Thermal Green Function Research Articles

Generalized forward scattering amplitudes in QCD at high temperature

We extend to a general class of covariant gauges an approach which relates the thermal Green functions to forward scattering amplitudes of thermal particles. A brief discussion of the non-transversality of the thermal gluon polarization tensor is given in this context. This method is then applied to the calculation of the ln(T) contributions associated with general configurations of 2 and 3-point gluon functions. The results are Lorentz covariant and have the same structure as the ultraviolet divergent contributions which occur at zero temperature.

Thermal green functions at zero energy

The thermal expectation values of all possible bosonic generalised retarded functions evaluated at zero energy are studied. The relationships of such functions to calculational schemes, technical problems and physical applications are outlined. It is then shown that all generalised retarded functions constructed from any one set of bosonic fields are equal at zero energy. This is done completely generally and is not limited to any approximation scheme such as perturbation theory.

Mesoscopic Fluctuations of the DC Josephson Current in a Dirty SNS Junction

We present theoretical studies on mesoscopic fluctuations of the dc Josephson current in superconductor (S)-dirty normal conductor (N)-superconductor junctions. The analytical expression for the Josephson-current fluctuation δ J 2 is obtained by using the thermal Green's function method, which is shown to be valid when the separation between two superconductors is much lager than the coherence length of the dirty superconductor. The effects of temperature and inelastic scattering on δ J 2 are examined. The results show that the characteristic temperature (size) for the reduction of δ J 2 is of the order of the Thouless correlation energy E c (the phase choherence length). From the current correlation function, the energy correlation range is estimated to be at about E c . In order to prepare a specific reference for the system under our consideration, we numerically examine the critical-current fluctuations δ J 2 c in the long-junction limit in a model system. Numerical results show that the magnitude of ...

Cutting rules in the real-time formalisms at finite temperature

In this paper, we review the set of rules specific to the calculation of the imaginary part of a Green's function at finite temperature in the real-time formalisms. Emphasis is put on the clarification of a recent controversy concerning these rules in the "1/2" formalism, more precisely on the issue related to the interpretation of these rules in terms of cut diagrams, like at T=0. On the second hand, new results are presented, enabling one to calculate the imaginary part of thermal Green's functions in other formulations of the real-time formalism, like the "retarded/advanced" formalism in which a lot of simplifications occur.

On superconductivity in the three-band two-dimensional repulsive hubbard model

The three-band Hubbard model, known also as the Emery model, is investigated in the framework of thermal Green functions. It is shown that antiferromagnetic and superconductive states can exist in this model at appropriate doping and sufficiently low temperatures. In the two-dimensional repulsive case under consideration, superconductivity turns out to be possible due to the closeness of the Fermi level to one of the energy function saddle points and the pairing occurs in channels with odd angular momenta.

Vacuum polarization at finite temperature around a magnetic flux cosmic string

We consider a general situation where a charged massive scalar field at finite temperature interacts with a magnetic flux cosmic string. We determine a general expression for the Euclidean thermal Green's function of the massive scalar field and a handy expression for a massless scalar field. With this result, we evaluate the thermal average and the thermal average of the energy--momentum tensor of a non-conformal massless scalar field.

A new representation for the supercurrent in 3He-A and its zero temperature limit

A new representation for the thermal Green's function of 3He-A and its zero the corresponding supercurrent at an arbitrary temperature. Expansion of this general expression in the orbital vector gradients is considered at zero temperature; the widely accepted first-order contribution with the anomalous part and the second-order corrections to it are obtained, thus confirming the existence of the anomalous current at zero temperature.

Chiral current at high temperatures.

The BP-FTW effective action is a good laboratory to study the nature of chiral symmetry at high $T$. It is invariant under a new Noether charge, $\Qbeta$. By explicit quantization, performed to order $\Tprime$ we show that the thermal vacuum is annihilated by $\Qbeta$, so that the new chiral symmetry is not broken spontaneously at high $T$. This high $T$ Noether charge is, however, different from the usual zero temperature chirality, $\Q$. Our quantization also shows that the thermal vacuum is not annihilated by $\Q$, so that the old chiral symmetry remains broken at high $T$. The thermal vacuum is thus every bit as `structured' and `complex' as the Nambu-Jona-Lasinio vacuum at zero temperature. We exhibit the relation between the normal mode expansion for $\Qbeta$ versus the usual expansion for $\Q$. In an appendix, we point out the analyticity properties of the fermion propagator in real time formalism, and verify the canonical nature of the thermal Green function.

Thermal Green's functions from quantum-mechanical path integrals. II. Inclusion of fermions.

In a previous paper we have shown how, for bosonic fields, the generating functional in both relativistic quantum field theory and thermal field theory can be evaluated by use of a standard quantum mechanical path integral. In this paper we extend this method to include fermionic fields. A particular problem is posed by Green's functions with external fermionic lines, where the different boundary conditions of bosons and fermions in imaginary time have to be accommodated within one path integral expression. The general procedure is worked out in the example of scalar and spinor self-energies in a simple model with a Yukawa coupling of a scalar to a Majorana spinor.

