Casimir effect at finite temperature for pure-photon sector of the minimal Standard Model Extension

Dynamics between particles is governed by Lorentz and CPT symmetry. There is a violation of Parity (P) and CP symmetry at low levels. The unified theory, that includes particle physics and quantum gravity, may be expected to be covariant with Lorentz and CPT symmetry. At high enough energies, will the unified theory display violation of any symmetry? The Standard Model Extension (SME), with Lorentz and CPT violating terms, has been suggested to include particle dynamics. The minimal SME in the pure photon sector is considered in order to calculate the Casimir effect at finite temperature.     

The probable fate of the Standard Model

Extrapolating the Standard Model to high scales using the renormalisation group, three possibilities arise, depending on the mass of the Higgs boson: if the Higgs mass is large enough the Higgs self-coupling may blow up, entailing some new non-perturbative dynamics; if the Higgs mass is small the effective potential of the Standard Model may reveal an instability; or the Standard Model may survive all the way to the Planck scale for an intermediate range of Higgs masses. This latter case does not necessarily require stability at all times, but includes the possibility of a metastable vacuum which has not yet decayed. We evaluate the relative likelihoods of these possibilities, on the basis of a global fit to the Standard Model made using the Gfitter package. This uses the information about the Higgs mass available directly from Higgs searches at LEP and now the Tevatron, and indirectly from precision electroweak data. We find that the ‘blow-up’ scenario is disfavoured at the 99% confidence level (96% without the Tevatron exclusion), whereas the ‘survival’ and possible ‘metastable’ scenarios remain plausible. A future measurement of the mass of the Higgs boson could reveal the fate of the Standard Model.     

On perturbation theory at finite temperature

We show that the largest temperature-dependent contribution to the fermion self-energy of order α² in QED goes as (α²T⁴/p²)ln[(E + p)/(E ? p)], where p is the 3-momentum and E is the energy, and we speculate on the form of higher-order terms in the perturbation expansion.     

On the asymptotic behavior of effective QED at finite temperature

The aim of this paper is to study finite temperature effects in effective quantum electrodynamics using Weisskopfs zero-point energy method in the context of thermo field dynamics. After a general calculation for a weak magnetic field at fixed T, the asymptotic behavior of the Euler-Kockel-Heisenberg Lagrangian density is investigated focusing on the regularization requirements in the high temperature limit. In scalar QED the same problem is also discussed.Received: 14 June 2003, Revised: 14 August 2003, Published online: 2 October 2003This revised version was published online in Oktober 2003 with corrections to the citation of equations in the text after equation (17).     

On the axial anomaly at finite temperature in the Schwinger model

The axial anomaly in 2 dimensional QED at finite temperature is carefully investigated in the real time formalism in the limit of vanishing fermion mass. We follow the dispersion approach of Dolgov and Zakharov. The temperature independence of the anomaly is recovered.     

On one-point functions for sinh-Gordon model at finite temperature

Using fermionic basis we conjecture the exact formulae for the expectation values of local fields in sinh-Gordon model. The conjecture is checked against previously known results.     

Merons at finite temperature

We prove the existence of solutions to the SU(2) Yang—Mills equations on IR⁴, periodic in time, with meron singularities along the time-axis.Supported in part by the Icelandic Science Foundation.     

Tunneling at finite temperature

In a two-dimensional scalar field theory the rate of the metastable vacuum decay at finite temperature is calculated.     

QCD at finite temperature

Quantum chromodynamics is studied at finite temperatures and densities using the temperature Green functions method. For the Green functions the renormalized Schwinger-Dyson equations are obtained and their qualitative properties are discussed. The equality of the renormalization constants for the equations obtained at T, μ ≠ 0 with those for quantum field theory is pointed out. General properties of the gluon polarization tensor are investigated at T, μ ≠ 0. The temperature Green functions are calculated within the one-loop approximation using both relativistic and axial gauges. The fulfilment of the Slavnov-Taylor identities is verified. The asymptotic behaviour of the polarization tensor at T, μ ≠ 0 is established and the excitation spectrum of quark-gluon plasma is found. Both Fermi and Bose excitations are considered and the gauge invariance of the spectra is demonstrated. The renormalization group extension of the dispersion laws into the regions of high temperatures and densities is presented. The exact representation of the thermodynamical potential in QCD is found in terms of the temperature Green functions. For the quark-gluon plasma the thermodynamical potential is calculated with the g³-term taken into account. The equation of state of the hot quark-gluon plasma is found and its properties are discussed. The complete evolutional diagram of the hadronic matter is outlined. The phase curve asymptotics, which put bounds on the quark-gluon plasma domain, are found for the two limiting cases (μ = 0, T → T₀; T = 0, μ → μ₀). The phase transition of the hot quark-gluon plasma placed in external Abelian field is studied. The instability of such plasma has been found and the program of its stabilization is indicated. The infrared behaviour of the non-Abelian gauge theory is studied for finite temperatures when power divergencies are essential. The propagator of transverse gluons is shown to be singular for momenta |p| ˜ g²T and this cannot be avoided by summing the simplest bubble chains. The infrared asymptotic behaviour of the tree-gluon vertex is found and the results obtained are checked using the Slavnov-Taylor identities. The Green functions asymptotics found indicate either an instability of the quark-gluon plasma in the infrared momentum domain or the inconsistency of the perturbational methods. A non-perturbative approach to the infrared problem in QCD is developed within the axial gauge. The closed equations for the structure functions that determine the gluon polarization tensor are obtained by using the Slavnov-Taylor identities to found approximately the three-gluon vertex. It is shown that the solution of the equations obtained by iterations does not remove the infrared singularity from the temperature Green functions. The nonperturbative solution of such equations is discussed.     

Quantum electrodynamics at finite temperature

We present a systematic examination of finite temperature effects in quantum electrodynamics at one loop order. We calculate mass, charge, and wavefunction renormalization, demonstrate the running of the coupling constant at high temperatures, and study the renormalized vertex function and the energy momentum tensor. The confusion in the literature concerning the finite temperature corrections to the electron's magnetic moment is resolved. We also present the finite temperature effects in scalar electrodynamics. Throughout we stress the need to provide a well-defined method to observe a given quantity when interpreting the results of a calculation, and we suggest new techniques which incorporate the novel features of finite temperature theories.     

Wick's theorem at finite temperature

We consider Wick's theorem for finite temperature and finite volume systems. Working at an operator level with a path ordered approach, we show that contrary to claims in the literature, expectation values of normal ordered products can be chosen to be zero and that results obtained are independent of volume. Thus the path integral and operator approaches to finite temperature and finite volume quantum field theories are indeed seen to be identical. The conditions under which normal ordered products have simple symmetry properties are also considered.     

Rotational motion at finite temperature

Moments of inertia and rotational velocity fields are calculated in the cranking model for the harmonic oscillator and the Nilsson potential for even-even rare earth nuclei. By means of a temperature-averaging procedure these quantities are decomposed into a smooth and a shell-structure-dominated part. The results are in good agreement with the corresponding Strutinsky-averaged results. The velocity fields are analyzed in terms of vector spherical harmonics and compared to rigid flow. The smooth velocity fields reveal rigid flow in the nuclear interior; in the surface region a deviation from rigid flow occurs, giving rise to a backflow in the inner system. The temperature dependence of the smooth moments of inertia is approximated by a quadratic function.