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A Direct Proof of Slavnov's Identity in Pure Yang‐Mills Theory
Author(s) -
Geyer B.,
Mülsch D.
Publication year - 1990
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.19905020208
Subject(s) - identity (music) , simple (philosophy) , cohomology , mathematical physics , yang–mills existence and mass gap , gauge theory , operator (biology) , mathematics , physics , pure mathematics , philosophy , epistemology , gene , biochemistry , chemistry , repressor , acoustics , transcription factor
For pure Yang‐Mills theories with semi‐simple compact gauge group a direct prove of the Slavnov identity is given without to solve the related cohomology problem explicitly. To achieve this use is made of two related identities which result by differentiating the Slavnov identity with respect to the fields carrying the same Faddeev‐Popov charge as the Slavnov operator itself. The method which is based on the renormalized quantum action principles may be extended to Yang‐Mills theories in interaction with matter fields and/or within external background configurations.