Abstract
The ultra-violet (UV) divergences appearing in quantum field theory at small distances (high momentum A → ∞) are well known to be intimately related to the properties of the theory with respect to the group of scale transformations. For a wide class of theories, known as multiplicatively renormalizable theories, the problem can be essentially simplified by the scale transformation of fields (Φ) and coupling constants (g)
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
J.R.Klauder and R.F.Streater, A wavelet transform for the Poincare group, J.Math.Phys., 32:1609–1611, 1991.
P. Ramond, “Field Theory: A modern Primer”, Benjamin/Cummings Publish- ing Company,Inc., Massachussets, 1981.
N.N. Bogoliubov and D.V. Shirkov, “Introduction to the theory of quantized fields”, John Wiley, New York, 1980.
K.G. Wilson, Quantum field-theory models in less than 4 dimensions, Physical Review D, 7(10):2911–2927, 1973.
A.L. Carey, Square-integrable representations of non-unimodular groups, Bull. Austr. Math. Soc., 15:1–12, 1976.
M. Duflo and C.C. Moore, On regular representations of nonunimodular locally compact group, J. Func. Anal., 21:209–243, 1976.
C.K.Chui, “An introduction to wavelets”, Academic Press, Inc., San Diego, 1992.
P. Federbush, A new formulation and regularization of Gauge theories using a non-linear wavelet expansion, Progr. Theor. Phys., 94:1135–1146,1995.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Science+Business Media New York
About this chapter
Cite this chapter
Altaisky, M.V. (2001). ϕ 4-Field theory on a Lie group. In: Sidharth, B.G., Altaisky, M.V. (eds) Frontiers of Fundamental Physics 4. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-1339-1_11
Download citation
DOI: https://doi.org/10.1007/978-1-4615-1339-1_11
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-5505-2
Online ISBN: 978-1-4615-1339-1
eBook Packages: Springer Book Archive