suggests that study of analogous algebraic structure in gravity gives an important perspective on the nature of the quantum theory. Significant departures from the subalgebra structure of local quantum field theory are found, working in the correspondence limit of long-distances/low-energies. Particularly, there are obstacles to identifying commuting algebras of localized operators. In addition to suggesting important properties of the algebraic structure, this and related observations pose challenges to proposals of amore » fundamental role for entanglement.« less

Authors:
 [1]
  1. Univ. of California, Santa Barbara, CA (United States)
Publication Date:
Research Org.:
Univ. of California, Santa Barbara, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25); National Science Foundation (NSF); Foundational Questions Institute
OSTI Identifier:
1436121
Grant/Contract Number:  
SC0011702; 1066293; FQXi-RFP3-1330
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2015; Journal Issue: 12; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Models of Quantum Gravity; Space-Time Symmetries

Citation Formats

Giddings, Steven B. Hilbert space structure in quantum gravity: an algebraic perspective. United States: N. p., 2015. Web. doi:10.1007/JHEP12(2015)099.
Giddings, Steven B. Hilbert space structure in quantum gravity: an algebraic perspective. United States. doi:10.1007/JHEP12(2015)099.
Giddings, Steven B. Wed . "Hilbert space structure in quantum gravity: an algebraic perspective". United States. doi:10.1007/JHEP12(2015)099. https://www.osti.gov/servlets/purl/1436121.
@article{osti_1436121,
title = {Hilbert space structure in quantum gravity: an algebraic perspective},
author = {Giddings, Steven B.},
abstractNote = {If quantum gravity respects the principles of quantum mechanics, suitably generalized, it may be that a more viable approach to the theory is through identifying the relevant quantum structures rather than by quantizing classical spacetime. Here, this viewpoint is supported by difficulties of such quantization, and by the apparent lack of a fundamental role for locality. In finite or discrete quantum systems, important structure is provided by tensor factorizations of the Hilbert space. However, even in local quantum field theory properties of the generic type III von Neumann algebras and of long range gauge fields indicate that factorization of the Hilbert space is problematic. Instead it is better to focus on the structure of the algebra of observables, and in particular on its subalgebras corresponding to regions. This paper suggests that study of analogous algebraic structure in gravity gives an important perspective on the nature of the quantum theory. Significant departures from the subalgebra structure of local quantum field theory are found, working in the correspondence limit of long-distances/low-energies. Particularly, there are obstacles to identifying commuting algebras of localized operators. In addition to suggesting important properties of the algebraic structure, this and related observations pose challenges to proposals of a fundamental role for entanglement.},
doi = {10.1007/JHEP12(2015)099},
journal = {Journal of High Energy Physics (Online)},
number = 12,
volume = 2015,
place = {United States},
year = {2015},
month = {12}
}

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Cited by: 17 works
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