We use the background field method along with a special gauge condition, to derive the hard thermal loop effective action in a simple manner. The new point in the paper is to relate the effective action explicitly to the S-matrix from the onset.

It is well known that Yang-Mills theory in vacuum has a perturbative instability to spontaneously form a large scale magnetic field (the Savvidy mechanism) and that a constant field is unstable so that a possible ground state has to be inhomogenous over the non-perturbative scale Lambda (the Copenhagen vacuum). We argue that this spontaneous instability does not occur at high temperature when the induced field strength gB ~ Lambda^2 is much weaker than the magnetic mass squared (g^2T)^2. At high temperature oscillations of gauge fields acquire a thermal mass M ~ gT and we show that this mass stabilizes a magnetic field which is constant over length scales shorter than the magnetic screening length (g^2T)^{-1}. We therefore conclude that there is no indication for any spontaneous generation of weak non-abelian magnetic fields in the early universe.

We present an analysis of the thermalization rate of Higgsinos and winos based on the imaginary part of the two-point Green function in the unbroken phase of the MSSM. We use improved propagators including resummation of hard thermal loops and the thermalization rate is computed at the one-loop level in the high temperature approximation. We find that the damping is typically dominated by scattering with gauge bosons, resulting in a damping rate of about γH̃≃0.025T, γW̃≃0.065T. The contribution from scattering with scalars is relatively small. Implications for baryogenesis are also discussed.

The anomaly equation can be derived from the ultraviolet properties of quantum field theory and should, therefore, not depend on infrared properties, such as the presence of a thermal heat bath. There is also an infrared explanation of anomalies which is related to fermionic zero modes. I show how the anomaly equation can be satisfied in a high temperature plasma in spite of the fact that all propagating fermionic excitations have a thermal mass.

We calculate thermal corrections to the non-linear QED effective action for low-energy photon interactions in a background electromagnetic field. The high-temperature expansion shows that at $T \gg m$ the vacuum contribution is exactly cancelled to all orders in the external field except for a non-trivial two-point function contribution. The high-temperature expansion derived reveals a remarkable cancellation of infrared sensitive contributions. As a result photon-splitting in the presence of a magnetic field is suppressed in the presence of an electron-positron QED-plasma at very high temperatures. In a cold and dense plasma a similar suppression takes place. At the same time Compton scattering dominates for weak fields and the suppression is rarely important in physical situations.

We consider the effect of the presence of a hypermagnetic field at the electroweak phase transition. Screening of the Z-component inside a bubble of the broken phase delays the phase transition and makes it stronger first order. We show that the sphaleron constraint can be evaded for m_H up to 100 GeV if a B_Y\gsim 0.3 T^2 exists at the time of the EW phase transition, thus resurrecting the possibility for baryogenesis within the minimal standard model (provided enough CP violation can be obtained). We estimate that for m_H\gsim 100 GeV the Higgs condendsate behaves like a type II superconductor with Z-vortices penetrating the bubble. Also, for such high Higgs masses the minimum B_Y field required for a strong first order phase transition is large enough to render the W-field unstable towards forming a condensate which changes the simple picture of the symmetry breaking.

The fermionic dispersion relation in the presence of a background magnetic field and a high temperature QED plasma is calculated exactly in the external field, using the Hard Thermal Loop effective action. As the field strength increases there is a smooth transition from the weak-field (qB ⪡ q2T2) thermal dispersion relations to the vacuum Landau levels when the backgroun field is much stronger than any thermal effects (qB ⪢ q2T2). The self-energy at finite field strength acquires an imaginary part. The spectral width becomes important for critical field strengths (qB ≈ q2T2), necessitating the use of the full spectral function. It is shown that the spectral function satisfies the usual condition of normalization and causality. Using the exact spectral function I also show that the production of chirality in an external electromagnetic field at high temperature is unaffected by the presence of the thermal masses of the fermions.

Correlation measurements on the states of two-level atoms having passed through a micromaser at different times can be used to infer properties of the quantum state of the radiation field in the cavity.Long(short) correlation length in time is to some extent associated with super(sub)-Poissonian photon statistics.The correlation length is also an indicator of a phase structure much richer than what is revealed by the usual single-time observables, like the atomic inversion or the Mandel quality factor.In realistic experimental situations the correlations may extend over many times the decay time of the cavity.Our assertions are verified by comparing theoretical calculations with a high-precision Monte-Carlo simulation of the micromaser system.

