• DOI:10.1088/1126-6708/2005/05/068
• Corpus ID: 53553633

Quasi-particle re-summation and integral gap equation in thermal field theory

@article{LeClair2004QuasiparticleRA,
  title={Quasi-particle re-summation and integral gap equation in thermal field theory},
  author={Andr{\'e} LeClair},
  journal={Journal of High Energy Physics},
  year={2004},
  volume={2005},
  pages={068-068}
}

• A. LeClair
• Published 3 September 2004
• Physics
• Journal of High Energy Physics

A new approach to quantum field theory at finite temperature and density in arbitrary space-time dimension D is developed. We focus mainly on relativistic theories, but the approach applies to non-relativistic ones as well. In this quasi-particle re-summation, the free energy takes the free-field form but with the one-particle energy ?() replaced by ?(), the latter satisfying a temperature-dependent integral equation with kernel related to a zero temperature form-factor of the trace of stress-energy tensor. For 2D integrable theories the approach reduces to the thermodynamic Bethe ansatz. For relativistic theories, a thermal c-function Cqs(T) is defined for any D based on the coefficient of the black body radiation formula. Thermodynamical constraints on it's flow are presented, showing that it can violate a ``c-theorem'' even in 2D. At a fixed point Cqs is a function of thermal gap parameters which generalizes Roger's dilogarithm to higher dimensions. This points to a strategy for classifying rational theories based on ``polylogarithmic ladders'' in mathematics, and many examples are worked out. Other applications are discussed, including the free energy of anyons in 2D and 3D, phase transitions with a chemical potential, and the equation of state for cosmological dark energy. For the latter we show that ?1 < w < ?1/3.