Related papers: Poincar\'e et les quanta
Relations between differential calculi, quantum groups, integrable systems, and q-analysis are studied. Some new Hirota type formulas are established for qKP along with variations on classical Hirota formulas.
Henri Poincar\'e formulated the mathematics of Lorentz transformations, known as the Poincar\'e group. He also formulated the Poincar\'e sphere for polarization optics. It is shown that these two mathematical instruments can be derived from…
We reply to Dukelsky, et al. regarding the article: L. A. Wu, M. S. Byrd and D. A. Lidar, Phys. Rev. Lett. 89, 057904 (2002).
In this paper we consider the extended q-Bernstein polynomials which are constructed by T. Kim and we investigate some properties.
We discuss some subtleties in connection with the new attempts to provide a firm basis for ths Witten-Veneziano formula.
We describe the quantum $\kappa$-deformation of super-Poincar\'{e} algebra, with fundamental mass-like deformation parameter $\kappa$. We shall describe the result in graded bicrossproduct basis, with classical Lorentz superalgebra sector…
Inspired by the work of Feynman, Deutsch, We formally propose the theory of physical computability and accordingly, the physical complexity theory. To achieve this, a framework that can evaluate almost all forms of computation using various…
This is a philosophical paper. It claims that there is a gap to be filled in the relationship between complexity theory (CT) and quantum theory (QT). This gap concerns two very distinct understandings of time. The paper provides the ground…
In this methodological review, we discuss the fundamental concepts of the theory of integral invariants. This theory originated with Poincare and Cartan \cite{Koz, Kart} and was further developed by Kozlov \cite{int_K}. We demonstrate how…
I correct two misapprehensions, one historical and one conceptual, in the recent literature on extensions of the Wigner's Friend thought-experiment. Perhaps fittingly, both concern the accurate description of some quantum physicists'…
Central to our understanding of quantum many particle physics are two ideas due to Landau. The first is the notion of the electron as a well-defined quasiparticle excitation in the many body state. The second is that of the order parameter…
This is a reply to the paper by S.C.Benjamin, quant-ph/0008127.
This paper collects into one place my replies to the questions posed by Maximilian Schlosshauer in his interview volume about the foundations of quantum mechanics, "Elegance and Enigma: The Quantum Interviews" (Springer, 2011).
We present some results that show that bounds from classical coding theory still work in many cases of quantum coding theory.
The paper focuses on various properties and applications of the homotopy operator, which occurs in the Poincar\'{e} lemma. In the first part, an abstract operator calculus is constructed, where the exterior derivative is an abstract…
Here are a few random thoughts on the interpretations of the quantum double slit experiment, the Mach Zehnder experiment, the delayed-choice experiment and the measurement problem.
We discuss preliminary work on a formulation of relativistic quantum mechanics that uses reflection-positive Euclidean Green functions or their generating functionals as phenomenological input. We discuss the construction of a Poincare…
Quantum Poincar\'e-Weyl group in two dimensional quantum Minkowski space-time is considered and an appriopriate relativistic kinematics is investigated. It is claimed that a consistent approach to the above questions demands a kind of a…
We recall the abstract theory of Hopf algebra bicrossproducts and double cross products due to the author. We use it to develop some less-well known results about the quantum double as a twisting, as an extension and as $q$-Lorentz group.
Quantum mechanics of photons is derived from the theory of representations of the Poincar\'e group developed by Wigner. This theory places helicity as the most fundamental property; angular momentum and polarization are secondary…