123654339
Effective potential for the order parameter of gauge theories at finite temperature
SU(n) gauge theories at finite temperature T = ..beta../sup -1/ are analyzed in terms of the spontaneous breakdown of a Z(n) symmetry corresponding to the order parameter L(x) = (1/n)Tr P exp(ig..integral../sup ..beta..//sub 0/ A/sub 0/(x,t)dt). An ''effective potential'' for L is evaluated in the one-loop approximation for both the continuum and the lattice gauge theories. It is shown that the Z(n) symmetry is broken, so that the continuum theory does not confine for high temperatures. Similarly the lattice theory does not confine for sufficiently weak coupling if the number of time sites N/sub t/ is finite. It is argued that as N/sub t/..-->..infinity the Z(n) symmetry is restored and the theory will confine for all values of the coupling.
6193348
How to distinguish a confining from a deconfining phase in gauge theories with fermions.
120480610
Screening Solutions to Classical Yang-Mills Theory
We present two new solutions to the classical Yang-Mills field equations in the presence of a localized external source. These solutions totally screen the charge of the source. They have lower energy than the corresponding Coulomb solution.
122529357
Momentum boundary conditions and Euclidean field theory
The authors discuss the effect of the imposition of momentum boundary conditions on the semiclassical approximation to Euclidean path integrals. For free field theories they derive an explicit simple expression for the resulting Euclidean path integral. As an example they discuss the relationship between the formulation of a massless scalar field theory in terms of a 2-form potential which is used in the context of wormholes and its usual formulation.
40079538
Consistency of Hamiltonian diagonalization for field theories in a Robertson-Walker background.
34427103
Cosmology with an extremely light scalar field.
A theory with a vanishing cosmological constant can have a nonzero effective cosmological constant of cosmological significance if the theory has a scalar field with a mass m of the order of the inverse age of the Universe (tau/similar to/10/sup 33/ eV/sup -1/) provided the field has a nonzero but evolving expectation value. We discuss the cosmological consequences of scalar fields with masses mapprox. <10/sup -28/ eV. The effect on the age of the Universe and on the growth of density perturbations is discussed in detail. For small masses (mapprox.
119300936
Differential rotation in fully convective stars
Under the assumption of thermal wind balance and effective entropy mixing in constant rotation surfaces, the isorotational contours of the solar convective zone may be reproduced with great fidelity. Even at this early stage of development, this helioseismology fit may be used to put a lower bound on the mid-latitude radial solar entropy gradient, which is in good accord with standard mixing length theory. In this paper, we generalize this solar calculation to fully convective stars (and potentially planets), retaining the assumptions of thermal wind balance and effective entropy mixing in isorotational surfaces. It is found that each isorotation contour is of the form R 2 = A + B� (r), where R is the radius from the rotation axis, � (r) is the (assumed spherical) gravitational potential, and A and B are constants along the contour. This result is applied to simple models of fully convective stars. Both solar-like surface rotation profiles (angular velocity decreasing toward the poles) as well as ‘antisolar’ profiles (angular velocity increasing toward the poles) are modelled; the latter bear some suggestive resemblance to numerical simulations. We also perform exploratory studies of zonal surface flows similar to those seen in Jupiter and Saturn. In addition to providing a practical framework for understanding the results of large-scale numerical simulations, our findings may also prove useful in dynamical calculations for which a simple but viable model for the background rotation profile in a convecting fluid is needed. Finally, our work bears directly on an important goal of the CoRoT programme: to elucidate the internal structure of rotating, convecting stars.
53074129
Magnetic buoyancy instabilities in the presence of magnetic flux pumping at the base of the solar convection zone
We perform idealized numerical simulations of magnetic buoyancy instabilities in three dimensions, solving the equations of compressible magnetohydrodynamics in a model of the solar tachocline. In particular, we study the effects of including a highly simplified model of magnetic flux pumping in an upper layer (‘the convection zone’) on magnetic buoyancy instabilities in a lower layer (‘the upper parts of the radiative interior – including the tachocline’), to study these competing flux transport mechanisms at the base of the convection zone. The results of the inclusion of this effect in numerical simulations of the buoyancy instability of both a preconceived magnetic slab and a shear-generated magnetic layer are presented. In the former, we find that if we are in the regime that the downward pumping velocity is comparable with the Alfven speed of the magnetic layer, magnetic flux pumping is able to hold back the bulk of the magnetic field, with only small pockets of strong field able to rise into the upper layer. 
