Related papers: Mathematical surprises and Dirac's formalism in qu…

As the first step in an approach to the solution of Hilbert's sixth problem, a general scheme of mechanics, called `supmech', is developed integrating noncommutative symplectic geometry and noncommutative probability theory in an algebraic…

A qualitative but formalized representation of microstates is first established quite independently of the quantum mechanical mathematical formalism, exclusively under epistemological-operational-methodological constraints. Then, using this…

We start to develop the quantization formalism in a hyperbolic Hilbert space. Generalizing Born's probability interpretation, we found that unitary transformations in such a Hilbert space represent a new class of transformations of…

We present a recent work on the Dirac equation in a curved spacetime. In addition to the standard equation, two alternative versions are considered, derived from wave mechanics, and based on the tensor representation of the Dirac field. The…

States of a quantum mechanical system are represented by rays in a complex Hilbert space. The space of rays has, naturally, the structure of a K\"ahler manifold. This leads to a geometrical formulation of the postulates of quantum mechanics…

In paper [Znojil M., Phys. Rev. D 78 (2008), 085003, 5 pages, arXiv:0809.2874] the two-Hilbert-space (2HS, a.k.a. cryptohermitian) formulation of Quantum Mechanics has been revisited. In the present continuation of this study (with the…

The dual wave-particle nature of quantum objects is a notoriously unintuitive feature of quantum theories. However, it is often deemed essential, due to quantum objects exhibiting diffraction and interference. We extend the work of…

Authoritative appraisals qualified this book as an axiomatic theory. However, being its essential content no more than an analogy, its theoretical organization cannot be an axiomatic one. In fact, in the first edition Dirac declares to…

Quantum mechanics is challenging even for advanced undergraduate and graduate students. Dirac notation is a convenient notation used extensively in quantum mechanics. We have been investigating the difficulties that the advanced…

A new framework for deriving equations of motion for constrained quantum systems is introduced, and a procedure for its implementation is outlined. In special cases the framework reduces to a quantum analogue of the Dirac theory of…

The traditional approach to accelerator optics, based mainly on classical mechanics, is working excellently from the practical point of view. However, from the point of view of curiosity, as well as with a view to explore quantitatively the…

Dirac notation is used commonly in quantum mechanics. However, many upper-level undergraduate and graduate students in physics have difficulties with representations of quantum operators corresponding to observables especially when using…

We present a heuristic derivation of Born's rule and unitary transforms in Quantum Mechanics, from a simple set of axioms built upon a physical phenomenology of quantization. This approach naturally leads to the usual quantum formalism,…

After some historical remarks concerning Schroedinger's discovery of wave mechanics, we present a unified formalism for the mathematical description of classical and quantum-mechanical systems, utilizing elements of the theory of operator…

After the development of a self-consistent quantum formalism nearly a century ago, there ensued a quest to understand the often counterintuitive predictions of the theory. These endeavors invariably begin with the assumption of the "truth"…

Classical mechanics is formulated in complex Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket, and a quasidensity operator. These are analogues of the star product, the Moyal bracket, and…

The basic physical problems that necessitated the emergence of quantum physics are summarized, along with the elements of wave mechanics and its traditional statistical interpretation. Alternative interpretations to the statistical one,…

Commutator anomalies obstruct solving the Wheeler-DeWitt constraint equation in Dirac quantization of quantum gravity-matter theory. When the obstruction is removed, there result quantal modifications to the constraints. The same classical…

The long-standing problem of time in canonical quantum gravity is the source of several conceptual and technical issues. Here, recent mathematical results are used to provide a consistent algebraic formulation of dynamical symplectic…

An extension of the Dirac procedure for the quantization of constrained systems is necessary to address certain issues that are left open in Dirac's original proposal. These issues play an important role especially in the context of…