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 some aspects of equilibrium and off equilibrium quantum dynamics of
dilute bosonic gases in the presence of a trapping potential. We consider
systems with a fixed number of particles N and study their scaling behavior
with increasing the trap size. We focus on one-dimensional (1D) bosonic
systems, such as gases described by the Lieb-Liniger model and its
Tonks-Girardeau limit of impenetrable bosons, and gases constrained in optical
lattices as described by the Bose-Hubbard model. We study their quantum
(zero-temperature) behavior at equilibrium and off equilibrium during the
unitary time evolution arising from changes of the trapping potential, which
may be instantaneous or described by a power-law time dependence, starting from
the equilibrium ground state for a initial trap size. Renormalization-group
scaling arguments, analytical and numerical calculations show that the
trap-size dependence of the equilibrium and off-equilibrium dynamics can be
cast in the form of a trap-size scaling in the low-density regime,
characterized by universal power laws of the trap size, in dilute gases with
repulsive contact interactions and lattice systems described by the
Bose-Hubbard model. The scaling functions corresponding to several physically
interesting observables are computed. Our results are of experimental relevance
for systems of cold atomic gases trapped by tunable confining potentials.

Equilibrium and off-equilibrium trap-size scaling in one-dimensional ultracold bosonic gases

We consider a noncompact lattice formulation of the three-dimensional electrodynamics with $N$-component complex scalar fields, i.e., the lattice Abelian-Higgs model with noncompact gauge fields. For any $N\ensuremath{\ge}2$, the phase diagram shows three phases differing for the behavior of the scalar-field and gauge-field correlations: The Coulomb phase (short-ranged scalar and long-ranged gauge correlations), the Higgs phase (condensed scalar-field and gapped gauge correlations), and the molecular phase (condensed scalar-field and long-ranged gauge correlations). They are separated by three transition lines meeting at a multicritical point. Their nature depends on the phases they separate, and on the number $N$ of components of the scalar field. In particular, the Coulomb-to-molecular transition line (where gauge correlations are irrelevant) is associated with the Landau-Ginzburg-Wilson ${\mathrm{\ensuremath{\Phi}}}^{4}$ theory sharing the same SU($N$) global symmetry but without explicit gauge fields. On the other hand, the Coulomb-to-Higgs transition line (where gauge correlations are relevant) turns out to be described by the continuum Abelian-Higgs field theory with explicit gauge fields. Our numerical study is based on finite-size scaling analyses of Monte Carlo simulations with ${C}^{*}$ boundary conditions (appropriate for lattice systems with noncompact gauge variables, unlike periodic boundary conditions), for several values of $N$, i.e., $N=2$, 4, 10, 15, and 25. The numerical results agree with the renormalization-group predictions of the continuum field theories. In particular, the Coulomb-to-Higgs transitions are continuous for $N\ensuremath{\gtrsim}10$, in agreement with the predictions of the Abelian-Higgs field theory.

Ettore Vicari

Papers

Equilibrium and off-equilibrium trap-size scaling in one-dimensional ultracold bosonic gases

Lattice Abelian-Higgs model with noncompact gauge fields

Coherent and dissipative dynamics at quantum phase transitions

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

The effective potential of N-vector models: a field-theoretic study to O(ϵ3)