To say that this is the best book on the quantum theory of fields is no praise, since to my knowledge it is the only book on this subject But it is a very good and most useful book The original was written in German and appeared in 1942 This is a translation with some minor changes A few remarks have been added, concerning meson theory and nuclear forces, also footnotes referring to modern work in this field, and finally an appendix on the symmetrization of the energy momentum tensor according to Belinfante Quantum Theory of Fields Prof Gregor Wentzel Translated from the German by Charlotte Houtermans and J M Jauch Pp ix + 224, (New York and London: Interscience Publishers, Inc, 1949) 36s

Quantum Theory of Fields

SUMMARY Ambient noise tomography is a rapidly emerging field of seismological research. This paper presents the current status of ambient noise data processing as it has developed over the past several years and is intended to explain and justify this development through salient examples. The ambient noise data processing procedure divides into four principal phases: (1) single station data preparation, (2) cross-correlation and temporal stacking, (3) measurement of dispersion curves (performed with frequency‐time analysis for both group and phase speeds) and (4) quality control, including error analysis and selection of the acceptable measurements. The procedures that are described herein have been designed not only to deliver reliable measurements, but to be flexible, applicable to a wide variety of observational settings, as well as being fully automated. For an automated data processing procedure, data quality control measures are particularly important to identify and reject bad measurements and compute quality assurance statistics for the accepted measurements. The principal metric on which to base a judgment of quality is stability, the robustness of the measurement to perturbations in the conditions under which it is obtained. Temporal repeatability, in particular, is a significant indicator of reliability and is elevated to a high position in our assessment, as we equate seasonal repeatability with measurement uncertainty. Proxy curves relating observed signal-to-noise ratios to average measurement uncertainties show promise to provide useful expected measurement error estimates in the absence of the long time-series needed for temporal subsetting.

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Processing seismic ambient noise data to obtain reliable broad-band surface wave dispersion measurements

R J Baxter 1982 London: Academic xii + 486 pp price £43.60 Over the past few years there has been a growing belief that all the twodimensional lattice statistical models will eventually be solved and that it will be Professor Baxter who solves them. Baxter has inherited the mantle of Onsager who started the process by solving exactly the two-dimensional Ising model in 1944.

Exactly Solved Models in Statistical Mechanics

We review recent developments in the physics of ultracold atomic and molecular gases in optical lattices. Such systems are nearly perfect realisations of various kinds of Hubbard models, and as such may very well serve to mimic condensed matter phenomena. We show how these systems may be employed as quantum simulators to answer some challenging open questions of condensed matter, and even high energy physics. After a short presentation of the models and the methods of treatment of such systems, we discuss in detail, which challenges of condensed matter physics can be addressed with (i) disordered ultracold lattice gases, (ii) frustrated ultracold gases, (iii) spinor lattice gases, (iv) lattice gases in “artificial” magnetic fields, and, last but not least, (v) quantum information processing in lattice gases. For completeness, also some recent progress related to the above topics with trapped cold gases will be discussed. Motto: There are more things in heaven and earth, Horatio, Than are dreamt of in your...

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Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond

Critical phenomena and renormalization-group theory

We study the effects of smooth inhomogeneities at first-order transitions. We show that a temperature gradient at a thermally driven first-order transition gives rise to nontrivial universal scaling behaviors with respect to the length scale l_{t} of the variation of the local temperature T_{x}. We propose a scaling ansatz to describe the crossover region at the surface where T_{x}=T_{c}, where the typical discontinuities of a first-order transition are smoothed out. The predictions of this scaling theory are checked, and get strongly supported, by numerical results for the two-dimensional (2D) Potts models, for a sufficiently large number of states to have first-order transitions. Comparing with analogous results at the 2D Ising transition, we note that the scaling behaviors induced by a smooth inhomogeneity appear quite similar in first-order and continuous transitions.

Universal scaling effects of a temperature gradient at first-order transitions

The renormalized zero-momentum four-point coupling $g_r$ of $O(N)$-invariant
scalar field theories in $d$ dimensions is studied by applying the $1/N$
expansion and strong coupling analysis. The $O(1/N)$ correction to the
$\beta$-function and to the fixed point value $g_r^*$ are explictly computed.
Strong coupling series for lattice non-linear $\sigma$ models are analyzed near
criticality in $d=2$ and $d=3$ for several values of $N$ and the corresponding
values of $g_r^*$ are extracted. Large-$N$ and strong coupling results are
compared with each other, finding a good general agreement. For small $N$ the
strong coupling analysis in 2-d gives the best determination of $g^*_r$ to date
(or comparable for $N=2,3$ with the available Monte Carlo estimates), and in
3-d it is consistent with available $\phi^4$ field theory results.

Four-point renormalized coupling constant in O(N) models

Erratum: Two-dimensional SU(N)×SU(N) chiral models on the lattice II. The Green's function [Phys. Rev. D 49, 6072 (1994)]

We show that, in the most general $N$-component theory with symmetry O(n_1)+O(n_2), N=n_1+n_2\geq 3, the O(N)-symmetric fixed point has (at least) three unstable directions: the temperature, the quadratic anisotropy, and the spin-4 quartic perturbation. This implies that in the SO(5) theory of high-$T_c$ superconductivity an additional tuning is required to obtain an enlarged SO(5) symmetry. This is in contrast with the recent numerical results reported by Hu, Phys. Rev. Lett. 87, 057004 (2001). \

Comment on ``Bicritical and Tetracritical Phenomena and Scaling Properties of the SO(5) Theory,'' [X. Hu, Phys. Rev. Lett. 87, 057004 (2001)]

Two dimensional large-N chiral models on the square and honeycomb lattices
are investigated by a strong coupling analysis. Strong coupling expansion turns
out to be predictive for the evaluation of continuum physical quantities, to
the point of showing asymptotic scaling. Indeed in the strong coupling region a
quite large range of beta values exists where the fundamental mass agrees,
within about 5% on the square lattice and about 10% on the honeycomb lattice,
with the continuum predictions in the %%energy scheme.

Ettore Vicari

Papers

Universal scaling effects of a temperature gradient at first-order transitions

Four-point renormalized coupling constant in O(N) models

Erratum: Two-dimensional SU(N)×SU(N) chiral models on the lattice II. The Green's function [Phys. Rev. D 49, 6072 (1994)]

Comment on ``Bicritical and Tetracritical Phenomena and Scaling Properties of the SO(5) Theory,'' [X. Hu, Phys. Rev. Lett. 87, 057004 (2001)]

Strong-coupling analysis of large-N two-dimensional lattice chiral models.