Quantum Electrodynamics at High Temperature: (I). One Spatial Dimension

Abstract

The photon sector of Quantum Electrodynamics (QED) in one spatial dimension is analyzed at high temperature to all orders of perturbation theory. The imaginary-time formalism is used. The photon self-energy and propagator at finite temperature with vanishing frequency are given to second order of perturbation theory. Based upon them, an improved perturbation theory which incorporates Debye screening if formulated. In the infinite-temperature limit, the photon sector becomes equivalent to a massive scalar boson field plus a masslees pure gauge field and both are decoupled: all connected Green's functions with given external momenta much smaller than the temperature and containing, at least, one closed fermion loop with four or more vertices vanish. An approximate generating functional yielding all leading high-temperature corrections to all connected Green's functions is preaented. The Iast result leads to establish for one spatial dimension a conjecture of Gross, Pisarski and Yaffe regarding the reduction of QED to a sort of ϕ4 theory at high temperature. The leading high temperature contribution to the thermodynamic potential to all perturbativc orders: i) is given in terms of the dominant high temperature contribution to the two-point photon Green's function for zero frequency, ii) is shown to be both ultraviolet and infrared finite.