J. Frenkel

Non-abelian eikonal exponentiation

Abstract Recently, Gatheral [1] has generalized the well-known exponentiation properties of soft photons in QED to the case of soft gluons in QCD in the eikonal approximation. We add three things to his work. (i) We clarify the definition of the colour weight factors which appear in the exponent. (ii) We show how the eikonal approximation can be renormalized, consistently with the exponentiation. (iii) We derive a differential equation obeyed by the cross section for emission of soft gluons with given maximum total energy. We also discuss the relationship between the exponentiation theorem and expectation values of Wilson loops.

Soft divergences in perturbative QCD

Abstract We demonstrate simply and directly that Bloch-Nordsieck inclusive cross sections are not in general infrared finite in non-abelian gauge theories treated by perturbation theory. We take the example q q →λ ∗ + (gluons) to order α s 2 , and use the Coulomb gauge in the lab frame, which greatly reduces the work. The relation to the Lee-Nauenberg theorem is discussed. In a very oversimplified model of bound quarks, the infrared divergence is replaced by a logarithm of the size of the bound state.

Finite temperature effective actions

Abstract We present, from first principles, a direct method for evaluating the exact fermion propagator in the presence of a general background field at finite temperature, which can be used to determine the finite temperature effective action for the system. As applications, we determine the complete one loop finite temperature effective actions for ( 0 + 1 )-dimensional QED as well as the Schwinger model. These effective actions, which are derived in the real time (closed time path) formalism, generate systematically all the Feynman amplitudes calculated in thermal perturbation theory and also show that the retarded (advanced) amplitudes vanish in these theories.

General structure of the photon self-energy in noncommutative QED

We study the behavior of the photon two point function, in noncommutative QED, in a general covariant gauge and in arbitrary space-time dimensions. We show, to all orders, that the photon self-energy is transverse. Using an appropriate extension of the dimensional regularization method, we evaluate the one-loop corrections, which show that the theory is renormalizable. We also prove, to all orders, that the poles of the photon propagator are gauge independent and briefly discuss some other related aspects.

High-temperature QCD and the classical Boltzmann equation in curved spacetime

Abstract It has been shown that the high-temperature limit of perturbative thermal QCD is easily obtained from the Boltzmann transport equation for “classical” coloured particles [P.F. Kelly et al., Phys. Rev. D 50 (1994) 4209]. We generalize this treatment to curved space-time. We are thus able to construct the effective stress-energy tensor. We give a construction for an effective action. As an example of the convenience of the Boltzmann method, we derive the high-temperature 3-graviton function. We discuss the static case.

Quark-antiquark annihilation is infrared safe at high energy to all orders

In perturbative QCD, the Bloch-Nordsieck cross section for quark-antiquark annihilation is known, to order g4, to be infrared finite, except for terms which are power-suppressed at high energies. We give a fairly simple explanation of this fact, using analyticity, unitarity and an analysis of mass singularities is both Feynman and axial gauges. The arguments applies fairly easily to order g6. Assuming a generalized unitarity principle, the argument can be extended to all orders.

On the energy-momentum tensor in non-commutative gauge theories

We study the properties of the energy-momentum tensor in non-commutative gauge theories by coupling them to a weak external gravitational field. In particular, we show that the stress tensor of such a theory coincides exactly with that derived from a theory where a Seiberg-Witten map has been implemented (namely, the procedure is commutative). Various other interesting features are also discussed.

Leading non-cancelling infrared divergences in perturbative QCD

Abstract In perturbative QCD, for the inclusive cross section for the scattering of two coloured particles, we identify graphs which contribute to the general leading order α s ( α s ln λ ) n of uncancelled IR divergences, and we sum these contributions (λ is the IR cut-off). The work is done in the Coulomb gauge; an appendix discusses the Feynman gauge.

General covariant gauge fixing for massless spin-two fields

The most general covariant gauge fixing Lagrangian is considered for a spin-two gauge theory in the context of the Faddeev-Popov procedure. In general, five parameters characterize this gauge fixing. Certain limiting values for these parameters give rise to a spin-two propagator that is either traceless or transverse, but for no values of these parameters is this propagator simultaneously traceless and transverse. Having a traceless-transverse propagator ensures that only the physical degrees of freedom associated with the tensor field propagate, and hence it is analogous to the Landau gauge in electrodynamics. To obtain such a traceless-transverse propagator, a gauge fixing Lagrangian which is not quadratic must be employed; this sort of gauge fixing Lagrangian is not encountered in the usual Faddeev-Popov procedure. It is shown that when this nonquadratic gauge fixing Lagrangian is used, two fermionic and one bosonic ghosts arise. As a simple application we discuss the energy-momentum tensor of the gravitational field at finite temperature.

Three-graviton vertex function in thermal quantum gravity.

The high-temperature limit of the three-graviton vertex function is studied in thermal quantum gravity, to one-loop order. The leading (