Boson fields with the :Φ4: Interaction in three dimensions

James Glimm

doi:10.1007/BF01654131

Boson fields with the :Φ⁴: Interaction in three dimensions

James Glimm

Applied Mathematics and Statistics

Stony Brook University

Research output: Contribution to journal › Article › peer-review

68 Scopus citations

Abstract

The :Φ⁴: interaction for boson fields is considered in three dimensional space time. A space cutoff is included in the interaction term. The main result is that the renormalized Hamiltonian H_ren is a densely defined symmetric operator. In addition to the infinite vacuum energy and infinite mass renormalizations, this theory has an infinite wave function renormalization. Consequently the Hilbert space (of physical particles) in which H_ren acts is disjoint from the bare particle Fock Hilbert space in which the unrenormalized Hamiltonian is defined.

Original language	English
Pages (from-to)	1-47
Number of pages	47
Journal	Communications in Mathematical Physics
Volume	10
Issue number	1
DOIs	https://doi.org/10.1007/BF01654131
State	Published - Feb 1968

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title = "Boson fields with the :Φ4: Interaction in three dimensions",

abstract = "The :Φ4: interaction for boson fields is considered in three dimensional space time. A space cutoff is included in the interaction term. The main result is that the renormalized Hamiltonian Hren is a densely defined symmetric operator. In addition to the infinite vacuum energy and infinite mass renormalizations, this theory has an infinite wave function renormalization. Consequently the Hilbert space (of physical particles) in which Hren acts is disjoint from the bare particle Fock Hilbert space in which the unrenormalized Hamiltonian is defined.",

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year = "1968",

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N2 - The :Φ4: interaction for boson fields is considered in three dimensional space time. A space cutoff is included in the interaction term. The main result is that the renormalized Hamiltonian Hren is a densely defined symmetric operator. In addition to the infinite vacuum energy and infinite mass renormalizations, this theory has an infinite wave function renormalization. Consequently the Hilbert space (of physical particles) in which Hren acts is disjoint from the bare particle Fock Hilbert space in which the unrenormalized Hamiltonian is defined.

AB - The :Φ4: interaction for boson fields is considered in three dimensional space time. A space cutoff is included in the interaction term. The main result is that the renormalized Hamiltonian Hren is a densely defined symmetric operator. In addition to the infinite vacuum energy and infinite mass renormalizations, this theory has an infinite wave function renormalization. Consequently the Hilbert space (of physical particles) in which Hren acts is disjoint from the bare particle Fock Hilbert space in which the unrenormalized Hamiltonian is defined.

UR - https://www.scopus.com/pages/publications/4243743075

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DO - 10.1007/BF01654131

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VL - 10

SP - 1

EP - 47

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 1

ER -

Boson fields with the :Φ⁴: Interaction in three dimensions

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