There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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

Singular Integral Equations. By N.I. Muskhelishvili. Translated fromthe 2nd Russian edition by J.R.M. Radok. Pp. 447. F1. 28.50. 1953. (Noordhoff, Groningen)

This paper presents a new event generator, ALPGEN, dedicated to the study of multiparton hard processes in hadronic collisions. The code performs, at the leading order in QCD and EW interactions, the calculation of the exact matrix elements for a large set of parton-level processes of interest in the study of the Tevatron and LHC data. The current version of the code describes the following final states: (W→f')Q+N jets (Q being a heavy quark, and f = l,q), with N ≤ 4;(Z/γ*→f)Q+N jets (f = l,ν), with N ≤ 4; W→f')+charm+N jets (f = l,q,N ≤ 5;W→f')+N jets (f = l,q and Z/γ*→f)+N jets (f = l,ν), with N ≤ 6; nW+mZ+lH+N jets, with n+m+l+N ≤ 8, N ≤ 3, including all 2-fermion decay modes of W and Z bosons, with spin correlations; Q+N jets, with t→bf' decays and relative spin correlations included where relevant, and N ≤ 6; QQ''+N jets, with Q and Q' heavy quarks (possibly equal) and N ≤ 4; HQ+N jets, with t→bf' decays and relative spin correlations included where relevant and N ≤ 4; N jets, with N ≤ 6. Parton-level events are generated, providing full information on their colour and flavour structure, enabling the evolution of the partons into fully hadronised final states.

/pdf/alpgen-a-generator-for-hard-multiparton-processes-in-4tuthlh5y0.pdf

ALPGEN, a generator for hard multiparton processes in hadronic collisions

Tables of integrals

A nonperturbative method which combines constraints from chiral symmetry breaking and coupled channel unitarity is used to describe the meson-meson interaction up to about 1.2 GeV. The approach uses the $\mathcal{O}{(p}^{2})$ and $\mathcal{O}{(p}^{4})$ chiral Lagrangians. The seven free parameters of the $\mathcal{O}{(p}^{4})$ Lagrangian are fitted to the data. The results are in good agreement with a vast amount of experimental analyses. The amplitudes develop poles in the complex plane corresponding to the ${f}_{0}, {a}_{0}, \ensuremath{\rho}, {K}^{*}, \ensuremath{\varphi}, \ensuremath{\sigma},$ and $\ensuremath{\kappa}$ resonances, the latter two being very broad. The total and partial decay widths of the resonances are also well reproduced. Further extensions and applications of this chiral nonperturbative scheme are also discussed.

/pdf/meson-meson-interactions-in-a-nonperturbative-chiral-1d0dejm3mf.pdf

Meson-meson interactions in a nonperturbative chiral approach

We improve our description of π π scattering data by imposing additional requirements on our previous fits, in the form of once-subtracted Roy-like equations, while extending our analysis up to 1100 MeV. We provide simple and ready to use parametrizations of the amplitude. In addition, we present a detailed description and derivation of these once-subtracted dispersion relations that, in the 450 to 1100 MeV region, provide an additional constraint which is much stronger than our previous requirements of forward dispersion relations and standard Roy equations. The ensuing constrained amplitudes describe the existing data with rather small uncertainties in the whole region from threshold up to 1100 MeV, while satisfying very stringent dispersive constraints. For the S0 wave, this requires an improved matching of the low and high energy parametrizations. Also for this wave we have considered the latest low energy K_(l4) decay results, including their isospin violation correction, and we have removed some controversial data points. These changes on the data translate into better determinations of threshold and subthreshold parameters which remove almost alldisagreement with previous chiral perturbation theory and Roy equation calculations below 800 MeV. Finally, our results favor the dip structure of the S0 inelasticity around the controversial 1000 MeV region.

/pdf/pion-pion-scattering-amplitude-iv-improved-analysis-with-rs5keh41n9.pdf

Pion-pion scattering amplitude. IV. Improved analysis with once subtracted Roy-like equations up to 1100 MeV

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.

/pdf/from-controversy-to-precision-on-the-sigma-meson-a-review-on-3umvi1vsss.pdf

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

We develop a coupled channel unitary approach describing the behavior at higher energies of systems whose low-energy dynamics is given by effective O(p^2) and O(p^4) chiral Lagrangians. Our free parameters are those of the O(p^4) Lagrangian. When applied to the meson-meson interaction, it yields a remarkable agreement with data up to √2≅1.2 GeV, dynamically generating the σ , f_0 α_0, ρ, and K* resonances. Further applications are also proposed.

/pdf/nonperturbative-approach-to-effective-chiral-lagrangians-and-1qxwp7a62c.pdf

José R. Peláez

Papers

Meson-meson interactions in a nonperturbative chiral approach

Pion-pion scattering amplitude. IV. Improved analysis with once subtracted Roy-like equations up to 1100 MeV

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

Nonperturbative approach to effective chiral lagrangians and meson interactions

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