Legendre transforms and r -particle irreducibility in quantum field theory : the formalism for fermions

Alan Cooper; Joel Feldman; Lon Rosen

Annales de l'I.H.P. Physique théorique (1985)

  • Volume: 43, Issue: 1, page 29-106
  • ISSN: 0246-0211

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Cooper, Alan, Feldman, Joel, and Rosen, Lon. "Legendre transforms and $r$-particle irreducibility in quantum field theory : the formalism for fermions." Annales de l'I.H.P. Physique théorique 43.1 (1985): 29-106. <http://eudml.org/doc/76293>.

@article{Cooper1985,
author = {Cooper, Alan, Feldman, Joel, Rosen, Lon},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {Euclidean field theories; boson field; fermi field; generating functional of connected Green's functions; Legendre transform; Grassmann algebra; Spencer's t-derivatives; cluster-irreducible; Bethe-Salpeter kernels},
language = {eng},
number = {1},
pages = {29-106},
publisher = {Gauthier-Villars},
title = {Legendre transforms and $r$-particle irreducibility in quantum field theory : the formalism for fermions},
url = {http://eudml.org/doc/76293},
volume = {43},
year = {1985},
}

TY - JOUR
AU - Cooper, Alan
AU - Feldman, Joel
AU - Rosen, Lon
TI - Legendre transforms and $r$-particle irreducibility in quantum field theory : the formalism for fermions
JO - Annales de l'I.H.P. Physique théorique
PY - 1985
PB - Gauthier-Villars
VL - 43
IS - 1
SP - 29
EP - 106
LA - eng
KW - Euclidean field theories; boson field; fermi field; generating functional of connected Green's functions; Legendre transform; Grassmann algebra; Spencer's t-derivatives; cluster-irreducible; Bethe-Salpeter kernels
UR - http://eudml.org/doc/76293
ER -

References

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  1. [1] A. Cooper, J. Feldman and L. Rosen, Legendre transforms and r-particle irreducibility in quantum field theory: the formalism for r = 1, 2, Ann. Phys., t. 137, 1981, p. 146-209. MR638890
  2. [2] A. Cooper, J. Feldman and L. Rosen, Legendre transforms and r-particle irreducibility in quantum field theory: the formal power series framework, Ann. Phys., t. 137, 1981, p. 213-261. Zbl0491.46064MR640319
  3. [3] A. Cooper, J. Feldman and L. Rosen, Higher Legendre transforms and their relationship to Bethe-Salpeter kernels and r-field projectors, J. Math. Phys., t. 23, 1982, p. 846-868. MR655903
  4. [4] A. Cooper, J. Feldman and L. Rosen, Cluster irreducibility of the third and fourth Legendre transforms in quantum field theory, Phys. Rev., t. D25, 1982, p. 1565-1578. MR649049
  5. [5] A. Cooper, J. Feldman and L. Rosen, The low energy spectrum of the Yukawa2 model, in preparation. 
  6. [6] J. Schwinger, On the Green's functions of quantized fields. I. Proc. N. A. S., t. 37, 1951, p. 452-455. Zbl0044.43001MR45065
  7. [7] F.A. Berezin, The method of second quantization, Academic Press, New York, 1966. Zbl0151.44001MR208930
  8. [8] S. Coleman, Secret symmetry: an introduction to spontaneous symmetry Breakdwon and gauge fields, in Laws of Hadronic matter, A Zichichi, ed., Academic Press, New York, 1973. MR468723
  9. [9] E. Seiler, Schwinger functions for the Yukawa model in two dimensions with space–time cutoff, Comm. Math. Phys., t. 42, 1975, p. 163-182. MR376022
  10. [10] A. Cooper and L. Rosen, The weakly coupled Yukawa2 field theory: cluster expansion and Wightman axioms, Trans. A. M. S., t. 234, 1977, p. 1-88. MR468872
  11. [11] J. Magnen and R. Sénéor, The Wightman axioms for the weakly coupled Yukawa model in two dimensions, Commun. Math. Phys., t. 51, 1976, p. 297-313. MR434224
  12. [12] T. Spencer, The decay of the Bethe-Salpeter kernel in P(φ)2 quantum field models, Commun. Math. Phys., t. 44, 1975, p. 143-164. MR389080

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