Related papers: This Week's Finds in Mathematical Physics (1-50)
This is the first of a series of papers in which we present a brief introduction to the relevant mathematical and physical ideas that form the foundation of Particle Physics, including Group Theory, Relativistic Quantum Mechanics, Quantum…
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…
This article surveys invariants of four-manifolds and their relation to Donaldson-Witten theory, and other topologically twisted Yang-Mills theories. The article is written for the second edition of the Encyclopedia of Mathematical Physics,…
I review some recent results on four-manifold invariants which have been obtained in the context of topological quantum field theory. I focus on three different aspects: (a) the computation of correlation functions, which give explicit…
These third-year lecture notes are designed for a 1-semester course in topological quantum field theory (TQFT). Assumed background in mathematics and physics are only standard second-year subjects: multivariable calculus, introduction to…
Particle physics has evolved in the past decade through evaluating the consequences of experimental measurements as well as exploiting theoretical tools that permit exploration of new model building and cosmological possibilities.…
The search for a quantum theory of gravity has been one of the main aims of theoretical physics for many years by now. However the efforts in this direction have been often hampered by the lack of experimental/observational tests able to…
I present a summary of the recent progress made in field and string theory which has led to a reformulation of quantum-group polynomial invariants for knots and links into new polynomial invariants whose coefficients can be described in…
This essay is based on a physics lecture given at the Hong Kong University of Science and Technology on May 24, 2006, Hong Kong. It has 5 sections and one page of references and suggested reading. The section titles are: 1. Origin of the…
This paper summarizes the recent state of the art of the following topics presented at the FQMT'04 conference: Quantum, mesoscopic and (partly) classical thermodynamics; Quantum limits to the second law of thermodynamics; Quantum…
In the second half of the 1920s, physicists and mathematicians introduced group theoretic methods into the recently invented ``new'' quantum mechanics. Group representations turned out to be a highly useful tool in spectroscopy and in…
With the discovery of gravitational waves, the search for the quantum of gravity, the graviton, is imminent. We discuss the current status of the bounds on graviton mass from experiments as well as the theoretical understanding of these…
These are extended lecture notes of the quantum mechanics course which I am teaching in the Weizmann Institute of Science graduate physics program. They cover the topics listed below. The first four chapter are posted here. Their content is…
Some theoretic results related to the cosmological constant, obtained in the 80's and 90's of last century, are reviewed. These results exhibit some interesting underlying pattern when viewed from a category-theoretic perspective. In doing…
Wilson observables for 2+1 quantum gravity with negative cosmological constant, when the spatial manifold is a torus, exhibit several novel features: signed area phases relate the observables assigned to homotopic loops, and their…
We introduce the key ideas behind the group field theory approach to quantum gravity, and the basic elements of its formalism. We also briefly report on some recent results obtained in this approach, concerning both the mathematical…
"Quantum Topology" deals with the general quantum theory as the theory of the functional quantum space; space time and energy momentum forms form a connected manifold; a functional quantum space on the quantum level. The general quantum…
We introduce here very briefly, through some selective choices of problems and through the sample computer simulation programs (following the request of the editor for this invited review in the Journal of Physics Through Computation), the…
Recent advances in cooling, control, and measurement of mechanical systems in the quantum regime have opened the possibility of the first direct observation of quantum gravity, at scales achievable in experiments. This paper gives a broad…
The fact that one can associate thermodynamic properties with horizons brings together principles of quantum theory, gravitation and thermodynamics and possibly offers a window to the nature of quantum geometry. This review discusses…