Related papers: Crystallography Without Periodicity
Notes from the lectures by the author at the 7th Jerusalem Winter School 1990 on Quantum Cosmology and Baby Universes. The lectures covered quantum mechanics for closed systems like the universe, generalized quantum mechanics, time in…
This article is based on an invited talk given at the Workshop on Mathematical Physics Towards XXIst Century, held at Beer-Sheva, Israel in 1993. It contains an introduction to quantum gravity for mathematical physicists with an emphasis on…
This is a survey paper on algebraic surfaces in positive characteristic based on a series of lectures that the author gave at the University of Edinburgh in March 2023. It is focused on certain positive characteristic phenomena like…
Crystallographic groups describe the symmetries of crystals and other repetitive structures encountered in nature and the sciences. These groups include the wallpaper and space groups. We derive linear and nonlinear representations of…
This is an expanded version of the lectures given at the Trieste Summer School 1992 on Low-dimensional Quantum Field Theories for Condensed Matter Physicists.
comment on Phys. Rev. Lett. 103, 042302 (2009)
Holography suggests a considerable reduction of degrees of freedom in theories with gravity. However it seems to be difficult to understand how holography could be realized in a closed re--contracting universe. In this letter we claim that…
The method of group quantization described in the preceeding paper I is extended so that it becomes applicable to some parametrized systems that do not admit a global transversal surface. A simple completely solvable toy system is studied…
We recall a group-theoretic description of the first non-vanishing homotopy group of a certain (n+1)-ad of spaces and show how it yields several formulae for homotopy and homology groups of specific spaces. In particular we obtain an…
Time crystals are quantum many-body systems which, due to interactions between particles, are able to spontaneously self-organize their motion in a periodic way in time by analogy with the formation of crystalline structures in space in…
The meaning of `tunneling' in a timeless theory such as quantum cosmology is discussed. A recent suggestion of `tunneling' of the macroscopic universe at the classical turning point is analyzed in an anisotropic and inhomogeneous toy model.…
An introduction to quantum groups and non-commutative differential calculus (Lecture at the III Workshop on Differential Geometry, Granada, September 1994)
The conditions under which stochastic systems of infinitely many interacting particles can maintain sufficient spatial order to move coherently along a time-periodic orbit, thereby breaking the time-translation invariance of the underlying…
This is an extended abstract for a talk given at the Oberwolfach workshop "The Renormalization Group", March 13th - March 19th, 2011.
The existence of a global time is often taken for granted but should instead be considered as a matter of investigation. By using the tools of global Lorentzian geometry I show that, under physically reasonable conditions, the impossibility…
In Section 5 of Christian (2014), published in IJTP, an experiment is described which is purported to have the capacity for exhibiting quantum correlations in a completely classical environment. Unfortunately the experiment has an…
The X-ray luminosity and temperature of clusters and groups of galaxies do not scale in a self-similar manner. This has often been interpreted as a sign that the intracluster medium has been substantially heated by non-gravitational…
GGR News: We hear that... by Jorge Pullin * Research Briefs: Too many coincidences?, by Laura Mersini The Quest for a Realistic Cosmology in String Theory, by Andrew Chamblin SFB/TR 7, by A. Gopakumar and D. Petroff The mock LISA data…
These notes are loosely based on lectures given at the CERN Winter School on Supergravity, Strings and Gauge theories, February 2009 and at the IPM String School in Tehran, April 2009. I have focused on a few concrete topics and also on…
Condensed account of the Lectures delivered at the Meeting on {\it Noncommutative Geometry in Field and String Theory}, Corfu, September 18 - 20, 2005.