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Group properties of osp(2/1;C) gauge transformations

Group properties of osp(2/1;C) gauge transformations

Given an explicit construction of the grade star hermitian adjoint representation of osp(2/1;C) graded Lie algebra, we consider the Baker-Campbell-Hausdorff formula and find reality conditions for the Grassmann-odd trans-formation parameters that multiply the pair of odd generators of the graded Lie...

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Bibliographic Details
Main Author: Ilyenko, K.
Format: Article
Language:English
Published: Національний науковий центр «Харківський фізико-технічний інститут» НАН України 2007
Series:Вопросы атомной науки и техники
Subjects:
Quantum field theory
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/110897
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Summary:Given an explicit construction of the grade star hermitian adjoint representation of osp(2/1;C) graded Lie algebra, we consider the Baker-Campbell-Hausdorff formula and find reality conditions for the Grassmann-odd trans-formation parameters that multiply the pair of odd generators of the graded Lie algebra. Utilization of su(2)-spinors clarifies the nature of Grassmann-odd transformation parameters and allows one an investigation of the corresponding infinitesimal gauge transformations. We also explore the action of a corresponding group element on an appropriately graded representation space and find that a proper (graded) generalization of hermitian conjugation is consistent with a natural generalization of Dirac adjoint. A corresponding generalization of a unitary transformation is discussed.

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