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The Quadratic Divergencies and Confinement in Non‐Abelian Gauge Theories
Author(s) -
Kaschluhn F.
Publication year - 1986
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.19860340302
Subject(s) - dimensional regularization , regularization (linguistics) , mathematical physics , physics , logarithm , renormalization , subtraction , abelian group , gauge theory , quadratic equation , mathematics , mathematical analysis , pure mathematics , geometry , arithmetic , artificial intelligence , computer science
Regularization and renormalization of loop functionals are discussed. A special regularization the so‐called superregularization, is developed which yields neither logarithmic nor linear divergencies when the regularization is removed. All integrals occurring in the perturbation expansion have a well‐defined limit for which gauge invariance can be maintained. Finite subtraction constants referring to the logarithmic and linear divergencies of the originally ill‐defined integrals can be included in their redefined form, the so‐called supervalues of the integrals. On the same basis the derivatives of the loop functionals can be treated. The Makeenko‐Migdal equation is studied in an once‐integrated form. Assuming its singular behaviour to be dominant for large contours the area law is derived. Minimality of the area enclosed by the loop is guaranteed by the Bianchi identities. The string tension involves a subtraction constant of dimension of (length) 2 to be determined experimentally.