Abstract
A general framework is derived for studying differential operations in renormalized perturbation theory. The method makes possible a simple, unified derivation of the renormalization group and Callan-Symanzik equations, as well as a direct test for broken symmetries (including broken scale invariance), without the necessity of defining currents and deriving their generalized Ward identites. A second-order differential equation of the Callan-Symanzik type is derived using similar methods.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bogoliubov, N.N., Shirkov, D.W.: Introduction to the theory of quantized fields, New York: Interscience Publishers 1959.
Coleman, S., Jackiw, R.: Canonical and non-canonical scale symmetry breaking, M.I.T. report (1970).
Callan, Jr., C.G.: Phys. Rev.D2, 1541 (1970).
Symanzik, K.: Commun. math. Phys.18, 227 (1970).
Zimmermann, W.: Lectures on elementary particles and quantum field theory, Vol. 1, p. 397, Cambridge: M.I.T. Press 1970.
Gell-Mann, M., Low, F.: Phys. Rev.95, 1300 (1954).
—— —— Phys. Rev.84, 350 (1951).
Courant, R., Hilbert, D.: Methods of mathematical physics, Vol. II, New York: Interscience Publishers 1953.
Lowenstein, J.: Univ. of Pittsburgh report NYO-3829-67 (1971).
Symanzik, K.: Commun. math. Phys.16, 48 (1970).
Wilson, K.: Phys. Rev.179, 1499 (1969).
Weinberg, S.: Phys. Rev.118, 838 (1960).
Symanzik, K.: Small-distance-behaviour analysis and Wilson expansions, DESY report (1971).
Author information
Authors and Affiliations
Additional information
Supported in part by the U.S. Atomic Energy Commission under Contract No. AT-30-1-3829.
Rights and permissions
About this article
Cite this article
Lowenstein, J.H. Differential vertex operations in Lagrangian field theory. Commun.Math. Phys. 24, 1–21 (1971). https://doi.org/10.1007/BF01907030
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01907030