Erratum: Closed-form expressions for thermal Green's functions in field theories

A resummed perturbative expansion is used to obtain the self-energy in the high-temperature \(g^2\phi^4\) field theory model up to order $g^4$. From this the zero momentum pole of the effective propagator is evaluated to determine the induced thermal mass and damping rate for the bosons in the plasma to order $g^3$. The calculations are performed in the imaginary time formalism and a simple diagrammatic analysis is used to identify the relevant diagrams at each order. Results are compared with similar real-time calculations found in the literature.

Thermal Green's functions from quantum-mechanical path integrals.

In this paper it is shown how the generating functional for Green's functions in relativistic quantum field theory and in thermal field theory can be evaluated in terms of a standard quantum mechanical path integral. With this calculational approach one avoids the loop-momentum integrals usually encountered in Feynman perturbation theory, although with thermal Green's functions, a discrete sum (over the winding numbers of paths with respect to the circular imaginary time) must be computed. The high-temperature expansion of this sum can be performed for all Green's functions at the same time, and is particularly simple for the static case. The procedure is illustrated by evaluating the two-point function to one-loop order in a $\phi^3_6$ model.

Real- and imaginary-time thermal field theory.

The formula is derived for the four-point real-time thermal Green's functions in terms of the analytic continuation of the four-point function in the imaginary-time formalism.Received 17 July 1992DOI:https://doi.org/10.1103/PhysRevD.47.725©1993 American Physical Society

The Euclidean thermal Green function in the spacetime of a cosmic string

Within the framework of the quantum field theory at finite temperature, the author determines the Euclidean thermal Green function for a massless scalar field in a conical spacetime. This result enables one to evaluate in integral form the mean-square field as a function of the temperature. The author is also able to calculate in the high-temperature limit the thermal average of the energy-momentum tensor for a conformal scalar field.

Real-Time Thermal Green's Functions in Rindler Space

The real-time thermal Green's functions with 2×2 matrix in Rindler field theory are derived for massless scalar fields by using both the Bogoliubov transformation method and path-integral formulation.

Eta - xi spacetime and thermo fields.

In this paper an intuitive picture of $\ensuremath{\eta}\ensuremath{-}\ensuremath{\xi}$ spacetime is given. It is shown why $\ensuremath{\eta}\ensuremath{-}\ensuremath{\xi}$ spacetime can be regarded as a geometric background of field theory at finite temperature. In particular, a new way is put forth. We can get the real-time thermal Green's function with a 2\ifmmode\times\else\texttimes\fi{}2 matrix by rotating the imaginary-time thermal Green's function from the Euclidean section to the Lorentzian section in $\ensuremath{\eta}\ensuremath{-}\ensuremath{\xi}$ spacetime.

Many-body Green functions of q-deformed oscillators

Certain thermal (Matsubara) Green functions are obtained for a “free” system of quantum-deformed harmonic oscillators. It is shown that the form of the single-particle Matsubara function is changed, with an explicit dependence on s = 1n q appearing in a simple form and suggesting that quantum-deformed commutation rules intrinsically incorporate interactions even in the “free case”. A two-particle Matsubara function gives no evidence of a bound state energy shift.

Closed-form expressions for thermal Green's functions in field theories.

We study finite-temperature effects to one-loop order in field theories by relating them to the forward scattering of thermal particles. This approach allows for an exact evaluation of all temperature-dependent contributions to the thermal self-energy in terms of generalized $\ensuremath{\zeta}$ functions. We obtain a closed-form expression for the two-point gluon function in thermal Yang-Mills theory.

Fermion fields in eta - xi spacetime.

Fermion fields in $\ensuremath{\eta}\ensuremath{-}\ensuremath{\xi}$ spacetime are discussed. By the path-integral formulation of quantum field theory, we show that the (zero-temperature) Green's functions for Dirac fields on the Euclidean section in $\ensuremath{\eta}\ensuremath{-}\ensuremath{\xi}$ spacetime are equal to the imaginary-time thermal Green's functions in Minkowski spacetime, and that the (zero-temperature) Green's functions on the Lorentzian section in $\ensuremath{\eta}\ensuremath{-}\ensuremath{\xi}$ spacetime correspond to the real-time thermal Green's functions in Minkowski spacetime. The antiperiodicity of fermion fields in $\ensuremath{\eta}\ensuremath{-}\ensuremath{\xi}$ spacetime originates from Lorentz transformation properties of the fields.

Green's function derivation of the thermal random phase approximation equations in open shell systems.

The thermal Green's functions are used to derive the thermal random phase approximation (TRPA) in open shell systems. The TRPA in the Sn isotopes is studied for a separable quadrupole interaction as a function of the temperature. The matrix elements of quadrupole particle-hole and two-particle operators as well as their energy-weighted sum rules are evaluated. The most noticeable features introduced by the temperature dependence are the big changes that happen when the superconductivity disappears.

Quantum field in eta - xi spacetime.

A new spacetime, $\ensuremath{\eta}\ensuremath{-}\ensuremath{\xi}$ spacetime, is constructed. The quantum field in $\ensuremath{\eta}\ensuremath{-}\ensuremath{\xi}$ spacetime is discussed. It is shown that the vacuum state of quantum field in $\ensuremath{\eta}\ensuremath{-}\ensuremath{\xi}$ spacetime is a thermal state for an inertial observer in Minkowski spacetime, and the vacuum Green's functions in $\ensuremath{\eta}\ensuremath{-}\ensuremath{\xi}$ spacetime are just the thermal Green's functions in usual statistical mechanics.