Related papers: Topos-Theoretic Approaches to Quantum Theory
The topic of the review is the application of new ideas of unconventional quantum states to the physics of condensed matter, in particular of solid state, in the context of modern field theory. A comparison is made with classical papers on…
Following my plenary lecture on ICMP2000 I review my results concerning two closely related topics: topological quantum field theories and the problem of quantization of gauge theories. I start with old results (first examples of…
We construct a topos of quantum sets and embed into it the classical topos of sets. We show that the internal logic of the topos of sets, when interpreted in the topos of quantum sets, provides the Birkhoff-von Neumann quantum propositional…
We give a review of concepts related to connection of classical and quantum theories, from the phase space perspective. Quantum theory is described by non-commutative operators of coordinates and momenta, results in values having a certain…
Prepared for the Quantum Field Theory section of the Encyclopedia of Mathematical Physics, Elsevier, 2006. A brief introduction to the methodology and techniques of perturbative relativistic quantum field theory is presented.
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…
We discuss several proposals for astrophysical and cosmological tests of quantum theory. The tests are motivated by deterministic hidden-variables theories, and in particular by the view that quantum physics is merely an effective theory of…
This book is an account of certain topics in general and algebraic topology. Instead of laying out a synopsis of each chapter, here is a sample of some of what is taken up: 1) Nilpotency and its role in homotopy theory. 2) Bousfield's…
A brief exposition of the point of higher topos theory in (mathematical) physics, commissioned for the Encyclopedia of Mathematical Physics 2nd ed.
One hundred years after the creation of quantum theory, there is no consensus on the kind of reality that is described by the theory. Here, I attribute the lack of progress to the prevailing interpretative methodology, which invariably…
The purpose of this work is to retrace the steps that were made by scientists of XX century, like Bohr, Schrodinger, Heisenberg, Pauli, Dirac, for the formulation of what today represents the modern quantum mechanics and that, within two…
This is a presentation of recent work on quantum permutation groups. Contains: a short introduction to operator algebras and Hopf algebras; quantum permutation groups, and their basic properties; diagrams, integration formulae, asymptotic…
A review is given of work by Abhay Ashtekar and his colleagues Carlo Rovelli, Lee Smolin, and others, which is directed at constructing a nonperturbative quantum theory of general relativity.
I briefly review several important formal theory developments in quantum field theory and string theory that were reported at ICHEP conferences in past decades, and explain how they underlie a new research area referred to as physical or…
Suggestions concerning the generalization of the geometric quantization to the case of nonlinear field theories are given. Results for the Liouville field theory are presented.
There exists a physically well motivated method for approximating manifolds by certain topological spaces with a finite or a countable set of points. These spaces, which are partially ordered sets (posets) have the power to effectively…
A brief review of various numerical techniques used in loop quantum cosmology and results is presented. These include the way extensive numerical simulations shed insights on the resolution of classical singularities, resulting in the key…
Many scientists seeking to understand the quantum mechanics of measurement situations (Copenhagen quantum theory) agree on its overwhelmingly successful algorithms to predict the outcomes of laboratory measurements but disagree on what…
It is argued that quantum gravity has an interpretation as a topological field theory provided a certain constraint from the path intergral measure is respected. The constraint forces us to couple gauge and matter fields to gravity for…
A brief synopsis of recent conceptions and results, the current status and future outlook of our research program of applying sheaf and topos-theoretic ideas to quantum gravity and quantum logic is presented.