https://biblio.ugent.be/publication/685594/file/1130605.pdf

Review of Particle Physics

The calculation of rate coefficients is a discipline of nonlinear science of importance to much of physics, chemistry, engineering, and biology. Fifty years after Kramers' seminal paper on thermally activated barrier crossing, the authors report, extend, and interpret much of our current understanding relating to theories of noise-activated escape, for which many of the notable contributions are originating from the communities both of physics and of physical chemistry. Theoretical as well as numerical approaches are discussed for single- and many-dimensional metastable systems (including fields) in gases and condensed phases. The role of many-dimensional transition-state theory is contrasted with Kramers' reaction-rate theory for moderate-to-strong friction; the authors emphasize the physical situation and the close connection between unimolecular rate theory and Kramers' work for weakly damped systems. The rate theory accounting for memory friction is presented, together with a unifying theoretical approach which covers the whole regime of weak-to-moderate-to-strong friction on the same basis (turnover theory). The peculiarities of noise-activated escape in a variety of physically different metastable potential configurations is elucidated in terms of the mean-first-passage-time technique. Moreover, the role and the complexity of escape in driven systems exhibiting possibly multiple, metastable stationary nonequilibrium states is identified. At lower temperatures, quantum tunneling effects start to dominate the rate mechanism. The early quantum approaches as well as the latest quantum versions of Kramers' theory are discussed, thereby providing a description of dissipative escape events at all temperatures. In addition, an attempt is made to discuss prominent experimental work as it relates to Kramers' reaction-rate theory and to indicate the most important areas for future research in theory and experiment.

Reaction-rate theory: fifty years after Kramers

QCD and resonance physics. theoretical foundations

http://cds.cern.ch/record/147992/files/198312192.pdf

Chiral perturbation theory to one loop

The possible domain structures which can arise in the universe in a spontaneously broken gauge theory are studied. It is shown that the formation of domain wall, strings or monopoles depends on the homotopy groups of the manifold of degenerate vacua. The subsequent evolution of these structures is investigated. It is argued that while theories generating domain walls can probably be eliminated (because of their unacceptable gravitational effects), a cosmic network of strings may well have been formed and may have had important cosmological effects.

https://iopscience.iop.org/article/10.1088/0305-4470/9/8/029/pdf

Topology of cosmic domains and strings

The structure of the gauge theory vacuum

A systematic study is made of the relevant degrees of freedom and the dynamics of quantum chromodynamics (QCD). We find that the dynamical properties of QCD are, to a large extent, a consequence of the structure of the vacuum arising from the tunneling between degenerate, classically stable, vacuums, and that the relevant degrees of freedom can be taken to be the Euclidean path histories that can be used to calculate the tunneling in the semiclassical approximation. This nonperturbative vacuum structure appears well suited to the major features of QCD, i.e., the dimensional transmutation that determines the size of the hadrons and the strong-interaction coupling constant, the source of dynamical chiral symmetry breaking, and the mechanism responsible for quark confinement.

Toward a Theory of the Strong Interactions

We have used a semiclassical method developed earlier to compute the particle spectrum of a field theory in two-dimensional space-time defined by the (sine-Gordon) Lagrangian $\frac{1}{2}{({\ensuremath{\partial}}_{\ensuremath{\mu}}\ensuremath{\varphi})}^{2}+(\frac{{m}^{4}}{\ensuremath{\lambda}}){cos[(\frac{\sqrt{\ensuremath{\lambda}}}{m})\ensuremath{\varphi}]\ensuremath{-}1}$. For weak coupling we find a heavy particle, the soliton, corresponding to a peculiar classical field configuration and an antisoliton. Below the soliton-antisoliton threshold there are a large number of further states. They can be viewed either as soliton-antisoliton bound states or as bound states of $n$ of the usual quanta of the theory. The "elementary particle" $\ensuremath{\varphi}$ is the lowest of these. As the coupling increases, the higher states successively unbind, decaying into soliton-antisoliton pairs. At $\frac{\ensuremath{\lambda}}{{m}^{2}}=4\ensuremath{\pi}$, the "elementary particle" unbinds leaving only solitons and antisolitons for $\frac{\ensuremath{\lambda}}{{m}^{2}}g4\ensuremath{\pi}$. Comparing our semiclassical results with recent exact results of Coleman and with perturbation theory, we find that the semiclassical calculations are exact. This field theory seems similar to the hydrogen atom for which the Bohr-Sommerfeld quantization rules give the energy levels exactly. We also treat a ${\ensuremath{\varphi}}^{4}$ theory in weak coupling and carry out a number of calculations which provide nontrivial illustrations of the semiclassical method.

