With the coupled Dyson-Schwinger equations in the framework of the unified QED3 theory,we study the phase transition between the antiferromagnet(AF) and the d-wave superconductor (dSC) of planar cuprates at T=0.By solving the coupled Dyson-Schwinger equations both analytically and numerically in rainbow approximation in Landau gauge and comparing the obtained results with that given in the 1/N expansion,we find that there exists a chiral symmetry breaking from dSC phase to AF phase when the quasi- fermion flavors N■4 in half-filling and the AF phase can possibly coexist with the dSC phase in the underdoped region.By comparing the pressure between the coexistent AF-dSC phase and dSC phase,we find that AF-dSC coexisting phase is the stable phase,the AF phase can then coexist with the dSC phase.With the coupled Dyson-Schwinger equations in the framework of the unified QED3 theory,we study the phase transition between the antiferromagnet(AF) and the d-wave superconductor (dSC) of planar cuprates at T=0.By solving the coupled Dyson-Schwinger equations both analytically and numerically in rainbow approximation in Landau gauge and comparing the obtained results with that given in the 1/N expansion,we find that there exists a chiral symmetry breaking from dSC phase to AF phase when the quasi- fermion flavors N■4 in half-filling and the AF phase can possibly coexist with the dSC phase in the underdoped region.By comparing the pressure between the coexistent AF-dSC phase and dSC phase,we find that AF-dSC coexisting phase is the stable phase,the AF phase can then coexist with the dSC phase.

Chinese Physics CJan 1, 20070 citations

Thermalization of an Interacting Quantum Field in the CTP-2PI Next-to-leading-order Large N Scheme

Esteban Calzetta, B. L. Hu

In this paper we use an O(N)-invariant scalar field of unbroken symmetry to investigate whether an interacting quantum field at the next-to-leading order Large $N$ approximation may show signs of thermalization. We develop the closed time-path (CTP) two-particle irreducible (2PI) effective action in powers of 1/N, retaining up to next to leading order (O(1)) terms, and write down the corresponding (truncated) Schwinger-Dyson equations for its two point function. We show that in this approximation, the only translation invariant solutions to the Schwinger - Dyson equations are thermal. This provides a useful temperature concept without invoking a heat bath. When combined with the familiar Kadanoff-Baym approach to quantum kinetic theory our result shows that at this order of approximation thermalization can occur, at least if initial conditions are smooth enough that a derivative expansion is valid. Our analytic result provides support for similar claims in recent literature based on numerical evidence.In this paper we use an O(N)-invariant scalar field of unbroken symmetry to investigate whether an interacting quantum field at the next-to-leading order Large $N$ approximation may show signs of thermalization. We develop the closed time-path (CTP) two-particle irreducible (2PI) effective action in powers of 1/N, retaining up to next to leading order (O(1)) terms, and write down the corresponding (truncated) Schwinger-Dyson equations for its two point function. We show that in this approximation, the only translation invariant solutions to the Schwinger - Dyson equations are thermal. This provides a useful temperature concept without invoking a heat bath. When combined with the familiar Kadanoff-Baym approach to quantum kinetic theory our result shows that at this order of approximation thermalization can occur, at least if initial conditions are smooth enough that a derivative expansion is valid. Our analytic result provides support for similar claims in recent literature based on numerical evidence.

arXiv:hep-ph/0205271May 23, 200230 citations

In this paper we use an O(N)-invariant scalar field of unbroken symmetry to investigate whether an interacting quantum field at the next-to-leading order Large

N

approximation may show signs of thermalization. We develop the closed time-path (CTP) two-particle irreducible (2PI) effective action in powers of 1/N, retaining up to next to leading order (O(1)) terms, and write down the corresponding (truncated) Schwinger-Dyson equations for its two point function. We show that in this approximation, the only translation invariant solutions to the Schwinger - Dyson equations are thermal. This provides a useful temperature concept without invoking a heat bath. When combined with the familiar Kadanoff-Baym approach to quantum kinetic theory our result shows that at this order of approximation thermalization can occur, at least if initial conditions are smooth enough that a derivative expansion is valid. Our analytic result provides support for similar claims in recent literature based on numerical evidence.