Zeta-Function and analytic renormalization

J. Madore

Annales de l'I.H.P. Physique théorique (1980)

  • Volume: 32, Issue: 3, page 249-256
  • ISSN: 0246-0211

How to cite

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Madore, J.. "Zeta-Function and analytic renormalization." Annales de l'I.H.P. Physique théorique 32.3 (1980): 249-256. <http://eudml.org/doc/76073>.

@article{Madore1980,
author = {Madore, J.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {zeta-function renormalization; analytic regularization; index of a differential operator on a compact manifold; Mellin transform; one-loop contribution to the effective potential of a self-interacting scalar field; gauge-invariance; eigenvalue problem; Fourier transform; symbol of an operator},
language = {eng},
number = {3},
pages = {249-256},
publisher = {Gauthier-Villars},
title = {Zeta-Function and analytic renormalization},
url = {http://eudml.org/doc/76073},
volume = {32},
year = {1980},
}

TY - JOUR
AU - Madore, J.
TI - Zeta-Function and analytic renormalization
JO - Annales de l'I.H.P. Physique théorique
PY - 1980
PB - Gauthier-Villars
VL - 32
IS - 3
SP - 249
EP - 256
LA - eng
KW - zeta-function renormalization; analytic regularization; index of a differential operator on a compact manifold; Mellin transform; one-loop contribution to the effective potential of a self-interacting scalar field; gauge-invariance; eigenvalue problem; Fourier transform; symbol of an operator
UR - http://eudml.org/doc/76073
ER -

References

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  1. [1] M. Atiyah, R. Bott, V.K. Patodi, Inventiones Math., t. 19, 1973, p. 279. Zbl0257.58008MR650828
  2. [2] P.B. Gilkey, The Index Theorem and the Heat Equation. Math. Lecture Series, t. 4, 1974. Zbl0287.58006MR458504
  3. [3] For a description of the classical ζ-and θ-functions see. for example, G. Sansone, J. Gerretsen, Lectures on the Theorey of Functions of a Complex Variable, P. Noordhoff-Groningen, 1960. Zbl0093.26803
  4. [4] J.S. Dowker, R. Critchley, Phys. Rev., t. D 13, 1976, p. 3224; t. D 15, 1977, p. 1484. MR449343
  5. [5] S.W. Hawking, Comm. math. Phys., t. 55, 1977, p. 133. Zbl0407.58024MR524257
  6. [6] A.S. Schwarz, Letters in Math. Physics, t. 2, 1978, p. 247. Zbl0383.70017
  7. [7] W. Heisenberg, H. Euler, Zeit. für Physik, t. 98, 1936, p. 714. Zbl0013.18503JFM62.1002.03
  8. [8] E.R. Speer, Dimensional and Analytic Renormalization, Ettore Majorana Summer School, Erice, August 1975, G. Velo, A. S. Wightman Editors, and references therein. MR522287
  9. [9] S. Coleman, E. Weinberg, Phys. Rev., t. D 7, 1973, p. 1888. 
  10. [10] J. Schwinger, Phys. Rev., t. 82, 1951, p. 664. Zbl0043.42201
  11. [11] See, for example, E.S. Abers, B.W. Lee, Physics Reports, t. 9 C, 1973, Number 1. 
  12. [12] E. Brezin, C. Itzykson, Phys. Rev., t. D 2, 1970, p. 1191. 
  13. [13] R.T. Seeley, Amer. Math. Soc. Proc. Symp. Pure Math., t. 10, 1967, p. 288. Zbl0159.15504MR237943

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