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.
119736417
Schroedinger particle as the source of a Yang-Mills field
Solutions to the Yang-Mills field equations in the presence of extended external sources are reviewed. Point sources have qualitatively different solutions than do extended sources. A model of a nonrelativistic particle in an external potential interacting self-consistently with the Yang-Mills field is used to see whether the particle's wave function acts as an extended source. This model is discussed in detail and a gauge, analogous to the London gauge, is used to set up an initial-value problem for its equations of motion. For small gauge coupling g we find no evidence of solutions with lower energy than a simple Abelian solution. Such a lower-energy solution may, however, exist for large coupling.
6193348
How to distinguish a confining from a deconfining phase in gauge theories with fermions.
17168396
Area law and continuum limit in “induced QCD”
We investigate a class of operators with non-vanishing averages in a D-dimensional matrix model recently proposed by Kazakov and Migdal. Among the operators considered are “filled Wilson loops” which are the most reasonable counterparts of Wilson loops in the convensional Wilson formulation of lattice QCD. The averages of interest are presented as partition functions of certain 2-dimensional statistical systems with nearest neighbor interactions. The “string tension” α′, which is the exponent in the area law for the “filled Wilson loop” is equal to the free energy density of the corresponding statistical system. The continuum limit of the Kazakov-Migdal model corresponds to the critical point of this statistical system. We argue that in the large N limit this critical point occurs at zero temperature. In this case we express α′ in terms of the density of eigenvalues of the matrix-valued master field. We show that the properties of the continuum limit and the description of how this limit is approached is very unusual and differs drastically from what occurs in both the Wilson theory (S ∝ (Tr Π U + c.c)) and in the “adjoint” theory (S ∝ |Tr Π U|2). Instead, the continuum limit of the model appears to be intriguingly similar to a c > 1 string theory.
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.
40079538
Consistency of Hamiltonian diagonalization for field theories in a Robertson-Walker background.
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.
16284410
Differential rotation and convection in the Sun
We show that the differential rotation profile of the solar convection zone, apart from inner and outer boundary layers, can be reproduced with great accuracy if the isorotation contours correspond to characteristics of the thermal wind equation. This requires that there be a formal quantitative relationship involving the entropy and the angular velocity. Earlier work has suggested that this could arise from magnetohydrodynamic stability constraints; here, we argue that purely hydrodynamical processes could also lead to such a result. Of special importance to the hydrodynamical solution is the fact that the thermal wind equation is insensitive to radial entropy gradients. This allows a much more general class of solutions to fit the solar isorotation contours, beyond just those in which the entropy itself must be a function of the angular velocity. In particular, for this expanded class, the thermal wind solution of the solar rotation profile remains valid even when large radial entropy gradients are present. A clear and explicit example of this class of solution appears to be present in published numerical simulations of the solar convective zone. Though hydrodynamical in character, the theory is not sensitive to the presence of weak magnetic fields. Thus, the identification of solar isorotation contours with the characteristics of the thermal wind equation appears to be robust, accommodating, but by no means requiring, magnetic field dynamics.
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 ...
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.