On the definition of renormalized field products

We study the redefinition of the field products appearing in a Lagrangian and its equations of motion in a Normal Product framework. We propose a method of defining these products, which give the finite Green's functions, in such a way that the canonical derivation of the equations of motion is...

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Published inAnnals of physics Vol. 105; no. 2; pp. 350 - 366
Main Author Collecott, P.S.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.01.1977
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ISSN0003-4916
1096-035X
DOI10.1016/0003-4916(77)90244-5

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Abstract We study the redefinition of the field products appearing in a Lagrangian and its equations of motion in a Normal Product framework. We propose a method of defining these products, which give the finite Green's functions, in such a way that the canonical derivation of the equations of motion is preserved. This involves the use of the Wilson Expansion in a Dimensionally Regularized form. As an example a ϕ 4, ϕ 3, field theory in four dimensions is fully redefined to the 1-loop level.
AbstractList We study the redefinition of the field products appearing in a Lagrangian and its equations of motion in a Normal Product framework. We propose a method of defining these products, which give the finite Green's functions, in such a way that the canonical derivation of the equations of motion is preserved. This involves the use of the Wilson Expansion in a Dimensionally Regularized form. As an example a ϕ 4, ϕ 3, field theory in four dimensions is fully redefined to the 1-loop level.
Author Collecott, P.S.
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Cites_doi 10.1103/PhysRevD.4.2281
10.1103/PhysRev.179.1499
10.1007/BF01878448
10.1016/S0550-3213(75)80010-1
10.1007/BF01907030
10.1016/0550-3213(74)90325-3
10.1016/0003-4916(73)90429-6
10.1016/0550-3213(73)90376-3
10.1016/0550-3213(75)90570-2
10.1103/PhysRevD.10.2500
10.1016/0003-4916(73)90430-2
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References Saclay Preprint DPh-T/74-56.
Lowenstein (BIB9) 1971; 4
Munchen Preprint MPI-PAE/PTh 25.
Wilson, Wilson (BIB12) 1964; 179
Zimmermann (BIB1) 1971; Vol. 1
Wilson, Zimmermann (BIB13) 1971; 24
Cambridge Preprint DAMTP
Lowenstein, Weinstein, Zimmermann (BIB8) 1974; 10
.
Zimmermann (BIB3) 1973; 77
submitted to
t Hooft, Veltman (BIB11) 1973; 61
Zimmermann (BIB2) 1973; 77
Lowenstein (BIB10) 1971; 24
Jegerlehner, Schroer (BIB6) 1974; 68
Collins (BIB4) 1975; 92
Collecott, Collins (BIB7) 1975; 93
Collecott (10.1016/0003-4916(77)90244-5_BIB7) 1975; 93
Jegerlehner (10.1016/0003-4916(77)90244-5_BIB6) 1974; 68
Wilson (10.1016/0003-4916(77)90244-5_BIB12_1) 1964
Wilson (10.1016/0003-4916(77)90244-5_BIB12_2) 1969; 179
10.1016/0003-4916(77)90244-5_BIB14
Zimmermann (10.1016/0003-4916(77)90244-5_BIB2) 1973; 77
10.1016/0003-4916(77)90244-5_BIB15
Lowenstein (10.1016/0003-4916(77)90244-5_BIB8) 1974; 10
Wilson (10.1016/0003-4916(77)90244-5_BIB13) 1971; 24
Zimmermann (10.1016/0003-4916(77)90244-5_BIB1) 1971; Vol. 1
Zimmermann (10.1016/0003-4916(77)90244-5_BIB3) 1973; 77
Lowenstein (10.1016/0003-4916(77)90244-5_BIB9) 1971; 4
Collins (10.1016/0003-4916(77)90244-5_BIB4) 1975; 92
t Hooft (10.1016/0003-4916(77)90244-5_BIB11) 1973; 61
10.1016/0003-4916(77)90244-5_BIB5
Lowenstein (10.1016/0003-4916(77)90244-5_BIB10) 1971; 24
References_xml – volume: 68
