
106$\mathfrak{D}$ Differentiation in Hilbert Space and the Structure of Quantum Mechanics Part II: Accelerated Observers and Fictitious Forces (review)Foundations of Physics 41 (4): 667685. 2011.We investigate a possible form of Schrödinger’s equation as it appears to moving observers. It is shown that, in this framework, accelerated motion requires fictitious potentials to be added to the original equation. The gauge invariance of the formulation is established. The example of accelerated Euclidean transformations is treated explicitly, which contain Galilean transformations as special cases. The relationship between an acceleration and a gravitational field is found to be compatible w…Read more

74$\mathfrak{D}$ Differentiation in Hilbert Space and the Structure of Quantum MechanicsFoundations of Physics 39 (5): 433473. 2009.An appropriate kind of curved Hilbert space is developed in such a manner that it admits operators of $\mathcal{C}$  and $\mathfrak{D}$ differentiation, which are the analogues of the familiar covariant and Ddifferentiation available in a manifold. These tools are then employed to shed light on the spacetime structure of Quantum Mechanics, from the points of view of the Feynman ‘path integral’ and of canonical quantisation. (The latter contains, as a special case, quantisation in arbitrary c…Read more

43A Minimal Framework for NonCommutative Quantum MechanicsFoundations of Physics 44 (11): 11681187. 2014.Deformation quantisation is applied to ordinary Quantum Mechanics by introducing the star product in a configuration space combining a Riemannian structure with a Poisson one. A Hilbert space compatible with such a configuration space is designed. The dynamics is expressed by a Hermitian Hamiltonian containing a scalar potential and a oneform potential. As a simple illustration, it is shown how a particular type of noncommutativity of the star product is interpretable as generating the Zeeman …Read more

31A Unified Framework for Relativity and CurvilinearTime Newtonian MechanicsFoundations of Physics 38 (4): 395408. 2008.Classical mechanics is presented so as to render the new formulation valid for an arbitrary temporal variable, as opposed to Newton’s Absolute Time only. Newton’s theory then becomes formally identical (in a precise sense) to relativity, albeit in a threedimensional manifold. (The ultimate difference between the two dynamics is traced to the existence of the relativistic ‘massshell’ condition.) A classical Lagrangian is provided for our formulation of the equations of motion and it is related …Read more
Springfield, Illinois, United States of America
Areas of Interest
Epistemology 
Philosophy of Social Science 