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 nature of the finite-temperature chiral transition in QCD with
N_f light quarks in the fundamental and adjoint representation. Universality
and renormalization-group (RG) arguments show that the possibility of having a
continuous transition is related to the existence of a stable fixed point (FP)
in the RG flow of a 3D Landau-Ginzburg-Wilson Phi^4 theory with the same chiral
symmetry-breaking pattern. The RG flow of these theories is studied by
field-theoretical approaches, computing and analyzing high-order perturbative
series, up to six loops. According to this RG analysis, the transition in QCD
can be continuous only for N_f=2. In this case it belongs to the 3D O(4)
universality class. We also find a stable FP corresponding to a 3D universality
class with symmetry breaking U(2)_L x U(2)_R -> U(2)_V, which implies that the
transition can be continuous also if the axial-anomaly effects are suppressed
at Tc. In the case of quarks in the adjoint representation, we can have a
continuous transition for N_f=1,2. For N_f=1 it belongs to the O(3)
universality class. For N_f=2 it belongs to a new 3D universality class
characterized by the symmetry breaking SU(4)->SO(4).

Finite-temperature chiral transition in QCD with quarks in the fundamental and adjoint representation

We investigate the critical behavior of trapped particle systems at the low-temperature superfluid transition. In particular, we consider the three-dimensional Bose-Hubbard model in the presence of a trapping harmonic potential coupled with the particle density, which is a realistic model of cold bosonic atoms in optical lattices. We present a numerical study based on quantum Monte Carlo simulations, analyzed in the framework of the trap-size scaling (TSS). We show how the critical parameters can be derived from the trap-size dependencies of appropriate observables, matching them with TSS. This provides a systematic scheme which is supposed to exactly converge to the critical parameters of the transition in the large-trap-size limit. Our numerical analysis may provide a guide for experimental investigations of trapped systems at finite-temperature and quantum transitions, showing how critical parameters may be determined by looking at the scaling of the critical modes with respect to the trap size, i.e., by matching the trap-size dependence of the experimental data with the expected TSS ansatz.

Critical parameters from trap-size scaling in systems of trapped particles

We study the finite-size behavior of two-dimensional spin-glass models. We consider the ±J model for two different values of the probability of the antiferromagnetic bonds and the model with Gaussian distributed couplings. The analysis of renormalization-group invariant quantities, the overlap susceptibility, and the two-point correlation function confirms that they belong to the same universality class. We analyze in detail the standard finite-size scaling limit in terms of TL(1/ν) in the ±J model. We find that it holds asymptotically. This result is consistent with the low-temperature crossover scenario in which the crossover temperature, which separates the universal high-temperature region from the discrete low-temperature regime, scales as T(c)(L)~L(-θ(S)) with θ(S)≈0.5.

Finite-size Scaling in Two-Dimensional Ising Spin-Glass Models

We study the critical behavior of a general class of cubic-symmetric spin systems in which disorder preserves the reflection symmetry ${s}_{a}\ensuremath{\rightarrow}{\ensuremath{-}s}_{a}$, ${s}_{b}\ensuremath{\rightarrow}{s}_{b}$ for $b\ensuremath{\ne}a$. This includes spin models in the presence of random cubic-symmetric anisotropy with probability distribution vanishing outside the lattice axes. Using nonperturbative arguments we show the existence of a stable fixed point corresponding to the random-exchange Ising universality class. The field-theoretical renormalization-group flow is investigated in the framework of a fixed-dimension expansion in powers of appropriate quartic couplings, computing the corresponding $\ensuremath{\beta}$ functions to five loops. This analysis shows that the random Ising fixed point is the only stable fixed point that is accessible from the relevant parameter region. Therefore, if the system undergoes a continuous transition, it belongs to the random-exchange Ising universality class. The approach to the asymptotic critical behavior is controlled by scaling corrections with exponent $\ensuremath{\Delta}={\ensuremath{-}\ensuremath{\alpha}}_{r}$, where ${\ensuremath{\alpha}}_{r}\ensuremath{\simeq}\ensuremath{-}0.05$ is the specific-heat exponent of the random-exchange Ising model.

Spin models with random anisotropy and reflection symmetry

We investigate the low-temperature behavior of two-dimensional (2D) ${\mathrm{RP}}^{N\ensuremath{-}1}$ models, characterized by a global $\mathrm{O}(N)$ symmetry and a local ${\mathbb{Z}}_{2}$ symmetry. For $N=3$ we perform large-scale simulations of four different 2D lattice models: two standard lattice models and two different constrained models. We also consider a constrained mixed $\mathrm{O}(3)\text{\ensuremath{-}}{\mathrm{RP}}^{2}$ model for values of the parameters such that vector correlations are always disordered. We find that all these models show the same finite-size scaling (FSS) behavior, and therefore belong to the same universality class. However, these FSS curves differ from those computed in the 2D O(3) $\ensuremath{\sigma}$ model, suggesting the existence of a distinct 2D ${\mathrm{RP}}^{2}$ universality class. We also performed simulations for $N=4$, and the corresponding FSS results also support the existence of an ${\mathrm{RP}}^{3}$ universality class, different from the O(4) one.

Ettore Vicari

Papers

Finite-temperature chiral transition in QCD with quarks in the fundamental and adjoint representation

Critical parameters from trap-size scaling in systems of trapped particles

Finite-size Scaling in Two-Dimensional Ising Spin-Glass Models

Spin models with random anisotropy and reflection symmetry

Asymptotic low-temperature behavior of two-dimensional RP N − 1 models