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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 give a general introduction to quantum phase transitions in strongly-correlated electron systems. These transitions which occur at zero temperature when a non-thermal parameter $g$ like pressure, chemical composition or magnetic field is tuned to a critical value are characterized by a dynamic exponent $z$ related to the energy and length scales $\Delta$ and $\xi$. Simple arguments based on an expansion to first order in the effective interaction allow to define an upper-critical dimension $D_{C}=4$ (where $D=d+z$ and $d$ is the spatial dimension) below which mean-field description is no longer valid. We emphasize the role of pertubative renormalization group (RG) approaches and self-consistent renormalized spin fluctuation (SCR-SF) theories to understand the quantum-classical crossover in the vicinity of the quantum critical point with generalization to the Kondo effect in heavy-fermion systems. Finally we quote some recent inelastic neutron scattering experiments performed on heavy-fermions which lead to unusual scaling law in $\omega /T$ for the dynamical spin susceptibility revealing critical local modes beyond the itinerant magnetism scheme and mention new attempts to describe this local quantum critical point.

https://arxiv.org/pdf/cond-mat/0102119.pdf

Quantum Phase Transitions

The authors review the theory and phenomenology of instantons in quantum chromodynamics (QCD). After a general overview, they provide a pedagogical introduction to semiclassical methods in quantum mechanics and field theory. The main part of the review summarizes our understanding of the instanton liquid in QCD and the role of instantons in generating the spectrum of light hadrons. The authors also discuss properties of instantons at finite temperature and how instantons can provide a mechanism for the chiral phase transition. They give an overview of the role of instantons in some other models, in particular low-dimensional sigma models, electroweak theory, and supersymmetric QCD.

http://wonka.physics.ncsu.edu/~tmschaef/physics/RevModPhys_Instantons.pdf

Instantons in QCD

The hidden-charm pentaquark and tetraquark states

Investigating the $Z_3$ symmetry in Quantum Chromodynamics (QCD) we show that full QCD with a vacuum of vanishing baryonic number does not lead to metastable phases. Rather in QCD with dynamical fermions, the degeneracy of $Z_3$ phases manifests itself in observables without open triality.

Fresh look on triality

The dominance of center degrees of freedom is observed in SU(3) lattice gauge theory in maximal center gauge. The full asymptotic string tension is reproduced, after center projection, by the center elements alone. When center vortices are removed from lattice configurations, the string tension tends to zero. This provides further evidence for the role played by center vortices in the mechanism of color confinement in quantum chromodynamics, but more extensive simulations with a better gauge-fixing procedure are still needed.

First Evidence for Center Dominance in SU(3) Lattice Gauge Theory

The cross sections for the reactions pp → p� 0 K + and pn → n� 0 K + are calculated near threshold of the final states. The theoretical ratio of the cross sections R = �(pn → n� 0 K + )/�(pp → p� 0 K + ) ≃ 3 shows the enhancement of the pn interaction with respect to the pp interaction near threshold of the strangeness production N� 0 K + . Such an enhancement is caused by the contribution of the np interaction in the isospin–singlet state, which is stronger than the pn interaction in the isospin–triplet state. For the confirmation of this result we calculate the cross sections for the reactions pp → pp� 0 , � 0 p → � 0 K + and � − p → � 0 K 0 near threshold of the final states. The theoretical cross sections agree well with the experimental data.

On strangeness production in the reactions pp → p 0 K + and pn → n 0 K + near threshold

Intersections of thick, plane SU(2) center vortices are characterized by the topological charge |Q| = 1/2. We compare such intersections with the distribution of zeromodes of the Dirac operator in the fundamental and adjoint representation using both the overlap and asqtad staggered fermion formulations in SU(2) lattice gauge theory. We analyze configurations with four intersections and find that the probability density distribution of fundamental zeromodes in the intersection plane differs significantly from the one obtained analytically in [1]. The Dirac eigenmodes are clearly sensitive to the traces of the Polyakov (Wilson) lines and do not exactly locate topological charge contributions. Although, the adjoint Dirac operator is able to produce zeromodes for configurations with topological charge |Q| = 1/2, they do not locate single vortex intersections, as we prove by forming arbitrary linear combinations of these zeromodes — their scalar density peaks at least at two intersection points. With pairs of thin and thick vortices we realize a situation similar to configurations with topological charge |Q| = 1/2. For such configurations the zeromodes do not localize in the regions of fractional topological charge contribution but spread over the whole lattice, avoiding regions of negative traces of Polyakov lines. This sensitivity to Polyakov lines we also confirm for single vortex-pairs, i.e., configurations with nontrivial Polyakov loops but without topological charge.

/pdf/intersections-of-thick-center-vortices-dirac-eigenmodes-and-1th5qq3q5q.pdf

Intersections of thick Center Vortices, Dirac Eigenmodes and Fractional Topological Charge in SU(2) Lattice Gauge Theory

We discuss a model with stable topological solitons in Minkowski space with only three degrees of freedom, the rotational angles of a spatial Dreibein. This model has four types of solitons differing in two topological quantum numbers which we identify with electric charge and spin. The vacuum has a two-dimensional degeneracy leading to two types of massless excitations, characterised by a topological quantum number which could have a physical equivalent in the photon number.

Manfried Faber

Papers

Fresh look on triality

First Evidence for Center Dominance in SU(3) Lattice Gauge Theory

On strangeness production in the reactions pp → p 0 K + and pn → n 0 K + near threshold

Intersections of thick Center Vortices, Dirac Eigenmodes and Fractional Topological Charge in SU(2) Lattice Gauge Theory

Charges and Electromagnetic radiation as topological excitations