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

A large number of experimental discoveries especially in the heavy quarkonium sector that did not at all fit to the expectations of the until then very successful quark model led to a renaissance of hadron spectroscopy Among various explanations of the internal structure of these excitations, hadronic molecules, being analogues of light nuclei, play a unique role since for those predictions can be made with controlled uncertainty We review experimental evidences of various candidates of hadronic molecules, and methods of identifying such structures Nonrelativistic effective field theories are the suitable framework for studying hadronic molecules, and are discussed in both the continuum and finite volumes Also pertinent lattice QCD results are presented Further, we discuss the production mechanisms and decays of hadronic molecules, and comment on the reliability of certain assertions often made in the literature

Hadronic molecules

We review lattice results related to pion, kaon, D- and B-meson physics with the aim of making them easily accessible to the particle physics community. More specifically, we report on the determination of the light-quark masses, the form factor f+(0), arising in semileptonic K -> pi transition at zero momentum transfer, as well as the decay constant ratio fK/fpi of decay constants and its consequences for the CKM matrix elements Vus and Vud. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of SU(2)LxSU(2)R and SU(3)LxSU(3)R Chiral Perturbation Theory and review the determination of the BK parameter of neutral kaon mixing. The inclusion of heavy-quark quantities significantly expands the FLAG scope with respect to the previous review. Therefore, for this review, we focus on D- and B-meson decay constants, form factors, and mixing parameters, since these are most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. In addition we review the status of lattice determinations of the strong coupling constant alpha_s.

https://link.springer.com/content/pdf/10.1140%2Fepjc%2Fs10052-014-2890-7.pdf

Review of lattice results concerning low-energy particle physics

We review lattice results related to pion, kaon, D- and B-meson physics with the aim of making them easily accessible to the particle-physics community. More specifically, we report on the determination of the light-quark masses, the form factor [Formula: see text], arising in the semileptonic [Formula: see text] transition at zero momentum transfer, as well as the decay constant ratio [Formula: see text] and its consequences for the CKM matrix elements [Formula: see text] and [Formula: see text]. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of [Formula: see text] and [Formula: see text] Chiral Perturbation Theory. We review the determination of the [Formula: see text] parameter of neutral kaon mixing as well as the additional four B parameters that arise in theories of physics beyond the Standard Model. The latter quantities are an addition compared to the previous review. For the heavy-quark sector, we provide results for [Formula: see text] and [Formula: see text] (also new compared to the previous review), as well as those for D- and B-meson-decay constants, form factors, and mixing parameters. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. Finally, we review the status of lattice determinations of the strong coupling constant [Formula: see text].

/pdf/review-of-lattice-results-concerning-low-energy-particle-4ppyuq45zk.pdf

Review of lattice results concerning low-energy particle physics: Flavour Lattice Averaging Group (FLAG).

Quantum chromodynamics (QCD), the generally accepted theory for strong interactions, describes the interactions between quarks and gluons. The strongly interacting particles that are seen in nature are hadrons, which are composites of quarks and gluons. Since QCD is a strongly coupled theory at distance scales that are characteristic of observable hadrons, there are no rigorous, first-principle methods to derive the spectrum and properties of the hadrons from the QCD Lagrangian, except for lattice QCD simulations that are not yet able to cope with all aspects of complex and short-lived states. Instead, a variety of “QCD inspired” phenomenological models have been proposed. Common features of these models are predictions for the existence of hadrons with substructures that are more complex than the standard quark-antiquark mesons and the three-quark baryons of the original quark model that provides a concise description of most of the low-mass hadrons. Recently, an assortment of candidates for nonstandard multiquark mesons, meson-gluon hybrids, and pentaquark baryons that contain heavy (charm or bottom) quarks has been discovered. Here the experimental evidence for these states is reviewed and some general comparisons of their measured properties with standard quark model expectations and predictions of various models for nonstandard hadrons are made. The conclusion is that the spectroscopy of all but the simplest hadrons is not yet understood.

