## Renormalized Quantum Field Theory'Et moi. ...• Ii j'avait su CClIIIIIIaIt CD 1'CVCDir, ODe scmcc matbcmatK:s bas I'CIIdcRd !be je D', semis paiDt ~. humaD mcc. It bas put common sease bact Jules Vcmc 'WIIcR it bdoDp, 011 !be topmost sbdl JlCXt 10 !be dully c:uista' t.bdlcd 'cIiIc:arded DOlI- The series is diverpt; therefore we may be sense'. Eric T. BcII able 10 do sometbiD& with it O. Heavilide Mathematics is a tool for thought. A highly ncceuary tool in a world where both feedback and non- 1inearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the l'Iison d'etre of this series. |

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### Contents

Parametric Representations for Renormalized | 3 |

The Chronological Products of Local Monomials | 15 |

Products | 29 |

Copyright | |

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### Common terms and phrases

according analytic arbitrary calculate called Chapter coefficient function coincides combination components composite fields connected consider constant construct contains contribution coordinates corresponding course cut-off defined definition depends derivatives diagram dimensional divergencies equal equation equivalent example exists expansion expression external fact factor Feynman amplitude Figure finite free field gauge give given Green functions hand identity initial integral interaction internal introduce invariance Lagrangian latter leads limit linear lines mass matrix means momenta monomials Namely normal obtain operator pairings parameters particular polynomial proof properties prove quantity R-operation recall regularization relation remark renormalization representation represented respect result right-hand side S-matrix satisfies scalar singular space subgraphs subsection subtraction operator Suppose symbol T-product takes theorem theory tion transform ultraviolet usual values variables vector vertex vertices zero