  start-page: 461
  year: 1974
  ident: BIB6
  publication-title: Nucl. Phys. B
– volume: 93
  start-page: 217
  year: 1975
  ident: BIB7
  publication-title: Nucl. Phys. B
– volume: 77
  start-page: 536
  year: 1973
  ident: BIB2
  publication-title: Ann. Physics
– reference: , Saclay Preprint DPh-T/74-56.
– volume: 77
  start-page: 570
  year: 1973
  ident: BIB3
  publication-title: Ann. Physics
– reference: , Munchen Preprint MPI-PAE/PTh 25.
– volume: 92
  start-page: 477
  year: 1975
  ident: BIB4
  publication-title: Nucl. Phys. B
– reference: , submitted to
– volume: 4
  start-page: 2281
  year: 1971
  ident: BIB9
  publication-title: Phys. Rev. D
– volume: 10
  start-page: 2500
  year: 1974
  ident: BIB8
  publication-title: Phys. Rev. D
– reference: , Cambridge Preprint DAMTP
– volume: 24
  start-page: 1
  year: 1971
  ident: BIB10
  publication-title: Comm. Math. Phys.
– volume: 61
  start-page: 469
  year: 1973
  ident: BIB11
  publication-title: Nucl. Phys. B
– volume: Vol. 1
  year: 1971
  ident: BIB1
  article-title: Renormalisation of composite field operators
  publication-title: Lectures in Elementary Particles and Quantum Field Theory
– volume: 179
  start-page: 1499
  year: 1964
  ident: BIB12
  article-title: Cornell Report
  publication-title: Phys. Rev.
– reference: .
– volume: 24
  start-page: 87
  year: 1971
  ident: BIB13
  publication-title: Comm. Math. Phys.
– volume: 4
  start-page: 2281
  year: 1971
  ident: 10.1016/0003-4916(77)90244-5_BIB9
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.4.2281
– volume: 179
  start-page: 1499
  year: 1969
  ident: 10.1016/0003-4916(77)90244-5_BIB12_2
  publication-title: Phys. Rev.
  doi: 10.1103/PhysRev.179.1499
– ident: 10.1016/0003-4916(77)90244-5_BIB14
– ident: 10.1016/0003-4916(77)90244-5_BIB15
– volume: 24
  start-page: 87
  year: 1971
  ident: 10.1016/0003-4916(77)90244-5_BIB13
  publication-title: Comm. Math. Phys.
  doi: 10.1007/BF01878448
– volume: 92
  start-page: 477
  year: 1975
  ident: 10.1016/0003-4916(77)90244-5_BIB4
  publication-title: Nucl. Phys. B
  doi: 10.1016/S0550-3213(75)80010-1
– volume: 24
  start-page: 1
  year: 1971
  ident: 10.1016/0003-4916(77)90244-5_BIB10
  publication-title: Comm. Math. Phys.
  doi: 10.1007/BF01907030
– ident: 10.1016/0003-4916(77)90244-5_BIB5
– volume: 68
  start-page: 461
  year: 1974
  ident: 10.1016/0003-4916(77)90244-5_BIB6
  publication-title: Nucl. Phys. B
  doi: 10.1016/0550-3213(74)90325-3
– volume: Vol. 1
  year: 1971
  ident: 10.1016/0003-4916(77)90244-5_BIB1
  article-title: Renormalisation of composite field operators
– year: 1964
  ident: 10.1016/0003-4916(77)90244-5_BIB12_1
– volume: 77
  start-page: 536
  year: 1973
  ident: 10.1016/0003-4916(77)90244-5_BIB2
  publication-title: Ann. Physics
  doi: 10.1016/0003-4916(73)90429-6
– volume: 61
  start-page: 469
  year: 1973
  ident: 10.1016/0003-4916(77)90244-5_BIB11
  publication-title: Nucl. Phys. B
  doi: 10.1016/0550-3213(73)90376-3
– volume: 93
  start-page: 217
  year: 1975
  ident: 10.1016/0003-4916(77)90244-5_BIB7
  publication-title: Nucl. Phys. B
  doi: 10.1016/0550-3213(75)90570-2
– volume: 10
  start-page: 2500
  year: 1974
  ident: 10.1016/0003-4916(77)90244-5_BIB8
  publication-title: Phys. Rev. D
  doi: 10.1103/PhysRevD.10.2500
– volume: 77
  start-page: 570
  year: 1973
  ident: 10.1016/0003-4916(77)90244-5_BIB3
  publication-title: Ann. Physics
  doi: 10.1016/0003-4916(73)90430-2
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