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    Chapter

    Canonical Forms of Positive Definite Matrices under Congruence: Extensions of the Schweinler-Wigner Extremum Principle

    It is well known that a N-dimensional real symmetric [complex hermitian] matrix V is congruent to a diagonal matrix modulo an orthogonal [unitary] matrix[1]. That is, V = S✝DS where D is diagonal and S ∈ SO(N) [S

    S. Chaturvedi, V. Srinivasan, R. Simon in Frontiers of Fundamental Physics 4 (2001)

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    Chapter

    The Two-Dimensional Symplectic and Metaplectic Groups and Their Universal Cover

    We give a detailed discussion of the group Sp(2, R), organized in such a way as to lead to explicit constructive descriptions of the metaplectic group Mp(2) and the universal covering group

    R. Simon, N. Mukunda in Symmetries in Science VI (1993)