| Co-Investigator(Kenkyū-buntansha) |
MOTEGI Kimihiko The College of Humanities and Sciences, Nihon Univ., Department of Math., Lect.,, 文理学部, 講師 (40219978)
YAGUCHI Teruo The College of Humanities and Sciences, Nihon Univ., Department of Math., Prof.,, 文理学部, 教授 (50059987)
NISHIOKA Kumiko The College of Humanities and Sciences, Nihon Univ., Department of Math., Asso., 文理学部, 助教授 (80144632)
SAKAI Shoichiro The College of Humanities and Sciences, Nihon Univ., Department of Math., Prof.,, 文理学部, 教授 (30130503)
SUZUKI Masahiko The College of Humanities and Sciences, Nihon Univ., Department of Math., Asso., 文理学部, 助教授 (00171249)
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| Research Abstract |
A new formalism for gauge connections is given and monlinear gauge eauations are solved and the divergence of quantu field theory is discussed. The following results are obtained.
(1) A gauge theory is formulated in termas of a certain kind of a decomposition of a linear space, whitch is called a "gauge decomposition." Then every gauge connection connection can be extended to a flat connection, when it admits a representation in some algebra (flat extension theorem).
(2) By use of the result (1), nonlinear gauge equations can be solved by use of a decomposition of a solution of a linear equation. Symmetry structures and special class of silutions can be discussed as a "Galois thery for differntial equations". When it has a representation in "algebroids", divergece appears and anomaly and renormalization can discussed in this case.
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