Related papers: Classical theory for non-perturbative dynamics in …
In high temperature QCD, the perturbation theory is plagued with infrared divergences which reflect long-range non-perturbative phenomena. I argue that it is possible to study such phenomena within a classical thermal field theory which can…
I discuss some non-perturbative aspects of hot gauge theories as related to the unscreened static magnetic interactions. I first review some of the infrared divergences which cause the breakdown of the perturbation theory. Then I show that…
Some notions in non-perturbative dynamics of supersymmetric gauge theories are being reviewed. This is done by touring through a few examples.
We derive an effective classical theory for real-time SU($N$) gauge theories at high temperature. By separating off and integrating out quantum fluctuations we obtain a 3D classical path integral over the initial fields and conjugate…
For a high temperature non-Abelian plasma, we reformulate the hard thermal loop approximation as an effective classical thermal field theory for the soft modes. The effective theory is written in local Hamiltonian form, and the thermal…
I give an introductory review of recent, fascinating developments in supersymmetric gauge theories. I explain pedagogically the miraculous properties of supersymmetric gauge dynamics allowing one to obtain exact solutions in many instances.…
I try to explain some recent progress in understanding the non-perturbative dynamics of hot non-Abelian gauge theories. The non-perturbative physics is due to soft spatial momenta $|\vec{p}|\sim g^2 T$ where $g$ is the gauge coupling and…
The dynamics of soft ($|\vec{p}|\sim g^2 T$) non-Abelian gauge fields at finite temperature is non-perturbative. The effective theory for the soft fields can be obtained by first integrating out the momentum scale T, which yields the well…
We consider a model of classical noncommutative particle in an external electromagnetic field. For this model, we prove the existence of generalized gauge transformations. Classical dynamics in Hamiltonian and Lagrangian form is discussed,…
I will review recent progress on addressing large N gauge theories on the lattice. The focus will be put on the use of large N volume independence as an effective tool to compute non-perturbative dynamics at, otherwise unreachable, large…
We study the formulation of statistical mechanics on noncommutative classical phase space, and construct the corresponding canonical ensemble theory. For illustration, some basic and important examples are considered in the framework of…
I review the appearance of classical integrable systems as an effective tool for the description of non-perturbative exact results in quantum string and gauge theories. Various aspects of this relation: spectral curves, action-angle…
At an elementary level, we present some non-perturbative aspects of non-abelian gauge theories in four dimensional space-time. Some rigorous results have been obtained in the framework of supersymmetric theories, and a very rich physics…
The dynamics of high temperature gauge fields, on scales relevant for non-perturbative phenomena such as electroweak baryogenesis, may be described by a remarkably simple effective theory. This theory, which takes the form of a local,…
Classical, self-consistent theory of statistical mechanics was developed for the thermodynamic and conservative Hamiltonian systems. Later there were many attempts (Sinai-Bowen-Ruelle's temperature, Tsallis' non-extensive theory) to apply…
After revealing difficulties of the standard time-dependent perturbation theory in quantum mechanics mainly from the viewpoint of practical calculation, we propose a new quasi-canonical perturbation theory. In the new theory, the dynamics…
The real-time dynamics of finite-temperature gauge theories can be approximated, to leading-order accuracy in the coupling constants, by a classical field theory with the hard thermal loop Lagrangian. I show how this approach can be used in…
The classical and quantum dynamics of noncanonically coupled os- cillators is investigated in its relation to Lie superalgebras. It is shown that the quantum dynamics admits a hidden (super)hamiltonian formulation and, hence, preserves the…
The classical and quantum dynamics of the noncanonically coupled oscillators is considered. It is shown that though the classical dynamics is well--defined for both harmonic and anharmonic oscillators, the quantum one is well--defined in…
In quantum many-body theory no generic microscopic principle at the origin of complex dynamics is known. Quite opposed, in classical mechanics the theory of non-linear dynamics provides a detailed framework for the distinction between…