Particle spectrum in model field theories from semiclassical functional integral techniques

Starting with the modern developments of current algebra and the hypothesis of partially conserved axial-vector current, it has gradually become apparent that the strong interactions are almost invariant under the group $\mathrm{SU}(3)\ensuremath{\bigotimes}\mathrm{SU}(3)$. In the limit that symmetry breaking is neglected, $\mathrm{SU}(3)\ensuremath{\bigotimes}\mathrm{SU}(3)$ does not appear as a symmetry of the particle states as $\mathrm{SU}(3)$ does, but rather as a symmetry realized by eight Goldstone bosons, i.e., the pseudoscalar octet. Most papers on $\mathrm{SU}(3)\ensuremath{\bigotimes}\mathrm{SU}(3)$ symmetry have been concerned with soft-meson theorems and their connection with effective Lagrangians. This paper is devoted to other aspects of the symmetry. Part of the paper is frankly pedagogical. The physics behind a symmetry realized by way of Goldstone bosons is brought out through a study of the $\ensuremath{\sigma}$ model. Then the general principles are stated abstractly and applied to the hadrons. One of the new results presented here is that there are two distinct ways in which $\mathrm{SU}(3)\ensuremath{\bigotimes}\mathrm{SU}(3)$ can be realized. In both cases there is an octet of massless pseudoscalar mesons. The two possibilities differ in the residual symmetry of the hadron spectrum: In one case, it is only $\mathrm{SU}(3)$; in the other, it is $\mathrm{SU}(3)$ times a discrete symmetry, which leads to parity doublets. It is conjectured that some of the observed parity doubling in nucleon resonances is a consequence of this new discrete symmetry. Symmetry breaking is discussed in detail and is found to be very complex. In particular, it is shown that, at least for the pseudoscalar-meson masses, octet enhancement can never occur for first-order perturbations around an $\mathrm{SU}(3)\ensuremath{\bigotimes}\mathrm{SU}(3)$-symmetrical limit. Since octet enhancement is an empirical fact, one is forced to conclude that lowest-order perturbation theory is not a good approximation. In connection with octet enhancement, we show how one can use a principle of pole dominance in the angular momentum plane to replace scalar "tadpole" mesons with Regge trajectories.

Chiral SU ( 3 ) ⊗ SU ( 3 ) as a Symmetry of the Strong Interactions

We have formulated the statistical mechanics in terms of the $S$ matrix, which describes the scattering processes taking place in the thermodynamical system of interest. Such a formulation is necessary for studying the systems whose microscopic constituents behave according to the laws of relativistic quantum mechanics. Our result is a simple prescription for calculating the grand canonical potential of any gaseous system given the free-particle energies and $S$-matrix elements. When applied to a nonrelativistic gas, it gives a simple prescription for calculating all virial coefficients. Simplified relativistic gas models are considered as examples of application. A general form of the Levinson's Theorem for any number of particles follows immediately from our formalism. Its applications in statistical mechanics are briefly discussed.

Roger Dashen

Papers

The structure of the gauge theory vacuum

Toward a Theory of the Strong Interactions

Particle spectrum in model field theories from semiclassical functional integral techniques

Chiral SU ( 3 ) ⊗ SU ( 3 ) as a Symmetry of the Strong Interactions

S Matrix formulation of statistical mechanics