Folk theories of objects in motion

There are three main strands of research which have investigated people’s intuitive knowledge of objects in motion. (1) Knowledge of the trajectories of objects in motion; (2) knowledge of the causes of motion; and (3) the categorisation of motion as to whether it has been produced by something animate or inanimate. We provide a brief introduction to each of these areas. We then point to some linguistic and cultural differences which may have consequences for people’s knowledge of objects in motion. Finally, we describe two experimental tasks and an ethnographic task that will allow us to collect data in order to establish whether, indeed, there are interesting cross-linguistic/cross-cultural differences in lay theories of objects in motion

A remark on non-Abelian classical kinetic theory

It is known that non-Abelian classical kinetic theory reproduces the Hard Thermal/Dense Loop (HTL/HDL) effective action of QCD, obtained after integrating out the hardest momentum scales from the system, as well as the first higher dimensional operator beyond the HTL/HDL level. We discuss here its applicability at still higher orders, by comparing the exact classical effective action obtained in the static limit, with the 1-loop quantum effective potential. We remark that while correct types of operators arise, the classical colour algebra reproduces correctly the prefactor of the 4-point function $tr A_0^4$ only for matter in asymptotically high dimensional colour representations.Comment: 6 page

Purely perturbative Boltzmann equation for hot non-Abelian gauge theories

In the perturbation theory, trasnport phenomena in hot non-Abelian gauge theories like QCD are often plagued with infrared singularities or nonperturbative effects. We show, in the context of the Kadanoff & Baym formalism, that there are certain nonequilibrium processes which are free from such difficulties. For these processes, due to an interplay between the macroscopic and microscopic physics, characteristic time scale (the mesoscale) naturally enters as an infrared cutoff and purely perturbative description by the Boltzmann equation is valid.Comment: 4 pages, revtex, to appear in Physical Review

Hard Thermal Loops and the Sphaleron Rate on the Lattice

We measure the sphaleron rate (topological susceptibility) of hot SU(2) gauge theory, using a lattice implementation of the hard thermal loop (HTL) effective action. The HTL degrees of freedom are implemented by an expansion in spherical harmonics and truncation. Our results for the sphaleron rate agree with the parametric prediction of Arnold, Son and Yaffe: Gamma ~ \alpha^5 T^4.Comment: 3 page

Electroweak Bubble Nucleation, Nonperturbatively

We present a lattice method to compute bubble nucleation rates at radiatively induced first order phase transitions, in high temperature, weakly coupled field theories, nonperturbatively. A generalization of Langer's approach, it makes no recourse to saddle point expansions and includes completely the dynamical prefactor. We test the technique by applying it to the electroweak phase transition in the minimal standard model, at an unphysically small Higgs mass which gives a reasonably strong phase transition (lambda/g^2 =0.036, which corresponds to m(Higgs)/m(W) = 0.54 at tree level but does not correspond to a positive physical Higgs mass when radiative effects of the top quark are included), and compare the results to older perturbative and other estimates. While two loop perturbation theory slightly under-estimates the strength of the transition measured by the latent heat, it over-estimates the amount of supercooling by a factor of 2.Comment: 48 pages, including 16 figures. Minor revisions and typo fixes, nothing substantial, conclusions essentially unchange

Chern-Simons Number Diffusion and Hard Thermal Loops on the Lattice

We develop a discrete lattice implementation of the hard thermal loop effective action by the method of added auxiliary fields. We use the resulting model to measure the sphaleron rate (topological susceptibility) of Yang-Mills theory at weak coupling. Our results give parametric behavior in accord with the arguments of Arnold, Son, and Yaffe, and are in quantitative agreement with the results of Moore, Hu, and Muller.Comment: 43 pages, 6 figure

Classical Sphaleron Rate on Fine Lattices

We measure the sphaleron rate for hot, classical Yang-Mills theory on the lattice, in order to study its dependence on lattice spacing. By using a topological definition of Chern-Simons number and going to extremely fine lattices (up to beta=32, or lattice spacing a = 1 / (8 g^2 T)) we demonstrate nontrivial scaling. The topological susceptibility, converted to physical units, falls with lattice spacing on fine lattices in a way which is consistent with linear dependence on $a$ (the Arnold-Son-Yaffe scaling relation) and strongly disfavors a nonzero continuum limit. We also explain some unusual behavior of the rate in small volumes, reported by Ambjorn and Krasnitz.Comment: 14 pages, includes 5 figure

Non-perturbative dynamics of hot non-Abelian gauge fields: beyond leading log approximation

Many aspects of high-temperature gauge theories, such as the electroweak baryon number violation rate, color conductivity, and the hard gluon damping rate, have previously been understood only at leading logarithmic order (that is, neglecting effects suppressed only by an inverse logarithm of the gauge coupling). We discuss how to systematically go beyond leading logarithmic order in the analysis of physical quantities. Specifically, we extend to next-to-leading-log order (NLLO) the simple leading-log effective theory due to Bodeker that describes non-perturbative color physics in hot non-Abelian plasmas. A suitable scaling analysis is used to show that no new operators enter the effective theory at next-to-leading-log order. However, a NLLO calculation of the color conductivity is required, and we report the resulting value. Our NLLO result for the color conductivity can be trivially combined with previous numerical work by G. Moore to yield a NLLO result for the hot electroweak baryon number violation rate.Comment: 20 pages, 1 figur

Two Higgs doublet dynamics at the electroweak phase transition: a non-perturbative study

Using a three-dimensional (3d) effective field theory and non-perturbative lattice simulations, we study the MSSM electroweak phase transition with two dynamical Higgs doublets. We first carry out a general analysis of spontaneous CP violation in 3d two Higgs doublet models, finding that this part of the parameter space is well separated from that corresponding to the physical MSSM. We then choose physical parameter values with explicit CP violation and a light right-handed stop, and determine the strength of the phase transition. We find a transition somewhat stronger than in 2-loop perturbation theory, leading to the conclusion that from the point of view of the non-equilibrium constraint, MSSM electroweak baryogenesis can be allowed even for a Higgs mass mH \approx 115 GeV. We also find that small values of the mass parameter mA (\lsim 120 GeV), which would relax the experimental constraint on mH, do not weaken the transition noticeably for a light enough stop. Finally we determine the properties of the phase boundary.Comment: 56 pages, 16 figures; small clarifications added, concerning e.g. Higgs mass bounds; to appear in NP

The Sphaleron Rate in SU(N) Gauge Theory

The sphaleron rate is defined as the diffusion constant for topological number NCS = int g^2 F Fdual/32 pi^2. It establishes the rate of equilibration of axial light quark number in QCD and is of interest both in electroweak baryogenesis and possibly in heavy ion collisions. We calculate the weak-coupling behavior of the SU(3) sphaleron rate, as well as making the most sensible extrapolation towards intermediate coupling which we can. We also study the behavior of the sphaleron rate at weak coupling at large Nc.Comment: 18 pages with 3 figure