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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dimension $D_{C}=4$ (where $D=d+z$ and $d$ is the spatial dimension) below which mean-field description is no longer valid.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

We consider a model of topological solitons where charged particles have finite mass and the electric charge is quantised already at the classical level. In the electrodynamic limit, which physically corresponds to electrodynamics of solitons of zero size, the Lagrangian of this model has two degrees of freedom only and reduces to the Lagrangian of the Maxwell field in dual representation. We derive the equations of motion and discuss their relations with Maxwell's equations. It is shown that Coulomb and Lorentz forces are a consequence of topology. Further, we relate the U(1) gauge invariance of electrodynamics to the geometry of the soliton field, give a general relation for the derivation of the soliton field from the field strength tensor in electrodynamics and use this relation to express homogeneous electric fields in terms of the soliton field.

Electromagnetic Field from the Skyrme Term

The relativistic field theory model of the deuteron (RFMD) is re- formulated from the first principles of QCD. The deuteron appears as a neutron-proton collective excitation, i.e. a Cooper np-pair, induced by a phenomenological local four-nucleon interaction in the nuclear phase of QCD. The RFMD describes the deuteron coupled to hadrons through one-nucleon loop exchanges providing a minimal transfer of nucleon flavours from initial to final nuclear states and accounting for contributions of nucleon-loop anomalies which are completely deter- mined by one-nucleon loop diagrams. The dominance of contributions of nucleon-loop anomalies to effective Lagrangians of low-energy nu- clear interactions is justified in the large NC expansion, where NC is the number of quark colours.

The relativistic field theory model of the deuteron from low-energy QCD

At large separations static color sources of non-vanishing N-ality give rise to gluonic flux tubes and a linearly rising potential. This behavior is caused by the non-perturbative QCD-vacuum which compresses the gluonic flux. Center vortices [1, 2],quantized magnetic flux lines, play an important role for the confinement of color charges, as has been shown by numerical calculations[3]. In addition, simulations have indicated that vortices could also account for phenomena related to chiral symmetry, such as topological charge and spontaneous chiral symmetry breaking (SCSB) [4, 5]. It is well-known that these non-perturbative features of QCD are intimately linked to the properties of the low-lying spectrum of the Dirac operator. The topological charge of a gauge field equals the index of the Dirac operator, while the chiral condensate, the order parameter for SCSB, is proportional to the spectral density of the near-zero modes. With the advent of the overlap operator [6, 7], the fundamental problems of investigating chiral features on the lattice have been overcome. The overlap operator has an exact chiral symmetry [8], implements a lattice version of the index theorem [6], and may even be used for the definition of a local topological charge density [4]. We work with SU(2) gauge fields on lattices with Ns sites in the x-, yand z-direction, and Nt sites in the t-direction. In four dimensions vortices form closed two-dimensional surfaces. We investigate thick classical center vortices in the shapes of planes (closed by lattice periodicity) and spheres. The details of the individual vortex types will be discussed along with our results. We report on our calculations with the overlap operator applied to thick classical center vortices. We investigate the localization of zero-modes with respect to the position of the thick vortices and find an interesting discrepancy in the topological charge determined by different methods.

/pdf/center-vortices-and-topological-charge-4te2uqtydh.pdf

Center vortices and topological charge

We show that mass generation in 1+1 and 3+1 dimensions may occur together with spontaneous symmetry breaking.

https://arxiv.org/pdf/hep-lat/0204031.pdf

Solitons and Spontaneous Symmetry Breaking in 2 and 4 Dimensions

The time evolution of a quantum wave packet in the linear gravity potential is known as Quantum Bouncing Ball. The qBounce collaboration recently observed such a system by dropping wave packets of ultracold neutrons by a height of roughly 30 microns. In this article, space and momentum spectra as well as Wigner functions of the neutron wave functions in the gravitational field of the Earth are analyzed. We investigate the quantum states in the "preparation region", into which they transition after exiting a narrow double-mirror system and where we would expect to observe free fall and bounces in classical physics. For this, we start from the stationary solutions and eigenvalues of the Schrodinger equation in terms of Airy functions and their zeros. Subsequently, we examine space and momentum distributions as well as Wigner functions in phase space for pure and mixed quantum states. The eventual influence of Yukawa-like forces for small distances of several micrometers from the mirror is included through first order perturbation calculations. Those allow us to study the resulting modifications of space and momentum distributions, and phase space functions.

Manfried Faber

Papers

Electromagnetic Field from the Skyrme Term

The relativistic field theory model of the deuteron from low-energy QCD

Center vortices and topological charge

Solitons and Spontaneous Symmetry Breaking in 2 and 4 Dimensions

Spectra of Neutron Wave Functions in Earth's Gravitational Field