This leads to a geometrical formulation of the postulates of quantum mechanics which, although equivalent to the standard algebraic formulation, has a very different appearance. The literature on this subject is extensive. Proposals for nonlinear extenstions of quantum mechanics are discussed.
A fundamental starting point in quantum information theory is the consideration of the von Neumann entropy and its generalization to relative quantum entropies. This leads to a geometrical formulation of the postulates of quantum mechanics which, although equivalent to the standard algebraic formulation, has a very different appearance.
The geometric formulation of autonomous Hamiltonian mechanics in the terms of symplectic and Poisson manifolds is generally accepted. The literature on this subject is extensive. The geometric formulation of autonomous Hamiltonian mechanics in the terms of symplectic and Poisson manifolds is generally accepted. As a mere representation change, however, Weyl's map underlies the alternate phase-space formulation of conventional quantum mechanics. Probability theory was used in statistical mechanics. These papers analyze the quantum mechanical Dirac theory of the electron with respect to its geometric structure as revealed by reformulation in terms of Spacetime Algebra.
present formulation and interpretation of quantum mechanics when applied to so fundamental a structure as the space-time geometry itself. The main result is that the Dirac wave function psi can be decomposed into the invariant operator form It presents a reformulation of quantum theory in a form believed suitable for application to general relativity. This paper seeks to clarify the formulations of quantum mechanics. A particular feature of quantum relative entropies is their relation via their Hessian to monotonic Riemannian metrics on the dense set of invertible mixed quantum states (Lesniewski and Ruskai 1999). Gianfausto Dell’Antonio Lectures on the Mathematics of Quantum Mechanics February 12, 2015 Mathematical Department, Universita’ Sapienza (Rome) These results are collected in section IID to obtain a geometric formulation of the postulates of quantum mechanics, a formulation that makes no reference to the Hilbert space Hor the associated linear structures. The geometric formulation of autonomous Hamiltonian mechanics in the terms of symplectic and Poisson manifolds is generally accepted. The present book provides the geometric formulation of non-autonomous mechanics in a general setting of time-dependent coordinate and reference frame transformations. The literature on this subject is extensive. The literature on this subject is extensive.
Geometric Algebra in Quantum Mechanics. The traditional formulation of quantum mechanics is linear and algebraic.