Related papers: Refinement of Robertson-type uncertainty principle…
Although classical mechanics and quantum mechanics are separate disciplines, we live in a world where Planck's constant \hbar>0, meaning that the classical and quantum world views must actually {\it coexist}. Traditionally, canonical…
An explicit Lorentz covariant formulation of the canonical theory for classical fields is established on a space-like hypersurface. Hamilton's equations and a Poisson bracket are defined on the space-like hypersurface. The Poisson bracket…
We show that an inequality recently proved by Kosaki and Yanagi-Furuichi-Kuriyama [arXiv:quant-ph/0501152] has a natural geometric interpretation in terms of monotone metrics associated to Wigner-Yanase-Dyson information. Moreover we give a…
It was generally believed that, in general relativity, the fundamental laws of nature should be invariant or covariant under a general coordinate transformation. In general relativity, the equivalence principle tells us the existence of a…
`Global' symmetries, such as the boost invariance of classical mechanics and special relativity, can give rise to direct empirical counterparts such as the Galileo-ship phenomenon. However, a widely accepted line of thought holds that…
We here consider a generalization of the Klein-Gordon scalar wave equation which involves a single arbitrary function. The quantization may be viewed as allowing $\hbar$ to be a function of the momentum or wave vector rather than a…
In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the…
General characterizations of physical measurements are discussed within the framework of the classical information theory. The uncertainty relation for simultaneous measurements of two physical observables is defined in this framework for…
This work concerns some issues about the interplay of standard and geometric (Hamiltonian) approaches to finite-dimensional quantum mechanics, formulated in the projective space. Our analysis relies upon the notion and the properties of…
Covariant classical particle dynamics is described, and the associated covariant relativistic particle quantum mechanics is derived. The invariant symmetric bracket is defined on the space of quantum amplitudes, and its relation to a…
The problem of observables in classical and quantum gravity is a long-standing one. It is sometimes argued that observable quantities should be diffeomorphsm invariant, following the philosophy of Dirac. We argue that diffeomorphism…
Measurement outcomes of a quantum state can be genuinely random (unpredictable) according to the basic laws of quantum mechanics. The Heisenberg-Robertson uncertainty relation puts constrains on the accuracy of two noncommuting observables.…
Mathematical tools related to coherence theory and classical-quantum equivalence, due to Wigner and Glauber, are essential to modern, practical and empirical understanding of electromagnetics in areas like quantum optics and…
We argue that a conformally invariant extension of general relativity coupled to the Standard Model is the fundamental theory that needs to be quantized. We show that it can be treated by loop quantum gravity techniques. Through a gauge…
It is shown that, with some reasonable assumptions, the theory of general relativity can be made compatible with quantum mechanics by using the field equations of general relativity to construct a Robertson-Walker metric for a quantum…
Bohmian mechanics offers a deterministic alternative to conventional quantum theory through well-defined particle trajectories. While successful in nonrelativistic contexts, its extension to curved spacetime-and hence quantum…
We introduce a particular nonlinear generalization of quantum mechanics which has the property that it is exactly solvable in terms of the eigenvalues and eigenfunctions of the Hamiltonian of the usual linear quantum mechanics problem. We…
In this work we analyze the deep link between the 20th Century positivist re-foundation of physics and the famous measurement problem of quantum mechanics. We attempt to show why this is not an "obvious" nor "self evident" problem for the…
A generalized Clifford manifold is proposed in which there are coordinates not only for the basis vector generators, but for each element of the Clifford group, including the identity scalar. These new quantities are physically interpreted…
Hamiltonian mechanics describes the evolution of a system through its Hamiltonian. The Hamiltonian typically also represents the energy observable, a Noether-conserved quantity associated with the time-invariance of the law of evolution. In…