Summary
We study a new set of functions that are given by the coefficients of the character expansion of the single-link action in theSU(3) lattice-gauge theory. The function is specified by the indices λ and μ of theSU(3) representation of the Young tableau. From the Schwinger-Dyson variational method we derive the recursion relations among the functions. By combining the recursion relation and the relation of the differentiation, we derive the linear differential equation of the sixth order for the function. We discuss the properties of the function in detail in comparison with the functions in theSU(2) group.
Similar content being viewed by others
References
T. D. Lee: inParticle Physics and Introduction to Field Theory (Harwood Academic Publishers, New York, N.Y., 1981).
K. Wilson:Phys. Rev. D,10, 2445 (1974).
M. Creuyz: InQuarks, Gluons and Lattice (Cambridge University Press, Cambridge, 1983), p. 63;J. B. Kogut, R. B. Pearson andJ. Schigemitsu:Phys. Rev. Lett.,43, 484 (1979).
R. Balian, J. M. Drouffe andC. Itzykson:Phys. Rev. D,11, 2104 (1975).
K. E. Eriksson, N. Svartholm andB. S. Skagerstam:J. Math. Phys. (N.Y.),22, 2276 (1981).
C. B. Lang, P. Salomonson andB. S. Skagerstam:Phys. Lett. B,100, 29 (1981);N. Tanimura:Phys. Lett. B,221, 55 (1989).
D. Foester:Phys. Lett. B,87, 87 (1978);T. Eguchi:Phys. Lett. B,87, 91 (1979);R. C. Brower andM. Nauenberg:Nucl. Phys. A,180, 221 (1981).
I. Bars:J. Math. Phys. (N.Y.),21, 2678 (1980).
T. D. Lee: inParticle Physics and Introduction to Field Theory (Harwood Academic Publishers, New York, N.Y., 1981), p. 260.
N. Tanimura andO. Tanimura:J. Math. Phys. (N.Y.),31, 721 (1990).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Tanimura, N., Tanimura, O. New Bessel-type function associated withSU(3) representation. Nuov Cim B 105, 1263–1275 (1990). https://doi.org/10.1007/BF02828979
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02828979