Relaxation from a marginal state in optical bistability

Characteristic decay times for relaxation close to the marginal point of optical bistability are studied. A model-independent formula for the decay time is given which interpolates between Kramers time for activated decay and a deterministic relaxation time. This formula gives the decay time as a universal scaling function of the parameter which measures deviation from marginality. The standard deviation of the first-passage-time distribution is found to vary linearly with the decay time, close to marginality, with a slope independent of the noise intensity. Our results are substantiated by numerical simulations and their experimental relevance is pointed out.

SL(3,C) elementary instanton configurations

Several SL(3,C) self-dual instanton solutions of the Yang-Mills equations are presented which have very striking properties. While one of them is regular and SU(3) inside (outside) a sphere of arbitrarily large (small) radius, another one has all the characteristics of a meron solution (in particular its topological charge is concentrated at one point) although its Pontryagin number equals one. Their continuation to Minkowski space is also studied.

Finite-temperature QED effects in atoms

We argue that low-temperature effects in QED can, if anywhere, only be quantitatively interesting for bound electrons. Unluckily the dominant thermal contribution turns out to be level independent, so that it does not affect the frequency of the transition radiation.

Gauge group and reality conditions in Ashtekar's complex formulation of canonical gravity

We discuss reality conditions and the relation between spacetime diffeomorphisms and gauge transformations in Ashtekars complex formulation of general relativity. We produce a general theoretical framework for the stabilization algorithm for the reality conditions, which is different from Diracs method of stabilization of constraints. We solve the problem of the projectability of the diffeomorphism transformations from configuration-velocity space to phase space, linking them to the reality conditions. We construct the complete set of canonical generators of the gauge group in the phase space which includes all the gauge variables. This result proves that the canonical formalism has all the gauge structure of the Lagrangian theory, including the time diffeomorphisms.

Spin-2 gravitational trace anomaly

The part proportional to the Euler-Poincar characteristic of the contribution of spin-2 fields to the gravitational trace anomaly is computed. It is seen to be of the same sign as all the lower-spin contributions, making anomaly cancellation impossible. Subtleties related to Weyl invariance, gauge independence, ghosts, and counting of degrees of freedom are pointed out.

BRST-invariant path integral for a spinning relativistic particle

The propagator of a relativistic spinning particle is calculated using the Becchi-Rouet-Stora-Tyutin-(BRST)-invariant path-integral formalism of Fradkin and Vilkovisky. The spinless case is considered as an introduction to the formalism.

1/c expansion of a separable model of direct-interaction type

The properties of a proposed model of N point particles in direct interaction are considered in the limit of small velocities. It is shown that, in this limit, time correlations cancel out and that Newtonian dynamics is recovered for the system in a natural way.

Batalin-Vilkovisky analysis of covariant and noncovariant actions

The equivalence between the covariant and the noncovariant versions of a constrained system is shown to hold after quantization in the framework of the field-antifield formalism. Our study covers the cases of electromagnetism and Yang-Mills fields and sheds light on some aspects of the Faddeev-Popov method, for both the covariant and noncovariant approaches, which have not been fully clarified in the literature.

The infrared behaviour of the static potential in perturbative QCD

The definition of the quark-antiquark static potential is given within an effective field theory framework. The leading infrared divergences of the static singlet potential in perturbation theory are explicitly calculated.