Spectral function at high temperature

For a weakly coupled quantum field at high temperature the classical approximation offers a possibility to gain insight into nonperturbative real-time dynamics. I use this to present a nonperturbative approach to the computation of spectral functions in real time. Results are shown for a scalar field in 2+1 dimensions.Comment: Lattice2001(hightemp), 3 pages with 3 eps figure

Can complex Langevin dynamics evade the sign problem?

I answer the question in the title for the relativistic Bose gas at finite chemical potential using numerical lattice simulations, complemented with analytical understanding.Comment: 7 pages, talk given at the XXVII International Symposium on Lattice Field Theory, July 26-31 2009, Peking University, Beijing, Chin

The Classical Approximation for Real-Time Scalar Field Theory at Finite Temperature

The use of classical thermal field to approximate real-time quantum thermal field theory is discussed. For a \lambda\phi^4 theory, it is shown that the classical Rayleigh-Jeans divergence can be canceled with the appropriate counterterms, and a comparison is made between the classical and quantum perturbative expansion. It is explained why Hard Thermal Loops prevent the same method to work for gauge theories.Comment: 5 pages, 2 eps figures, talk presented at the 5th International Workshop on Thermal Field Theories and Their Applications, Regensburg, Germany, August 10-14, 199

Can stochastic quantization evade the sign problem? -- the relativistic Bose gas at finite chemical potential

A nonperturbative study of field theories with a complex action, such as QCD at finite baryon density, is difficult due to the sign problem. We show that the relativistic Bose gas at finite chemical potential has a sign and `Silver Blaze' problem, similar to QCD. We then apply stochastic quantization and complex Langevin dynamics to study this theory with nonperturbative lattice simulations. Independence of chemical potential at small and a transition to a condensed phase at large chemical potential are found. Lattices of size N^4, with N=4,6,8,10, are used. We show that the sign problem is severe, however, we find that it has no negative effect using this approach. This improves the prospects of applying stochastic quantization to QCD at nonzero density.Comment: 4 pages, 4 eps figures, v2: minor changes, outlook expanded, references added, to appear in PR

Complex Langevin dynamics and other approaches at finite chemical potential

I review the presence of the sign problem in lattice QCD at nonzero baryon density and its relation with the overlap and Silver Blaze problems. I then discuss progress in some cases where the sign problem can be handled, either because the sign problem is absent or because it is milder than in full QCD. Some time is spent on effective three-dimensional models, which can be treated with a variety of methods. I conclude with a discussion of the applicability of complex Langevin dynamics at nonzero density.Comment: 22 pages, several figures, invited plenary talk at Lattice 2012, Cairns, Australia, June 24-29 2012; ref [36] properly correcte

Transport and spectral functions in high-temperature QCD

The current status of transport coefficients in relativistic field theories at high temperature is reviewed. I contrast weak coupling results obtained using kinetic theory/diagrammatic techniques with strong coupling results obtained using gauge/gravity duality, and describe the recent developments in extracting transport coefficients and spectral functions from lattice QCD simulations. The fate of quarkonium at high temperature as seen from the lattice is briefly mentioned as well.Comment: 15 pages, 9 eps figures, plenary talk at Lattice 2007, Regensburg, German

Nonequilibrium Fields: Exact and Truncated Dynamics

The nonperturbative real-time evolution of quantum fields out of equilibrium is often solved using a mean-field or Hartree approximation or by applying effective action methods. In order to investigate the validity of these truncations, we implement similar methods in classical scalar field theory and compare the approximate dynamics with the full nonlinear evolution. Numerical results are shown for the early-time behaviour, the role of approximate fixed points, and thermalization.Comment: 5 pages, 6 eps figures, talk presented at Strong and Electroweak Matter (SEWM2000), Marseille, France, 14-17 June, 200

Lefschetz thimbles and stochastic quantisation: Complex actions in the complex plane

Lattice field theories with a complex action can be studied numerically by allowing a complexified configuration space to be explored. Here we compare the recently introduced formulation on a Lefschetz thimble with the result from stochastic quantisation (or complex Langevin dynamics) in the case of a simple model and contrast the distributions being sampled. We also study the role of the residual phase on the Lefschetz thimble.Comment: 13 pages, 7 figure

Renormalizability of hot classical field theory

I discuss the possibility of using classical field theory to approximate hot, real-time quantum field theory. I calculate, in a scalar theory, the classical two point and four point function in perturbation theory. The counterterms needed to make the classical correlation functions finite are dictated by the superrenormalizability of the static theory. The classical expressions approximate the quantum ones, when the classical parameters are chosen according to the dimensional reduction matching rules. I end with an outlook to gauge theories.Comment: 5 pages, 1 eps figure. To appear in the Proceedings of Strong and Electroweak Matter '97, Eger, Hungary, 21-25 May 199

Complex Langevin dynamics at finite chemical potential: mean field analysis in the relativistic Bose gas

Stochastic quantization can potentially be used to simulate theories with a complex action due to a nonzero chemical potential. We study complex Langevin dynamics in the relativistic Bose gas analytically, using a mean field approximation. We concentrate on the region with a Silver Blaze problem and discuss convergence, stability, fixed points, and the severeness of the sign problem. The real distribution satisfying the extended Fokker-Planck equation is constructed and its nonlocal form is explained. Finally, we compare the mean field results in finite volume with the numerical data presented in Ref. [1].Comment: 20 pages, 6 eps figures, discussion on the severeness of the sign problem added, to appear in JHE