Basics of Thermal Field Theory pp 197-274 | Cite as

# Applications

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## Abstract

A number of physical applications of relativistic thermal field theory are considered. First the basic formalism for addressing the existence of a scalar field driven phase transition is developed (Sect. 9.1). Then the concept of instantons is introduced with the example of a bubble nucleation rate related to a first order phase transition (Sect. 9.2). This is followed by a general discussion concerning the formalism for particle production rate computations, relevant both for heavy ion collision experiments and cosmology (Sect. 9.3). How a particle production rate can be embedded in an expanding cosmological background is explained in detail (Sect. 9.4). Turning to so-called transport coefficients, we first consider the effective mass and friction coefficient that a scalar field evolving within a thermal environment feels (Sect. 9.5). Then transport coefficients are discussed more generally, culminating in the definition of shear and bulk viscosities, diffusion coefficients, and the electric conductivity of QCD matter (Sect. 9.6). Transport coefficients are closely related to the rate at which a slightly disturbed system equilibrates, and the corresponding formalism is introduced, stressing the idea of employing operator equations of motion in order to simplify the correlation function to be computed (Sect. 9.7). Finally a somewhat different but physically important topic, that of the behaviour of resonances made of a heavy quark and an antiquark within a hot QCD medium, is outlined, with emphasis on the roles that “virtual” and “real” corrections play at finite temperature (Sect. 9.8).

## Keywords

Effective potential Condensate First order phase transition Semiclassical approximation Saddle point Instanton Fluctuation determinant Tunnelling Sphaleron Classical limit Critical bubble Latent heat Surface tension Particle production On-shell field operator Landau-Pomeranchuk-Migdal effect Decay rate Einstein equations Yield parameter Boltzmann equation Friction coefficient Damping rate Thermal mass Dilaton Axion Chern-Simons diffusion Equilibration Kubo formula Transport peak Flavour diffusion Conductivity Viscosity Brownian motion Langevin equation Quarkonium Debye screening Decoherence Thermal width Real and virtual processes at finite temperature## References

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