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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- Partial requirement for: Ph.D., Arizona State University, 2011Note typethesis
- Includes bibliographical references (p. 91-97)Note typebibliography
- Field of study: Mathematics