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

Superstring theoryをめぐって(放談室)

Tables of integrals

Glueballs, Hybrids, Multiquarks. Experimental facts versus QCD inspired concepts

Various holographic approaches to QCD in five dimensions are explored using input both from the putative five-dimensional non-critical string theory as well as QCD. It is argued that a gravity theory in five dimensions coupled to a dilaton and an axion may capture the important qualitative features of pure YM theory. A part of the effects of higher α'-corrections is resummed into a dilaton potential. The potential is shown to be in one-to-one correspondence with the exact β-function of QCD, and its knowledge determines the full structure of the vacuum solution. The geometry near the UV boundary is that of AdS5 with logarithmic corrections reflecting the asymptotic freedom of QCD. We find that all relevant confining backgrounds have an IR singularity of the ``good" kind that allows unambiguous spectrum computations. Near the singularity the 't Hooft coupling is driven to infinity. Asymptotically linear glueball masses can also be achieved. The classification of all confining asymptotics, the associated glueball spectra and meson dynamics are addressed in a companion paper arXiv:0707.1349

https://iopscience.iop.org/article/10.1088/1126-6708/2008/02/032/pdf

Exploring improved holographic theories for QCD: part I

We consider a new approach towards constructing approximate holographic duals of QCD from experimental hadron properties. This framework allows us to derive a gravity dual which reproduces the empirically found linear square-mass trajectories of universal slope for radially and orbitally excited hadrons. Conformal symmetry breaking in the bulk is exclusively due to infrared deformations of the anti-de Sitter metric and governed by one free mass scale proportional to Lambda_QCD. The resulting background geometry exhibits dual signatures of confinement and provides the first examples of holographically generated linear trajectories in the baryon sector. The predictions for the light hadron spectrum include new relations between trajectory slopes and ground state masses and are in good overall agreement with experiment.

Linear square-mass trajectories of radially and orbitally excited hadrons in holographic QCD

We consider a new approach towards constructing approximate holographic duals of QCD from experimental hadron properties. This framework allows us to derive a gravity dual which reproduces the empirically found linear square-mass trajectories of universal slope for radially and orbitally excited hadrons. Conformal symmetry breaking in the bulk is exclusively due to infrared deformations of the anti-de Sitter metric and governed by one free mass scale proportional to ΛQCD. The resulting background geometry exhibits dual signatures of confinement and provides the first examples of holographically generated linear trajectories in the baryon sector. The predictions for the light hadron spectrum include new relations between trajectory slopes and ground state masses and are in good overall agreement with experiment.

http://iopscience.iop.org/article/10.1088/1126-6708/2007/07/077/pdf

I derive and systematically analyze scalar glueball correlation functions in both the hard-wall and dilaton soft-wall approximations to holographic QCD. The dynamical content of the holographic correlators is uncovered by examining their spectral density and by relating them to the operator product expansion, a dilatational low-energy theorem and a recently suggested two-dimensional power correction associated with the short-distance behavior of the heavy-quark potential. This approach provides holographic estimates for the three lowest-dimensional gluon condensates or alternatively their Wilson coefficients, the two leading moments of the instanton size distribution in the QCD vacuum and an effective UV gluon mass. A remarkable complementarity between the nonperturbative physics of the hard- and soft-wall correlators emerges, and their ability to describe detailed QCD results can be assessed quantitatively. I further provide the first holographic estimates for the decay constants of the ${0}^{++}$ glueball and its excitations. The hard-wall background turns out to encode more of the relevant QCD physics, and its prediction ${f}_{S}\ensuremath{\simeq}0.8\char21{}0.9\text{ }\text{ }\mathrm{GeV}$ for the phenomenologically important ground-state decay constant agrees inside errors with recent QCD sum rule and lattice results.

Holographic glueball structure

The impact of QCD instantons on scalar glueball properties is studied in the framework of an instanton-improved operator product expansion (IOPE) for the ${0}^{++}$ glueball correlation function. Direct instanton contributions are found to strongly dominate over those from perturbative fluctuations and soft vacuum fields. All IOPE sum rules, including the one involving a subtraction constant, show a high degree of stability and are, in contrast to previous glueball sum rules, consistent with the low-energy theorem for the zero-momentum correlator. The predicted glueball mass ${m}_{G}=1.53\ifmmode\pm\else\textpm\fi{}0.2 \mathrm{GeV}$ is less sensitive to the instanton contributions then the glueball coupling (residue) ${f}_{G}=1.01\ifmmode\pm\else\textpm\fi{}0.25 \mathrm{GeV},$ which increases by about half an order of magnitude. Both glueball properties are shown to obey scaling relations as a function of the average instanton size and density.

Scalar gluonium and instantons

These are the (twice) extended notes of a set of lectures given at the ``12th Workshop on Hadronic Interactions'' at the IF/UERJ, Rio de Janeiro (31. 5. - 2. 6. 2000). The lectures aim at introducing essential concepts of instanton physics, with emphasis on the role of instantons in generating tunneling amplitudes, vacuum structure, and the induced quark interactions associated with the axial anomaly. A few examples for the impact of instantons on the physics of hadrons are also mentioned.

Hilmar Forkel

Papers

Linear square-mass trajectories of radially and orbitally excited hadrons in holographic QCD

Linear square-mass trajectories of radially and orbitally excited hadrons in holographic QCD

Holographic glueball structure

Scalar gluonium and instantons

A Primer on Instantons in QCD