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The theory of geometric quantum mechanics describes a quantum system as a Hamiltonian dynamical system, with a projective Hilbert space regarded as the phase space. This thesis extends the theory

The theory of geometric quantum mechanics describes a quantum system as a Hamiltonian dynamical system, with a projective Hilbert space regarded as the phase space. This thesis extends the theory by including some aspects of the symplectic topology of the quantum phase space. It is shown that the quantum mechanical uncertainty principle is a special case of an inequality from J-holomorphic map theory, that is, J-holomorphic curves minimize the difference between the quantum covariance matrix determinant and a symplectic area.

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    Date Created
    • 2011
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  • Text
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    • Partial requirement for: Ph.D., Arizona State University, 2011
      Note type
      thesis
    • Includes bibliographical references (p. 91-97)
      Note type
      bibliography
    • Field of study: Mathematics

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    by Barbara Sanborn

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