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

We report results of a search for Weakly Interacting Massive Particles (WIMPS) with the silicon detectors of the CDMS II experiment. This blind analysis of 140.2 kg-days of data taken between July 2007 and September 2008 revealed three WIMP-candidate events with a surface-event background estimate of 0.41^{+0.20}_{-0.08}(stat.)^{+0.28}_{-0.24}(syst.). Other known backgrounds from neutrons and 206Pb are limited to < 0.13 and <0.08 events at the 90% confidence level, respectively. The exposure of this analysis is equivalent to 23.4 kg-days for a recoil energy range of 7-100 keV for a WIMP of mass 10 GeV/c2. The probability that the known backgrounds would produce three or more events in the signal region is 5.4%. A profile likelihood ratio test of the three events that includes the measured recoil energies gives a 0.19% probability for the known-background-only hypothesis when tested against the alternative WIMP+background hypothesis. The highest likelihood occurs for a WIMP mass of 8.6 GeV/c2 and WIMP-nucleon cross section of 1.9e-41 cm2.

Silicon Detector Dark Matter Results from the Final Exposure of CDMS II

The existence and properties of the sigma meson have been controversial for almost six decades, despite playing a central role in the spontaneous chiral symmetry of QCD or in the nucleon-nucleon attraction. This controversy has also been fed by the strong indications that it is not an ordinary quark-antiquark meson. Here we review both the recent and old experimental data and the model independent dispersive formalisms which have provided precise determinations of its mass and width, finally settling the controversy and leading to its new name: $f_0(500)$. We then provide a rather conservative average of the most recent and advanced dispersive determinations of its pole position $\sqrt{s_\sigma}=449^{+22}_{-16}-i(275\pm12)$. 
In addition, after comprehensive introductions, we will review within the modern perspective of effective theories and dispersion theory, its relation to chiral symmetry, unitarization techniques, its quark mass dependence, popular models, as well as the recent strong evidence, obtained from the QCD $1/N_c$ expansion or Regge theory, for its non ordinary nature in terms of quarks and gluons.

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From controversy to precision on the sigma meson: a review on the status of the non-ordinary $f_0(500)$ resonance

Electromagnetic excitation of the Δ(1232)-resonance

From controversy to precision on the sigma meson: A review on the status of the non-ordinary f(0)(500) resonance

We point out that the spectrum of pseudoscalar and scalar mesons exhibits a quasidegenerate chiral nonet in the energy region around 1.4 GeV whose scalar component has a slightly inverted spectrum. Based on the empirical linear rising of the mass of a hadron with the number of constituent quarks which yields a mass around 1.4 GeV for tetraquarks, we conjecture that this quasichiral nonet arises from the mixing of a chiral nonet composed of tetraquarks with conventional $\overline{q}q$ states. We explore this possibility in the framework of a chiral model assuming a tetraquark chiral nonet around 1.4 GeV with chiral symmetry realized directly. We stress that ${U}_{A}(1)$ transformations can distinguish $\overline{q}q$ from tetraquark states, although it cannot distinguish specific dynamics in the later case. We find that the measured spectrum is consistent with this picture. In general, pseudoscalar states arise as mainly $\overline{q}q$ states but scalar states turn out to be strong admixtures of $\overline{q}q$ and tetraquark states. We work out also the model predictions for the most relevant couplings and calculate explicitly the strong decays of the ${a}_{0}(1450)$ and ${K}_{0}^{*}(1430)$ mesons.

Chiral model forq¯qandqq¯qqmesons

We employ the two independent Casimir operators of the Poincare group, the squared four--momentum, P^2, and the squared Pauli-Lubanski vector, W^2, in the construction of a covariant mass-m, and spin-3/2 projector in the four-vector-spinor, \psi_{\mu}. This projector provides the basis for the construction of an interacting Lagrangian that describes a causally propagating spin-3/2} particle coupled to the electromagnetic field by a gyromagnetic ratio of g_{3/2}=2.

