Mass renormalization in non-relativistic quantum electrodynamics with spin 1/2

F. Hiroshima; K. R. Ito

doi:10.1142/S0129055X07003012

Mass renormalization in non-relativistic quantum electrodynamics with spin 1/2

F. Hiroshima
, K. R. Ito

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

7 Citations (Scopus)

Abstract

The effective mass m_eff of the Pauli-Fierz Hamiltonian with ultraviolet cutoff Λ and the bare mass m in non-relativistic quantum electrodynamics (QED) with spin 1/2 is investigated. Analytic properties of m_eff in coupling constant e are shown. Let us set m_eff/m = 1 +a₁(Λ/m)e² + a₂(Λ/m)e ⁴ + script O sign (e⁶). The explicit form of constant a₂(Λ/m) depending on Λ/m is given. It is shown that the spin interaction enhances the effective mass and that there exist strictly positive constants c₁ and c₂ such that equation presented In particular though it is known that a₁(Λ/m) diverge log(Λ/m) as Λ → ∞, a₂2(Λ/m) does not diverge as ±[log(Λ/m)]² but -(Λ/m)².

Original language	English
Pages (from-to)	405-454
Number of pages	50
Journal	Reviews in Mathematical Physics
Volume	19
Issue number	4
DOIs	https://doi.org/10.1142/S0129055X07003012
Publication status	Published - May 2007

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1142/S0129055X07003012

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title = "Mass renormalization in non-relativistic quantum electrodynamics with spin 1/2",

abstract = "The effective mass meff of the Pauli-Fierz Hamiltonian with ultraviolet cutoff Λ and the bare mass m in non-relativistic quantum electrodynamics (QED) with spin 1/2 is investigated. Analytic properties of meff in coupling constant e are shown. Let us set meff/m = 1 +a1(Λ/m)e2 + a2(Λ/m)e 4 + script O sign (e6). The explicit form of constant a2(Λ/m) depending on Λ/m is given. It is shown that the spin interaction enhances the effective mass and that there exist strictly positive constants c1 and c2 such that equation presented In particular though it is known that a1(Λ/m) diverge log(Λ/m) as Λ → ∞, a22(Λ/m) does not diverge as ±[log(Λ/m)]2 but -(Λ/m)2.",

author = "F. Hiroshima and Ito, \{K. R.\}",

year = "2007",

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doi = "10.1142/S0129055X07003012",

language = "English",

volume = "19",

pages = "405--454",

journal = "Reviews in Mathematical Physics",

issn = "0129-055X",

publisher = "World Scientific",

number = "4",

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TY - JOUR

T1 - Mass renormalization in non-relativistic quantum electrodynamics with spin 1/2

AU - Hiroshima, F.

AU - Ito, K. R.

PY - 2007/5

Y1 - 2007/5

N2 - The effective mass meff of the Pauli-Fierz Hamiltonian with ultraviolet cutoff Λ and the bare mass m in non-relativistic quantum electrodynamics (QED) with spin 1/2 is investigated. Analytic properties of meff in coupling constant e are shown. Let us set meff/m = 1 +a1(Λ/m)e2 + a2(Λ/m)e 4 + script O sign (e6). The explicit form of constant a2(Λ/m) depending on Λ/m is given. It is shown that the spin interaction enhances the effective mass and that there exist strictly positive constants c1 and c2 such that equation presented In particular though it is known that a1(Λ/m) diverge log(Λ/m) as Λ → ∞, a22(Λ/m) does not diverge as ±[log(Λ/m)]2 but -(Λ/m)2.

AB - The effective mass meff of the Pauli-Fierz Hamiltonian with ultraviolet cutoff Λ and the bare mass m in non-relativistic quantum electrodynamics (QED) with spin 1/2 is investigated. Analytic properties of meff in coupling constant e are shown. Let us set meff/m = 1 +a1(Λ/m)e2 + a2(Λ/m)e 4 + script O sign (e6). The explicit form of constant a2(Λ/m) depending on Λ/m is given. It is shown that the spin interaction enhances the effective mass and that there exist strictly positive constants c1 and c2 such that equation presented In particular though it is known that a1(Λ/m) diverge log(Λ/m) as Λ → ∞, a22(Λ/m) does not diverge as ±[log(Λ/m)]2 but -(Λ/m)2.

UR - https://www.scopus.com/pages/publications/34249035267

UR - https://www.scopus.com/pages/publications/34249035267#tab=citedBy

U2 - 10.1142/S0129055X07003012

DO - 10.1142/S0129055X07003012

M3 - Article

AN - SCOPUS:34249035267

SN - 0129-055X

VL - 19

SP - 405

EP - 454

JO - Reviews in Mathematical Physics

JF - Reviews in Mathematical Physics

IS - 4

ER -

Mass renormalization in non-relativistic quantum electrodynamics with spin 1/2

Abstract

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