Derivation of transport equations for a strongly interacting Lagrangian in powers of anti-H and 1 / N(c)

Aug, 1997
41 pages
Published in:
  • Annals Phys. 261 (1997) 37-73
e-Print:
Report number:
  • HD-TVP-97-02

Citations per year

1997200320092015202102468
Abstract:
Transport theory for an interacting fermionic system is reviewed and applied to the chiral Lagrangian of the Nambu-Jona-Lasinio model. Two expansions must be applied: an expansion in the inverse number of colors, 1/Nc1/N_c, due to the nature of the strong coupling theory, and a semiclassical expansion, in powers of \hbar. The quasiparticle approximation is implemented at an early stage, and spin effects are omitted. The self-energy is evaluated, self-consistently only in the Hartree approximation, and semi-perturbatively in the collision integral. In the Hartree approximation, O((1/Nc)0)O((1/N_c)^0), the Vlasov equation is recovered to O(1)O(\hbar^1), together with an on-mass shell constraint equation, that is automatically fulfilled by the quasiparticle ansatz. The expressions for the self-energy to order O((1/Nc))O((1/N_c)) lead to the collision term. Here one sees explicitly that particle-antiparticle creation and annihilation processes are suppressed that would otherwise be present, should an off-shell energy spectral function be admitted. A clear identification of the ss, tt and uu channel scattering processes in connection with the self-energy graphs is made and the origin of the mixed terms is made evident. Finally, after ordering according to powers in \hbar, a Boltzmann-like form for the collision integral is obtained.
Note:
  • Dedicated to Professor R.H. Lemmer on the occasion of his 65th birthday
  • Jona-Lasinio-Nambu model
  • model: chiral
  • transport theory
  • expansion 1/N
  • energy
  • Hartree approximation
  • approximation: semiclassical
  • Feynman graph