Related papers: Bogdan Mielnik, geometry and quanta
We present an overview of recent developments concerning modifications of the geometry of space-time to describe various physical processes of interactions among classical and quantum configurations. We concentrate in two main lines of…
This is the introduction I wrote for the multi-authored book "From Riemann to differential geometry and relativity", edited by L. Ji, A. Papadopoulos and S. Yamada (Berlin, Springer verlag, 2017). The book consists of twenty chapters,…
In this scientific preface to the first issue of International Journal of Geometric Methods in Modern Physics, we briefly survey some peculiarities of geometric techniques in quantum models.
We summarize our work on spherically symmetric midi-superspaces in loop quantum gravity. Our approach is based on using inhomogeneous slicings that may penetrate the horizon in case there is one and on a redefinition of the constraints so…
The phenomenon of quantum entanglement is thoroughly investigated, focussing especially on geometrical aspects and on bipartite systems. After introducing the formalism and discussing general aspects, some of the most important separability…
Classical limits of quantum systems are shown to lead to different conceptions of spaces different from the classical one underlying the process of quantization of such systems. The accent is put in situations where traces of…
Gravity with incorporation of additional dimensions and noncommutative geometry.
During the past decades, quantum mechanical methods have undergone an amazing transition from pioneering investigations of experts into a wide range of practical applications, made by a vast community of researchers. First principles…
After stating the author's ontic position, a collage of relevant thoughts of some distinguished foundationally-minded physicists are quoted and polemically commented upon. Thus, a kind of historical background of the recent ontic…
Despite many successes of quantum electrodynamics (QED), we do not presently have a good understanding of this field of physics. QED has all of the foundational problems that standard non-relativistic quantum mechanics has, and further ones…
Feyerabend frequently discussed physics. He also referred to the history of the subject when motivating his philosophy of science. Alas, as some examples show, his understanding of physics remained superficial. In this respect, Feyerabend…
Throughout John Wheeler's career, he wrestled with big issues like the fundamental length, the black hole and the unification of quantum mechanics and relativity. In this essay, I argue that solid state physics -- historically the study of…
With the two most profound conceptual revolutions of XXth century physics, quantum mechanics and relativity, which have culminated into relativistic spacetime geometry and quantum gauge field theory as the principles for gravity and the…
The extravagances of quantum mechanics never fail to enrich daily the debate around natural philosophy. Entanglement, non-locality, collapse, many worlds, many minds, and subjectivism have challenged generations of thinkers. Its approach…
In 1917 F. Klein proposed his work on projective geometry to A. Einstein for further developments of general relativity. Klein had a peculiar way to consider the relationship between mathematics and physics, based on his Erlanger Programm…
Discussed are some geometric aspects of the phase space formalism in quantum mechanics in the sense of Weyl, Wigner, Moyal and Ville. We analyze the relationship between this formalism and geometry of the Galilei group, classical momentum…
This set of lectures contain a brief review of some basic supersymmetry and its representations, with emphasis on superspace and superfields. Starting from the Poincar\'e group, the supersymmetric extensions allowed by the Coleman-Mandula…
Starting from the groupoid approach to Schwinger's picture of Quantum Mechanics, a proposal for the description of symmetries in this framework is advanced.It is shown that, given a groupoid $G\rightrightarrows \Omega$ associated with a…
Building on parallels between geometric quantum mechanics and classical mechanics, we explore an alternative basis for quantum thermodynamics that exploits the differential geometry of the underlying state space. We develop both…
Contrary to the opinion of J. Polchinski [Phys.Rev.Lett. {\bf 66}, 397-400 (1991)], the phenomenon of superluminal messages in nonlinear versions of quantum mechanics is not a specific difficulty in a class of theories formulated by S.…