Related papers: Quantum Spaces: Notes and Comments on a Lecture by…
Some formulas and speculations are presented relative to integrable systems and quantum mechanics.
In this paper, we expose the construction of a possible, simple quantum matrix group (according to Woronowicz), related to elementary formal aspects of the Einstein field equations of General Relativity, and its possible symmetries.
This article is based on the opening lecture at the third quantum geometry and quantum gravity school sponsored by the European Science Foundation and held at Zakopane, Poland in March 2011. The goal of the lecture was to present a broad…
We present the summary of the general discussion on the probabilistic foundations of quantum theory that took place during the round table at the Int. Conf. "Foundations of Probability and Physics", V\"axj\"o, Sweden-2000. It is possible to…
In a recently proposed interpretation of quantum mechanics, U. Mohrhoff advocates original and thought-provoking views on space and time, the definition of macroscopic objects, and the meaning of probability statements. The interpretation…
This paper discusses the role of the Skorokhod space and the convergence of probability measures on it in some recent studies of the foundations of quantum mechanics, both in the conventional setting over the real number field and in the…
We report on joint work, past and in progress, with K.Fredenhagen and with J.E,Roberts, on the quantum structure of spacetime in the small which is dictated by the principles of Quantum Mechanics and of General Relativity; we comment on how…
This is a set of lecture notes for the first author's lectures on the difference equations in 2019 at the Institute of Advanced Study for Mathematics at Zhejiang University. We focus on explicit computations and examples. The convergence of…
In this short note, based on the talk given at the 3rd Conference of the Polish Society on Relativity, I present the basic points of our recent paper "Symmetries of quantum spacetime in three dimensions", stressing their physical meaning,…
Comment on "Backflow in relativistic wave equations" by I. Bialynicki-Birula, Z. Bialynicka-Birula, and S. Augustynowicz [Journal of Physics A: Mathematical and Theoretical, volume 55, page 255702 (2022)].
Kotlarski's theorem (see H. Kotlarski. Bounded Induction and Satisfaction Classes. Mathematical Logic Quarterly, vol. 32, 31-34, 1986, P. 531--544.) formalized in $WKL_0$.
The purpose of this note is threefold: (i) to recall (with some points made more explicit) the mathematical Weyl algebra model formulation, given before, of the Staruszkiewicz theory of quantum Coulomb field; (ii) to add some new elements…
Inspired by the work of L. Drewnowski in [Studia Math. 77 (1984) 373--391], our research reveals new insights and characterizes the notion of spaceability in the context of complements of subspaces (not necessarily closed) within the…
Quasi-Polish spaces were introduced by de Brecht as a possibly non-Hausdorff generalization of Polish spaces sharing many of their descriptive set-theoretic properties. We give a self-contained exposition of the basic theory of quasi-Polish…
These are expanded notes of a course on basics of quantum field theory for mathematicians given by the author at MIT.
The structure and properties of possible $q$-Minkowski spaces is discussed, and the corresponding non-commutative differential calculi are developed in detail and compared with already existing proposals. This is done by stressing its…
The paper below is a written version of the 17th Andrzej Lasota Lecture presented on January 12th, 2024 in Katowice. During the lecture we tried to show the impact of Andrzej Lasota's results on the author's research concerning various…
These are the notes from my courses on the arithmetic of quadratic forms.
These lecture notes are based on a course given at Institut de Physique Th\'eorique of CEA/Saclay in January/February 2013.
This is the extended version of a talk presented at the J.W.Goethe Universitaet Frankfurt a. M. and at the same time a preview at a forthcoming extensive publication on the same subject. It is shown that there is a common background…