Neutrinos with a magnetic moment μ change their helicity when interacting with an electromagnetic field. Various aspects of this effect have been described as spin precession, spin-flip scattering, and magnetic Cherenkov radiation. These perspectives are unified in an expression for the νL → νR transition rate which involves the correlators of the electromagnetic field distribution. Our general formula corrects a previous result and generalizes it to the case where the fields cannot be viewed as classical and where the momentum transfers need not be small. We evaluate our result explicitly for a relativistic QED plasma and determine the depolarization rate to leading order in the fine structure constant. Assuming that big-bang nucleosynthesis constraints do not allow a right-handed neutrino in equilibrium we derive the limit μ < 6.2×10−11μB on the neutrino magnetic moment. Bounds on μ from a possible large scale magnetic fields are found to be more stringent even for very weak fields.

We derive general expressions for the neutrino dispersion relation in a magnetized plasma with a wide range of temperatures, chemical potentials, and magnetic field strengths. If the electron and proton chemical potentials vanish, as in the early Universe, there is no magnetization contribution to the neutrino refractive index to leading order in the Fermi coupling constant, contrary to claims in the recent literature. Therefore, as long as the magnetic field satisfies B ≲ T2, the neutrino refractive index in the early Universe is dominated by the standard “non-local term”. If neutrinos are Dirac particles with magnetic moment μ, then their right-handed components are thermally populated before the nucleosynthesis epoch by magnetically induced spin oscillations if μB0 > 10−6μB G, where μB = e/2,e is the Bohr magneton and B0 is a large-scale primordial magnetic field at T0 ≈ 1 MeV For a typically expected random field distribution, even smaller values for μB0 would suffice to thermalize the right-handed Dirac components.

Dispersion relations for fermions at high temperature and in a background magnetic field are calculated in two different ways. First from a straightforward one-loop calculation where, in the weak field limit, we find an expression closely related to the standard dispersion relations in the absence of the magnetic field. Secondly, we derive the dispersion relations directly from the Hard Thermal Loop effective action, which allows for an exact solution (i.e. to all orders in the external field), up to the last numerical integrals.

The free propagator for the scalar λφ4-theory is calculated exactly up to the second derivative of a background field. Using this propagator I compute the one-loop effective action, which then contains all powers of the field but with at most two derivatives acting on each field. The standard derivative expansion, which only has a finite number of derivatives in each term, breaks down for small fields when the mass is zero, while the expression obtained here has a well-defined expansion in φ. In this way the resummation of derivatives cures the naive IR divergence. The extension to finite temperature is also discussed.

The one-loop effective action for a slowly varying electromagnetic field is computed at finite temperature and density using a real-time formalism. We discuss the gauge invariance of the result. Corrections to the Debye mass from an electric field are computed at high temperature and high density. The effective coupling constant, defined from a purely electric weak-field expansion, behaves at high temperature very differently from the case of a magnetic field, and does not satisfy the renormalization group equation. The issue of pair production in the real-time formalism is discussed and also its relevance for heavy-ion collisions.

We show that the relativistic charged scalar boson gas exhibits a genuine Meissner-Ochsenfeld effect of the Schafroth form at fixed supercritical density. As in the well-known non-relativistic case, this total expulsion of a magnetic field is caused by the condensation of the Bose gas at vanishing magnetic field. In the course of these considerations, we present alternative proofs of the absence of Bose-Einstein condensation of a relativistic scalar boson gas, in any finite local magnetic field in less than five dimensions. The results are discussed in the context of kaon condensation in neutron stars.

Previous calculations of the thermal beta-function in a hot Yang--Mills gas at the one--loop level have exposed problems with the gauge dependence and with the sign, which is opposite to what one would expect for asymptotic freedom. We show that inclusion of higher--loop effects through a static Braaten--Pisarski resummation is necessary to consistently obtain the leading term, but alters the results only quantitatively. The sign, in particular, remains the same. We also explore, by a crude parameterization, the effects a (non--perturbative) magnetic mass may have on these results.

The thermalization rate for long wavelength fluctuations in the Higgs field is calculated from the imaginary part of the finite temperature effective action in the unbroken phase of the Standard Model. We use improved propagators including a resummation of hard thermal loops. The thermalization rate is computed at one-loop level, but an estimate of the two-loop contribution appears to give an indication that they are comparable to the one-loop result for small thermal Higgs mass. We show also that the Higgs field fluctuations are likely to thermalize very fast compared with the electroweak phase transition time.