Imaginary-time Formalism Research Articles

Thermodynamics of the Schwinger and Thirring models.

The thermodynamical partition functions for both the Schwinger and Thirring models are evaluated. The imaginary time formalism of quantum field theory at finite temperature and pathintegral methods are used. For the Schwinger model, the partition function displays two features: (i) no physical (transverse) photons exist in 1+1 dimensions; (ii) the theory also describes just free massive bosons. For the Thirring model, the partition function equals that for free massless fermions. The complete thermodynamical propagators and the energies per unit volume at finite temperature are also given.

Photon sector of quantum electrodynamics at high temperature in two spatial dimensions

The photon sector of quantum electrodynamics (QED) in two spatial dimensions is analyzed at high temperature to all orders of perturbation theory. Imaginary-time formalism is used. The photon self-energy and propagator at finite temperature with vanishing frequency is calculated to the second order of perturbation theory. Based upon the latter, an improved perturbation theory which incorporates Debye screening is formulated. By virtue of the latter and gauge invariance, infrared finitness holds. The temperature dependence of any contribution to the connected Green's functions in the improved perturbation theory is analyzed systematically. At very high temperature, the photon sector becomes equivalent to a very massive scalar boson field plus a massless electromagnetic field and both become decoupled: all connected Green's functions containing, at least, one closed fermion loop with four or more vertices are shown to tend to zero.

The transverse plasmon effect

It is shown using both the imaginary- and real-time formalisms that the so-called transverse plasmon effect of the order O( g 3), repeated several times in the literature, is a result of miscalculation. In the imaginary-time formalism, it is rather easy to see that the contribution of the transverse gluons to the correlation pressure is of the order O( g 4). On the other hand, in the real-time formalism, where the calculations are more complicated, this is demonstrated for the case of massless fermions by using the polarization tensor evaluated in the high-temperature limit.

Higher order calculation in thermo field theory

We perform higher order calculations at finite temperature by the use of thermo field theory. It is shown that the terms involving δN(k2−m2) (N≧2) characteristic of the real time formalism become well-defined in thermo field theory. The taming of the singularity is concisely understood by the use of a derivative formula. Further we find a great simplification in the calculation of the singular diagrams. The calculation is partially carried out also in the Imaginary Time Formalism for the sake of comparison. The disposition of the imaginary parts in thermo field theory is also discussed.

Effective electron mass in finite temperature QED

A quasi-particle description of a quantum electrodynamical plasma at finite temperature and density is sought in the context of the imaginary-time formalism of quantum field theory. Functional techniques and analytic continuation are used to derive an expression for the charge density, of the same form as valid for a non-interacting system, in terms of an effective propagator similar to, but different from, the conventional many-body fermion propagator. In contrast to the latter, the effective propagator possesses a pole on the real axis. This defines a statistical quasi-particle, in the sense of Balian and de Dominicis, having a real mass, which is explicitly evaluated at the one-loop level. Remarkable features of this lowest-order mass are that it is independent of the chemical potential, and that it implies a zero-temperature mass shift.

Thermo field theory versus imaginary time formalism

We calculate a two-loop diagram at finite temperature to compare thermo-field theory (TFTh) with the conventional imaginary time formalism (ITF). The summation over the Matsubara frequency in ITF is carried out at two-loop level, and the result is shown to coincide with that of TFTh. We confirm that in ITF the temperature dependent divergences cancell out at least in the calculation of effective potential of ϕ 4 theory, as in TFTh.

QUANTUM FIELD THEORY AND STATISTICAL MECHANICS

QUANTUM FIELD THEORY AND STATISTICAL MECHANICS

Thermal green functions in an expanding universe

We examine the problem of formulating thermal Green functions for conformally non-invariant field theories in an FRW cosmology. In contrast to the conformally invariant case, the problem is one in non-equilibrium thermodynamics. Our method which involves choosing an appropriate density matrix leads to a version of the imaginary time formalism. The results make contact with elementary relativistic kinetic theory. Renormalisation is discussed in low order and a running coupling constant dependent on the cosmological scale emerges naturally as an expansion parameter.