Related papers: Classical Mechanics
Sometime ago it was shown that the operatorial approach to classical mechanics, pioneered in the 30's by Koopman and von Neumann, can have a functional version. In this talk we will extend this functional approach to the case of classical…
This book includes my lectures, together with their problem sets and solutions, on 1) classical mechanics (one semester), 2) thermodynamics and statistical mechanics (one semester), and 3) quantum mechanics (one semester), which I have been…
In this talk I shall try to give an elementary introduction to certain areas of mathematical physics where the idea of moduli space is used to help solve problems or to further our understanding. In the wide area of gauge theory, I shall…
In this paper we extend the geometric formalism of the Hamilton-Jacobi theory for hamiltonian mechanics to the case of classical field theories in the framework of multisymplectic geometry and Ehresmann connections.
We briefly show how classical mechanics can be rederived and better understood as a consequence of three assumptions: infinitesimal reducibility, deterministic and reversible evolution, and kinematic equivalence.
This write-up starts by introducing lattice chirality to people possessing a fairly modern mathematical background, but little prior knowledge about modern physics. I then proceed to present two new and speculative ideas.
A didatic approach of the Noether's theorem in classical mechanics is derived and used to obtain the laws of conservation.
A diagram approach to classical nonlinear stochastic field theory is introduced. This approach is intended to serve as a link between quantum and classical field theories, resulting in an independent constructive characterisation of the…
These lecture notes provide an introduction to quantum information and quantum computation, which are strongly related disciplines and subject of intense research. The lecture notes contain only a small selection of topics in these…
This is an informal introduction to the ideas of decoherence and emergent classicality, including a simple account of the decoherent histories approach to quantum theory. It is aimed at undergraduates with a basic appreciation of quantum…
These lectures present some basic facts in field theory necessary to understand the quantum theory of the Standard Model of weak and electromagnetic interactions.
We give an elementary introduction to classical and quantum bosonic string theory.
These are the lecture notes for an introductory course on black holes and some aspects of their interaction with the classical and quantum world. The focus is on phenomena of "fundamental physics" in the immediate surroundings of the black…
Interpretational problems with quantum mechanics can be phrased precisely by only talking about empirically accessible information. This prompts a mathematical reformulation of quantum mechanics in terms of classical mechanics. We survey…
We present a general method to derive the classical mechanics of a system of identical particles in a way that retains information about quantum statistics. The resulting statistical mechanics can be interpreted as a classical version of…
We discuss the deformation quantization approach for the teaching of quantum mechanics. This approach has certain conceptual advantages which make its consideration worthwhile. In particular, it sheds new light on the relation between…
These notes are a self-contained introduction to Galois theory, designed for the student who has done a first course in abstract algebra.
We analyze the onset of classical field configurations after a phase transition. Firstly, we motivate the problem by means of a toy model in quantum mechanics. Subsequently, we consider a scalar field theory in which the system-field…
Expanded lecture notes. Preliminary version, comments are welcome.
In 1931 Koopman and von Neumann extended previous work of Liouville and provided an operatorial version of Classical Mechanics (CM). In this talk we will review a path-integral formulation of this operatorial version of CM. In particular we…