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Caianiello E.R. — Combinatorics and renormalization in quantum field theory
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Название: Combinatorics and renormalization in quantum field theoryАвтор: Caianiello E.R. Аннотация: This volume is based upon work done by the author and his collaborators over a period of approximately twenty years and is dedicated to some selected topics of quantum field theory, which have proved of increasing importance with the passing of time. There are three parts: Combinatoric Methods; Equations for Green's Functions and Perturbative Expansions; Regularization, Renormalization, and Mass Equations. This work will be useful to anyone interested in learning or using quantum field theory, many-body physics and, as well, to many applied mathematicians, because it introduces a number of combinatoric and analytic tools which drastically simplify, and at times bypass, treatments which customarily take up most of the bulk of the standard texts. It is part of the Frontiers in Physics series, edited by David Pines.
Язык: Рубрика: Физика /Квантовая теория поля /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1973Количество страниц: 121Добавлена в каталог: 22.08.2005Операции: Положить на полку |
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56 109 58 59 Asymptotic expansion 59 Branching equations 52 54 57 Branching equations, renormalization of 86 Clifford algebra 8 10 Clifford algebra, totally antisymmetric tensors of 9 Clifford algebra, transition from Grassman algebra 26 Clifford product 8 10 26 Determinant, Arnaldi's theorem 27 28 29 Determinant, expansion rules 27 Determinant, Hadamard's inequality 49 Dirac matrices 15 Dirac matrices, traces of products of 15 Equations for single propagators, theory 56 57 Exchange of infinite operations 60 Feynman diagrams 46 48 Fields, photon 33 Fields, scalar 85 Fields, vector 33 Finite part integral 80 81 82 83 84 Fredholm equation 23 Fredholm equation with symmetric kernel 25 Functions of Hadamard class "2" 61 91 Functions of Hadamard class 61 Functions, quasi-analytic 60 Gauge properties, gauge properties of propagators 62 Grassman algebra 7 10 Grassman algebra, relation with Clifford algebra 33 Grassman algebra, transition to Clifford algebra 26 Grassman product 7 9 10 19 26 Grassman product of linear forms 7 Grassman product of quadratic forms 8 Grassman product, differentiation law for 26 Green's functions 43 see Green's functions, analytic behavior in coupling constant 90 91 Green's functions, gauge invariance of 62 Hafnian 3 13 24 27 Hafnian, Boson fields 36 Inequivalent representation 108 111 Infrared divergences 63 68 Lee Model, mass equation of 113 Lee Model, renormalized Green's function 112 Linked cluster expansion 54 56 Liouville theorem 19 20 Permanent 3 24 27 Perturbative expansion 32 54 89 Perturbative expansion in quantum electrodynamics 35 Perturbative expansion, perturbative expansion for Green's functions 54 55 Perturbative expansion, scalar electrodynamics 90 Pfaffian 3 5 6 8 15 27 Pfaffian, application to ecology 20 Pfaffian, de Bruijn's theorem 13 Pfaffian, Fermion fields 36 Polynomial Lagrangians 111 112 Products of distributions, evaluation of "divergent" contributions 78 Products of distributions, partie finie of 79 Products of distributions, point loop 79 Propagators 43 48 Propagators, boson propagator 45 Propagators, connection with Green's function 39 Propagators, connection with matrix elements 37 Propagators, electron propagator 47 Propagators, equations for propagators 50 Propagators, equations of the I type 50 53 54 Propagators, equations of the II type 50 51 52 53 Regularization of products of distributions 92 93 Regularization, 85 86 Regularization, 74 75 Regularization, finite part integrals 73 Regularization, ultraviolet divergences 7 5 Regularization, x-space regularization 7 3 Renormalization 92 93 94 95 104 Renormalization group 104 107 Renormalization, finite 94 Renormalization, infinitesimal 87 94 Renormalization, regularized equations for Green's functions 96 97 S-matrix 44 Self-consistent approximations 108 109 Soft-photon emission, cross-section for 68 69 Spontaneous breakdown of symmetries 108 111 Spontaneous breakdown of symmetries, mass equations 109 110 111 Super renormalizable theory, 85 U-matrix 35 44 Unitarity 44 Volterra equation 20 Wick's theorem 32
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