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Caianiello E.R. — Combinatorics and renormalization in quantum field theory
Caianiello E.R. — Combinatorics and renormalization in quantum field theory

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Название: Combinatorics and renormalization in quantum field theory

Автор: 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: en

Рубрика: Физика/Квантовая теория поля/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1973

Количество страниц: 121

Добавлена в каталог: 22.08.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$g\phi^{4}$ theory, equation for single propagators      56
$g\phi^{4}$ theory, Hartree — Fock approximation      109
$g\phi^{4}$ theory, numerical model      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 $\mathscr{A}$, $\mathscr{a}$      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, $\delta$-procedure      85 86
Regularization, $\sigma$-procedure      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, $\phi^{3}$ theory      85
U-matrix      35 44
Unitarity      44
Volterra equation      20
Wick's theorem      32
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