A Lattice of Von Neumann Algebras Associated with the Quantum Theory of a Free Bose Field
Journal Article
·
· Journal of Mathematical Physics
Von Neumann algebras associated with the normal representation of canonical commutation relations are studied. Corresponding to each subspace of a real Hilbert space (test function space), a von Neumann algebra on another complex Hilbert space (the Fock space) is defined. This correspondence is proved to be an isomorphism between a certain complemented lattice of subspaces and that of the von Neumann algebras. This result has an application to the duality theorem in the theory of a free scalar field. A necessary and sufficient condition on a subspace, in order that the corresponding von Neumann algebra is of type I, is obtained.
- Research Organization:
- Univ. of Illinois, Urbana
- Sponsoring Organization:
- USDOE
- NSA Number:
- NSA-18-000926
- OSTI ID:
- 4167477
- Journal Information:
- Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 11 Vol. 4; ISSN JMAPAQ; ISSN 0022-2488
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- Country unknown/Code not available
- Language:
- English
Similar Records
On the representation of elements of a von Neumann algebra in the form of finite sums of products of projections. III. Commutators in C*-algebras
Asymptotic properties of von Neumann algebras
von Neumann algebras in JT gravity
Journal Article
·
Wed Apr 30 00:00:00 EDT 2008
· Sbornik. Mathematics
·
OSTI ID:21096791
Asymptotic properties of von Neumann algebras
Journal Article
·
Sat Jun 20 00:00:00 EDT 1987
· J. Sov. Math.; (United States)
·
OSTI ID:5551000
von Neumann algebras in JT gravity
Journal Article
·
Tue Jun 13 00:00:00 EDT 2023
· Journal of High Energy Physics (Online)
·
OSTI ID:2420204