Renormalization of the bilocal sine-Gordon model

The functional renormalization group treatment is presented for the two-dimensional sine-Gordon model including a bilocal term in the potential, which contributes to the flow at the tree level. It is shown that the flow of the bilocal term can substitute the evolution of the wave function renormalization constant, since it can recover the Kosterlitz–Thouless type phase transition. The flows can also reveal the connection between the sine-Gordon and the noninteracting Thirring models at a special value of the wave number parameter.

SPECTRAL FUNCTION SUM RULE FOR GAUGE FIELDS

An exact evaluation of the wave function renormalization constant for the color gauge field is carried out because of the close relationship that it bears to color confinement. Since this constant can be expressed as an integral of the absorptive part or the spectral function of the gauge field propagator, the result takes the form of a sum rule for the spectral function. It should be emphasized that asymptotic freedom plays an essential role in its derivation.

NON-FERMI LIQUID BEHAVIOR OF A SYSTEM WITH SADDLE POINTS IN THE ENERGY

We present a simple demonstration that the two-dimensional fermionic system with the energy ε(k)=kxky has a non-Fermi behavior. The calculation of the wave function renormalization constant Z will be performed using the “poor man’s renormalization” method and we will show that Z→0 with the infrared cutoff Λ as Z(Λ)=Λζ where ζ is a constant.