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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dimension $D_{C}=4$ (where $D=d+z$ and $d$ is the spatial dimension) below which mean-field description is no longer valid.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 argue that in the canonical ensemble description of full QCD there exist domains of different Z ( N ) phases which are degenerate and possess normal physical properties. This contradicts the predictions of the grand canonical ensemble. Further, we propose a new order parameter to test the realization of the discrete Z ( N ) symmetry at finite temperature and calculate it for the case of Z (2) gauge fields coupled to fundamental fermions.

Deconfining phase in QCD

The phase structure of hot gauge theories with dynamical matter fields is reexamined in the canonical ensemble with respect to triality. Since this ensemble implies a projection to the zero triality sector of the theory we introduce a proper quantity which is able to reveal a critical behaviour of the theory with fundamental quarks. We discuss the properties of both the chromoelectric and chromomagnetic sectors of the theory and show while electric charges carrying a unit of Z(N) charge are screened at high temperatures by dynamical matter loops, this is not the case for the Z(N) magnetic flux. An order parameter is constructed to probe the realization of local discrete Z(N) symmetry in the magnetic sector. We argue it can be used to detect a deconfinement phase being defined in terms of the screening mechanism as a phase of unscreened Z(N) flux. It may be detectable at long range via the Aharonov-Bohm effect. We discuss the possible phase structure of QCD in this approach.

https://arxiv.org/pdf/hep-lat/9804009.pdf

On the Deconfinement Phase Transition in Hot Gauge Theories with Dynamical Matter Fields

There exist two calculations for the interface tension a of coexisting quark and hadron matter with two different methods. We perform an independent computation of a for time extension Nt = 2 and 4 and find that (i) the interface tension vanishes for our volume within error bars and (ii) there are systematic deviations between the differential and integral method.

Inhomogeneous Universes in the Framework of Lattice QCD

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.

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

We investigate the structure of center projected vortices of SU(2) lattice gauge theory at zero and finite temperature. At zero temperature we find, in agreement with the area law behaviour of Wilson loops, that most of the P-vortex plaquettes are parts of a single huge vortex. This vortex is an unorientable surface and has a very irregular structure with many handles. Small P-vortices, and short-range fluctuations of the large vortex surface, do not contribute to the string tension. At finite temperature P-vortices exist also in the deconfined phase. However, they form cylindric objects which extend in time direction and consist only of space-space plaquettes.

Manfried Faber

Papers

Deconfining phase in QCD

On the Deconfinement Phase Transition in Hot Gauge Theories with Dynamical Matter Fields

Inhomogeneous Universes in the Framework of Lattice QCD

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

The Structure of Projected Center Vortices at Zero and Finite Temperature