Yukawa coupling of quantum fields in two dimensions. I

James Glimm

doi:10.1007/BF01646449

Yukawa coupling of quantum fields in two dimensions. I

James Glimm

Applied Mathematics and Statistics

Stony Brook University

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

42 Scopus citations

Abstract

A renormalization procedure is proposed. It gives rigorous mathematical meaning to the infinite cancellations in this model. A space cutoff is introduced in the interaction term V and so V has the form {Mathematical expression}, but there are no momentum cutoffs in V. There is an infinite constant and an infinite boson mass renormalization in this model. The main result is that the renormalized Hamiltonian is rigorously defined as a bilinear form in the Fock Hilbert space.

Original language	English
Pages (from-to)	343-386
Number of pages	44
Journal	Communications in Mathematical Physics
Volume	5
Issue number	5
DOIs	https://doi.org/10.1007/BF01646449
State	Published - Oct 1967

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title = "Yukawa coupling of quantum fields in two dimensions. I",

abstract = "A renormalization procedure is proposed. It gives rigorous mathematical meaning to the infinite cancellations in this model. A space cutoff is introduced in the interaction term V and so V has the form \{Mathematical expression\}, but there are no momentum cutoffs in V. There is an infinite constant and an infinite boson mass renormalization in this model. The main result is that the renormalized Hamiltonian is rigorously defined as a bilinear form in the Fock Hilbert space.",

author = "James Glimm",

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T1 - Yukawa coupling of quantum fields in two dimensions. I

AU - Glimm, James

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N2 - A renormalization procedure is proposed. It gives rigorous mathematical meaning to the infinite cancellations in this model. A space cutoff is introduced in the interaction term V and so V has the form {Mathematical expression}, but there are no momentum cutoffs in V. There is an infinite constant and an infinite boson mass renormalization in this model. The main result is that the renormalized Hamiltonian is rigorously defined as a bilinear form in the Fock Hilbert space.

AB - A renormalization procedure is proposed. It gives rigorous mathematical meaning to the infinite cancellations in this model. A space cutoff is introduced in the interaction term V and so V has the form {Mathematical expression}, but there are no momentum cutoffs in V. There is an infinite constant and an infinite boson mass renormalization in this model. The main result is that the renormalized Hamiltonian is rigorously defined as a bilinear form in the Fock Hilbert space.

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DO - 10.1007/BF01646449

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JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 5

ER -

Yukawa coupling of quantum fields in two dimensions. I

Abstract

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