Related papers: Fractional Fourier Transform and Geometric Quantiz…
A theory of non-unitary-invertible as well as unitary canonical transformations is formulated in the context of Weyl's phase space representations. That all quantum canonical transformations without an explicit $\hbar$ dependence are also…
We propose a mathematical structure, based on a noncommutative geometry, which combines essential aspects of general relativity and quantum mechanics, and leads to correct "limiting cases" of both these theories. We quantize a groupoid…
In this first of a series of four articles, it is shown how a hamiltonian quantum dynamics can be formulated based on a generalization of classical probability theory using the notion of quasi-invariant measures on the classical phase space…
We present a new variational method for investigating the ground state and out of equilibrium dynamics of quantum many-body bosonic and fermionic systems. Our approach is based on constructing variational wavefunctions which extend Gaussian…
A review of fundamentals and physical applications of fractional quantum mechanics has been presented. Fundamentals cover fractional Schr\"odinger equation, quantum Riesz fractional derivative, path integral approach to fractional quantum…
"Quantum Topology" deals with the general quantum theory as the theory of the functional quantum space; space time and energy momentum forms form a connected manifold; a functional quantum space on the quantum level. The general quantum…
The description of states and dynamics in non-Hermitian systems is fundamentally linked to the choice of an appropriate theoretical framework -- a point of ongoing debate in the field. This work addresses this issue by proposing a…
In describing a dynamical system, the greatest part of the work for a theoretician is to translate experimental data into differential equations. It is desirable for such differential equations to admit a Lagrangian and/or an Hamiltonian…
Is quantum mechanics about 'states'? Or is it basically another kind of probability theory? It is argued that the elementary formalism of quantum mechanics operates as a well-justified alternative to 'classical' instantiations of a…
The conventional phase space of classical physics treats space and time differently, and this difference carries over to field theories and quantum mechanics (QM). In this paper, the phase space is enhanced through two main extensions.…
The quantum Fourier transform (QFT) plays an important role in many known quantum algorithms such as Shor's algorithm for prime factorisation. In this paper we show that the QFT algorithm can, on a restricted set of input states, be…
The description of a closed quantum system is extended with the identification of an underlying substructure enabling an expanded formulation of dynamics in the Heisenberg picture. Between measurements a ``state point" moves in an…
In this paper, the generic part of the gauge theory of gravity is derived, based merely on the action principle and on the general principle of relativity. We apply the canonical transformation framework to formulate geometrodynamics as a…
It is shown that the Schrodinger equation is a byproduct of more deterministic Boltzmann-like equation. All physical information is derived from the solution of this equation, which is a function of space and momentum. The additional terms…
Trajectory-based approaches to quantum mechanics include the de Broglie-Bohm interpretation and Nelson's stochastic interpretation. It is shown that the usual route to establishing the validity of such interpretations, via a decomposition…
According to quantum theory, pure physical states correspond to equivalence classes of state vectors, where any two members of one class differ by a complex factor. The point is that such a factor does not change the probability for the…
The geometric formulation of quantum mechanics is a very interesting field of research which has many applications in the emerging field of quantum computation and quantum information, such as schemes for optimal quantum computers. In this…
We represent both the states and the evolution of a quantum computer in phase space using the discrete Wigner function. We study properties of the phase space representation of quantum algorithms: apart from analyzing important examples,…
We present a simple new way - called Schrodingerisation - to simulate general linear partial differential equations via quantum simulation. Using a simple new transform, referred to as the warped phase transformation, any linear partial…
The Projection Postulate from Standard Quantum Mechanics relies fundamentally on measurements. But measurements implicitly suggest the existence of anthropocentric notions like measuring devices, which should rather emerge from the theory.…