Abstract
In this talk we review the progress we have made in determining the renormalized strong coupling expansion in quantum field theory. We restrict ourselves here to λϕ4 field theory in d-dimensions. Our starting point is the lattice version of the path integral representation for the Green’s functions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
S. Hori, Nucl. Phys. 30, 644 (1962).
H. Kaiser, Zeuthen Preprint PHE 74-11 (1974). Unpublished.
B.F.L. Ward, Nuovo Cim. 45A, 1 (1978).
P. Castoldi and C. Schomblond, Nucl. Phys. B, 139, 269 (1978).
C.M. Bender, F. Cooper, G. Guralnik and D. Sharp, Phys. Rev. D19, 1865 (1979).
R. Benzi, G. Martinelli, G. Parisi, Frascati Preprint 1978.
G. Baker, Jr. and J.M. Kincaid, Phys.Rev.Lett. 42, 1431 (1979).
The high temperature expansion of Ref. 7 is purely a kinetic energy expansion. The A2n are evaluated numerically for various values of a, λ, and M02.
Certain conditions under which the Qn will not converge to the correct answer having to do with finite saddle points in the function Qn(ε) are discussed by R.J. Rivers, Phys. Rev. D (to be published).
F.J. Hioe and E.W. Montroll, J. Math. Phys. 16, 1945 (1975).
C.M. Bender, F. Cooper, G. Guralnik, H. Rose, and D. Sharp, Advances in Mathematics (to be published).
C.M. Bender, F. Cooper, G. Guralnik, R. Roskies, D. Sharp, Phys. Rev. Lett. 43, 537 (1979).
We thank G. Baker for explaining to us this method of determining critical indices and for his sharing of his knowledge of this problem prior to publication.
G. Baker and J.M. Kincaid (Private Communication).
D. Isaacson, Commun. Math. Phys. 53, 257 (1977).
A.M. Polyakov, Nucl. Phys. B120, 429 (1977).
E. Gildener, and A. Patrascioiu, Phys. Rev. D16, 423 (1977).
The double well evaluation of ZO[µ2] of Eq.(4.20) has been used to calculate λ* in 1, 2, and 3 dimensions. At sixth order perturbation theory we obtain λ*=5.56, λ*=10.62, λ*=28.42. These results are consistent with the results obtained by George Baker using a high temperature series.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1980 Plenum Press, New York
About this chapter
Cite this chapter
Bender, C.M., Cooper, F., Guralnik, G.S., Roskies, R., Sharp, D. (1980). Renormalizing the Strong-Coupling Expansion for Quantum Field Theory: Present Status. In: Perlmutter, A., Scott, L.F. (eds) Recent Developments in High-Energy Physics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3165-0_15
Download citation
DOI: https://doi.org/10.1007/978-1-4613-3165-0_15
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-3167-4
Online ISBN: 978-1-4613-3165-0
eBook Packages: Springer Book Archive