Spin 3/2 Beyond the Rarita-Schwinger Framework

We study multipole decompositions of the electromagnetic currents of spin-$1/2$, 1, and $3/2$ particles described in terms of representation-specific wave equations which are second order in the momenta and which emerge within the recently elaborated Poincar\'e covariant-projector method, where the respective Lagrangians explicitly depend on the Lorentz group generators of the representations of interest. The currents are then the ordinary linear Noether currents related to phase invariance, and present themselves always as two-terms motion--plus spin-magnetization currents. The spin-magnetization currents appear weighted by the gyromagnetic ratio $g$, a free parameter in the method which we fix either by unitarity of forward Compton scattering amplitudes in the ultraviolet for spin-1 and spin-$3/2$, or in the spin-$1/2$ case, by their asymptotic vanishing, thus ending up in all three cases with the universal $g$ value of $g=2$. Within the method under discussion, we calculate the electric multipoles of the above spins for the spinor, the four-vector, and the four-vector--spinor representations, and find it favorable in some aspects, specifically in comparison with the conventional Proca and Rarita-Schwinger frameworks. We furthermore attend to the most general non-Lagrangian spin-$3/2$ currents, which are allowed by Lorentz invariance to be up to third order in the momenta and construct the linear-current equivalent of identical multipole moments of one of them. We conclude that nonlinear non-Lagrangian spin-$3/2$ currents are not necessarily more general and more advantageous than the linear spin-$3/2$ Lagrangian current emerging within the covariant-projector formalism. Finally, we test the representation dependence of the multipoles by placing spin-1 and spin-$3/2$ in the respective $(1,0)\ensuremath{\bigoplus}(0,1)$ and $(3/2,0)\ensuremath{\bigoplus}(0,3/2)$ single-spin representations. We observe representation independence of the charge monopoles and the magnetic dipoles, in contrast to the higher multipoles, which turn out to be representation-dependent. In particular, we find the bi-vector $(1,0)\ensuremath{\bigoplus}(0,1)$ to be characterized by an electric quadrupole moment of opposite sign to the one found in $(1/2,1/2)$, and consequently to the $W$ boson. This observation allows us to explain the positive electric quadrupole moment of the $\ensuremath{\rho}$ meson extracted from recent analyses of the $\ensuremath{\rho}$ meson electric form factor. Our finding points toward the possibility that the $\ensuremath{\rho}$-meson could transform as part of an antisymmetric tensor with an ${a}_{1}$ mesonlike state as its representation companion, a possibility consistent with the empirically established $\ensuremath{\rho}$ and ${a}_{1}$ vector meson dominance of the hadronic vector and axial-vector currents.

Electromagnetic multipole moments of elementary spin- 1 / 2 , 1, and 3 / 2 particles

It is shown that most of the unusual properties of the lowest lying scalar (and pseudoscalar) mesons can be understood, at the qualitative and quantitative level, on the basis of the breakdown of the $U_A(1)$ symmetry coupled to the vacuum expectation values of scalars by the spontaneous breaking of chiral symmetry.

$U_A(1)$ Symmetry Breaking and the Scalar Sector of QCD

We develop a second order formalism for massive spin $1/2$ fermions based on the projection over Poincar\'e invariant subspaces in the $(\frac{1}{2},0)\ensuremath{\bigoplus}(0,\frac{1}{2})$ representation of the homogeneous Lorentz group. Using the $U(1{)}_{\mathrm{em}}$ gauge principle we obtain a second order description for the electromagnetic interactions of a spin $1/2$ fermion with two free parameters, the gyromagnetic factor $g$ and a parameter $\ensuremath{\xi}$ related to odd-parity Lorentz structures. We calculate Compton scattering in this formalism. In the particular case $g=2$, $\ensuremath{\xi}=0$, and for states with well-defined parity, we recover Dirac results. In general, we find the correct classical limit and a finite value ${r}_{c}^{2}$ for the forward differential cross section, independent of the photon energy and of the value of the parameters $g$ and $\ensuremath{\xi}$. The differential cross section vanishes at high energies for all $g$, $\ensuremath{\xi}$ except in the forward direction. The total cross section at high energies vanishes only for $g=2$, $\ensuremath{\xi}=0$. We argue that this formalism is more convenient than Dirac theory in the description of low energy electromagnetic properties of baryons and illustrate the point with the proton case.

S. Rodríguez

Papers

Chiral model forq¯qandqq¯qqmesons

Spin 3/2 Beyond the Rarita-Schwinger Framework

Electromagnetic multipole moments of elementary spin- 1 / 2 , 1, and 3 / 2 particles

$U_A(1)$ Symmetry Breaking and the Scalar Sector of QCD

Second order formalism for spin (1/2) fermions and Compton scattering