 
In simulations in which the magnetic layer is generated by shear, we find that the shear velocity is not necessarily required to exceed that of the pumping (therefore the kinetic energy of the shear is not required to exceed that of the overlying convection) for strong localized pockets of magnetic field to be produced which can rise into the upper layer. This is because magnetic flux pumping acts to store the field below the interface, allowing it to be amplified both by the shear and by vortical fluid motions, until pockets of field can achieve sufficient strength to rise into the upper layer. In addition, we find that the interface between the two layers is a natural location for the production of strong vertical gradients in the magnetic field. If these gradients are sufficiently strong to allow the development of magnetic buoyancy instabilities, strong shear is not necessarily required to drive them (cf. previous work by Vasil & Brummell). We find that the addition of magnetic flux pumping appears to be able to assist shear-driven magnetic buoyancy in producing strong flux concentrations that can rise up into the convection zone from the radiative interior.
13025462
Convective intensification of magnetic fields in the quiet Sun
Kilogauss-strength magnetic fields are often observed in intergranular lanes at the photosphere in the quiet Sun. Such fields are stronger than the equipartition field Be, corresponding to a magnetic energy density that matches the kinetic energy density of photospheric convection, and comparable with the field Bp that exerts a magnetic pressure equal to the ambient gas pressure. We present an idealised numerical model of three-dimensional compressible magnetoconvection at the photosphere, for a range of values of the magnetic Reynolds number. In the absence of a magnetic field, the convection is highly supercritical and is characterised by a pattern of vigorous, timedependent, “granular” motions. When a weak magnetic field is imposed upon the convection, magnetic flux is swept into the convective downflows where it forms localised concentrations. Unless this process is significantly inhibited by magnetic diffusion, the resulting fields are often much greater than Be, and the high magnetic pressure in these flux elements leads to their being partially evacuated. Some of these flux elements contain ultra-intense magnetic fields that are significantly greater than Bp. Such fields are contained by a combination of the thermal pressure of the gas and the dynamic pressure of the convective motion, and they are constantly evolving. These ultra-intense fields develop owing to nonlinear interactions between magnetic fields and convection; they cannot be explained in terms of “convective collapse” within a thin flux tube that remains in overall pressure equilibrium with its surroundings.
119105808
Global model of differential rotation in the Sun
The isorotation contours of the solar convective zone (SCZ) show three distinct morphologies, corresponding to two boundary layers (inner and outer), and the bulk of the interior. Previous work has shown that the thermal wind equation (TWE) together with informal arguments on the nature of convection in a rotating fluid could be used to deduce the shape of the isorotation surfaces in the bulk of the SCZ with great fidelity, and that the tachocline contours could also be described by relatively simple phenomenology. In this paper, we show that the form of these surfaces can be understood more broadly as a mathematical consequence of the TWE and a narrow convective shell. The analysis does not yield the angular velocity function directly; an additional surface boundary condition is required. However, much can already be deduced without constructing the entire rotation profile. The mathematics may be combined with dynamical arguments put forth in previous works to the mutual benefit of each. An important element of our approach is to regard the constant angular velocity surfaces as an independent coordinate variable for what is termed the ‘residual entropy’, a quantity that plays a key role in the equation of thermal wind balance. The difference between the dynamics of the bulk of the SCZ and the tachocline is due to a different functional form of the residual entropy in each region. We develop a unified theory for the rotational behaviour of both the SCZ and the tachocline, using the solutions for the characteristics of the TWE. These characteristics are identical to the isorotation contours in the bulk of the SCZ, but the two deviate in the tachocline. The outer layer may be treated, at least descriptively, by similar mathematical techniques, but this region probably does not obey thermal wind balance.
7847831
FINE STRUCTURE IN SUNSPOTS
▪ Abstract Important physical processes on the Sun, and especially in sunspots, occur on spatial scales at or below the limiting resolution of current solar telescopes. Over the past decade, using ...