abstract: 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. An immediate consequence is that a minimal determinant is a topological invariant, within a fixed homology class of the curve. Various choices of quantum operators are studied with reference to the implicatio...
A geometric approach to quantum mechanics with unitary evolution and non-unitary collapse processes ...
In this thesis, a new generalized signal transform along with a new uncertainty principle is elabora...
This dissertation focuses on one question: how should one drive an experimentally prepared state of ...
Quantum mechanics is one of two foundational parts of modern physics. Along with relativity, quantum...
States of a quantum mechanical system are represented by rays in a complex Hilbert space. The space ...
A positive de\u85nite symmetric matrix quali\u85es as a quantum me-chanical covariance matrix if an...
Geometric Quantum Mechanics is a mathematical framework that shows how quantum theory may be express...
We develop a geometrical approach to Schrodinger quantum mechanics, alternative to the usual one, wh...
Geometric Quantum Mechanics is a mathematical framework that shows how quantum theory may be express...
The subject of this thesis is the geometry of the space of quantum states. The aim of this thesis is...
Some recent developments in topological quantum field theory have focused on localization techniques...
Some recent developments in topological quantum field theory have focused on localization techniques...
We propose the conjecture according to which the fact that quantum mechanics does not admit sharp va...
Phase space is the state space of classical mechanics, and this manifold is normally endowed only wi...
This thesis is concerned with a concept of geometrising time evolution of quantum systems. This conc...
A geometric approach to quantum mechanics with unitary evolution and non-unitary collapse processes ...
In this thesis, a new generalized signal transform along with a new uncertainty principle is elabora...
This dissertation focuses on one question: how should one drive an experimentally prepared state of ...
Quantum mechanics is one of two foundational parts of modern physics. Along with relativity, quantum...
States of a quantum mechanical system are represented by rays in a complex Hilbert space. The space ...
A positive de\u85nite symmetric matrix quali\u85es as a quantum me-chanical covariance matrix if an...
Geometric Quantum Mechanics is a mathematical framework that shows how quantum theory may be express...
We develop a geometrical approach to Schrodinger quantum mechanics, alternative to the usual one, wh...
Geometric Quantum Mechanics is a mathematical framework that shows how quantum theory may be express...
The subject of this thesis is the geometry of the space of quantum states. The aim of this thesis is...
Some recent developments in topological quantum field theory have focused on localization techniques...
Some recent developments in topological quantum field theory have focused on localization techniques...
We propose the conjecture according to which the fact that quantum mechanics does not admit sharp va...
Phase space is the state space of classical mechanics, and this manifold is normally endowed only wi...
This thesis is concerned with a concept of geometrising time evolution of quantum systems. This conc...
A geometric approach to quantum mechanics with unitary evolution and non-unitary collapse processes ...
In this thesis, a new generalized signal transform along with a new uncertainty principle is elabora...
This dissertation focuses on one question: how should one drive an experimentally prepared state of ...