Related papers: The connection between statistical mechanics and q…
We study how the spin-statistics theorem relates to the geometric structures on phase space that are introduced in quantisation procedures (namely a U(1) bundle and connection). The relation can be proved in both the relativistic and the…
In recent years a statistical mechanics description of particles, fields and spacetime based on the concept of quantum open systems and the influence functional formalism has been introduced. It reproduces in full the established theory of…
One of the simplest examples of a PT-symmetric quantum system is the scaling Yang-Lee model, a quantum field theory with cubic interaction and purely imaginary coupling. We give a historical review of some facts about this model in d <= 2…
A previous derivation of the single-particle Schr\"odinger equation from statistical assumptions is generalized to an arbitrary number $N$ of particles moving in three-dimensional space. Spin and gauge fields are also taken into account. It…
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…
The physics of non-zero temperature dynamics and transport near quantum-critical points is discussed by a detailed study of the O(N)-symmetric, relativistic, quantum field theory of a N-component scalar field in $d$ spatial dimensions. A…
The quantum field theories (QFT) constructed in [1,2] include phenomenology of interest. The constructions approximate: scattering by $1/r$ and Yukawa potentials in non-relativistic approximations; and the first contributing order of the…
These lecture notes give an introduction to the theory of interacting particle systems. The main subjects are the construction using generators and graphical representations, the mean field limit, stochastic order, duality, and the relation…
A hidden gauge theory structure of quantum mechanics which is invisible in its conventional formulation is uncovered. Quantum mechanics is shown to be equivalent to a certain Yang-Mills theory with an infinite-dimensional gauge group and a…
These lecture notes are an informal introduction to the theory of computational complexity and its links to quantum computing and statistical mechanics.
Four lectures given at Nankai Institute of Mathematics, Tianjin, China, 5--13 April 1991 present an elementary introduction into the quantum integrable models aimed for mathematical physicists and mathematicians. The stress is made on the…
We present a conceptually clear introduction to quantum theory, deriving the theory from scratch from the point of view of quantum information. Different subsets of these lectures were taught to a wide variety of audiences, including…
The treatment of the number-theoretical problem of integer partitions within the approach of statistical mechanics is discussed. Historical overview is given and known asymptotic results for linear and plane partitions are reproduced. From…
Schwinger pair production in spatially and temporally inhomogeneous electric and magnetic fields is studied. The focus is on the particle phase-space distribution within a high-intensity few-cycle pulse. Accurate numerical solutions of a…
A class of fermionic quantum field theories with interactions is shown to be equivalent to probabilistic cellular automata, namely cellular automata with a probability distribution for the initial states. Probabilistic cellular automata on…
In this paper, we show how classical statistical field theory techniques can be used to efficiently perform the numerical evaluation of the non-perturbative Schwinger mechanism of particle production by quantum tunneling. In some…
These notes offer a lightening introduction to topological quantum field theory in its functorial axiomatisation, assuming no or little prior exposure. We lay some emphasis on the connection between the path integral motivation and the…
The non-perturbative mapping between different Quantum Field Theories and other features of two-dimensional massive integrable models are discussed by using the Form Factor approach. The computation of ultraviolet data associated to the…
These are lectures presented at the Les Houches Summer School ``Topology and Geometry in Physics'', July 1998. They provide a simple introduction to non perturbative methods of field theory in 1+1 dimensions, and their application to the…
Relational formulation of quantum mechanics is based on the idea that relational properties among quantum systems, instead of the independent properties of a quantum system, are the most fundamental elements to construct quantum mechanics.…