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Casimir invariants and characteristic identities for generators of the general linear, special linear and orthosymplectic graded Lie algebras
Peter D. Jarvis,H.S. Green +1 more
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In this paper, the authors present the commutation and anticommutation relations, satisfied by the generators of the graded general linear, special linear and orthosymplectic Lie algebras, in canonical two-index matrix form.Abstract:
We present the commutation and anticommutation relations, satisfied by the generators of the graded general linear, special linear and orthosymplectic Lie algebras, in canonical two‐index matrix form. Tensor operators are constructed in the enveloping algebra, including powers of the matrix of generators. Traces of the latter are shown to yield a sequence of Casimir invariants. The transformation properties of vector operators under these algebras are also exhibited. The eigenvalues of the quadratic Casimir invariants are given for the irreducible representations of ggl(m ‖ n), gsl(m ‖ n), and osp(m ‖ n) in terms of the highest‐weight vector. In such representations, characteristic polynomial identities of order (m+n), satisfied by the matrix of generators, are obtained in factorized form. These are used in each case to determine the number of independent Casimir invariants of the trace form.read more
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Supergauge Transformations in Four-Dimensions
Julius Wess,Bruno Zumino +1 more
TL;DR: In this article, supergauge transformations are defined in four space-time dimensions and their commutators are shown to generate γ5 transformations and conformal transformations, respectively.
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Symmetries of baryons and mesons
TL;DR: In this article, it is suggested that the group is in fact U(3)×U(3), exemplified by the symmetrical Sakata model, and the symmetrized Sakata models are used to define the structure of baryons and mesons.
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Note on Unitary Symmetry in Strong Interactions
TL;DR: In this article, a mass formula for particles belonging to the same irreducible representation is derived and compared with experiments, assuming invariance of a theory under three-dimensional unitary group.
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Super-gauge transformations
TL;DR: In this paper, a method for constructing Wess-Zumino supergauge transformations is presented, which is based on the method described in Section 3.2.1.