https://link.aps.org/accepted/10.1103/RevModPhys.90.015003

Nonstandard heavy mesons and baryons: Experimental evidence

We perform renormalization group transformations to construct optimally local perfect lattice actions for free scalar fields of any mass. Their couplings decay exponentially. The spectrum is identical to the continuum spectrum, while thermodynamic quantities have tiny lattice artifacts. To make such actions applicable in simulations, we truncate the couplings to a unit hypercube and observe that spectrum and thermodynamics are still drastically improved compared to the standard lattice action. We show how preconditioning techniques can be applied successfully to this type of action. We also consider a number of variants of the perfect lattice action, such as the use of an anisotropic or triangular lattice, and modifications of the renormalization group transformations motivated by wavelets. Along the way we illuminate the consistent treatment of gauge fields, and we find a new fermionic fixed point action with attractive properties.

Perfect Scalars on the Lattice

We sketch the basic ideas of the lattice regularization in Quantum Field Theory, the corresponding Monte Carlo simulations, and applications to Quantum Chromodynamics (QCD). This approach enables the numerical measurement of observables at the non-perturbative level. We comment on selected results, with a focus on hadron masses and the link to Chiral Perturbation Theory. At last, we address two outstanding issues: topological freezing and the sign problem.

Hadron physics from lattice QCD

We use perturbation theory to construct perfect lattice actions for quarks and gluons. The renormalized trajectory for free massive quarks is identified by blocking directly from the continuum. We tune a parameter in the renormalization group transformation such that for 1-d configurations the perfect action reduces to the nearest neighbor Wilson fermion action. The fixed point action for free gluons is also obtained by blocking from the continuum. For 2-d configurations it reduces to the standard plaquette action. Classically perfect quark and gluon fields, quark-gluon composite operators and vector and axial vector currents are constructed as well. Also the quark-antiquark potential is derived from the classically perfect Polyakov loop. The quark-gluon and 3-gluon perfect vertex functions are determined to leading order in the gauge coupling. We also construct a new block factor $n$ renormalization group transformation for QCD that allows to extend our results beyond perturbation theory. For weak fields it leads to the same perfect action as blocking from the continuum. For arbitrarily strong 2-d Abelian gauge fields the Manton plaquette action is classically perfect for this transformation.

Perfect Lattice Actions for Quarks and Gluons

In gauge theories the field configurations often occur in distinct topological sectors. In a lattice regularised system with chiral fermions, these sectors can be defined by referring to the Atiyah-Singer Index Theorem. However, if such a model is simulated with local updates of the lattice gauge configuration, the Monte Carlo history tends to get stuck in one sector for many steps, in particular on fine lattices. Then expectation values can be measured only within specific sectors. Here we present a pilot study in the 2-flavour Schwinger model which explores methods of approximating the complete result for an observable - corresponding to a suitable sum over all sectors - based on numerical measurements in a few specific topological sectors. We also probe various procedures for an indirect evaluation of the topological susceptibility, starting from such topologically restricted measurements.

Topological Summation in Lattice Gauge Theory

We review a number of topics related to block variable renormalisation group transformations of quantum fields on the lattice, and to the emerging perfect lattice actions. We first illustrate this procedure by considering scalar fields. Then we proceed to lattice fermions, where we discuss perfect actions for free fields, for the Gross-Neveu model and for a supersymmetric spin model. We also consider the extension to perfect lattice perturbation theory, in particular regarding the axial anomaly and the quark gluon vertex function. Next we deal with properties and applications of truncated perfect fermions, and their chiral correction by means of the overlap formula. This yields a formulation of lattice fermions, which combines exact chiral symmetry with an optimisation of further essential properties. We summarise simulation results for these so-called overlap-hypercube fermions in the two-flavour Schwinger model and in quenched QCD. In the latter framework we establish a link to Chiral Perturbation Theory, both, in the p-regime and in the epsilon-regime. In particular we present an evaluation of the leading Low Energy Constants of the chiral Lagrangian - the chiral condensate and the pion decay constant - from QCD simulations with extremely light quarks.

Optimised Dirac Operators on the Lattice: Construction, Properties and Applications

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