Field-theoretic extended particles in two space dimensions

A family of Lagrangian models of two scalar fields in (2 + 1) dimensions is studied. All their localized static classical solutions are obtained, and interpreted as representing systems of extended particles. The models are generalized by taking into account general-relativistic gravirational coupling, for which case the general static solutions are also obtained explicitly.     

Existence of a phase transition in reggeon field theory in two transverse dimensions

We show that a reggeon field theory, in the physical number of dimensions, with a linear bare trajectory and a constant triple-pomeron coupling, undergoes a phase transition as the bare pomeron intercept is increased through a certain critical value.     

Instantons in two and four dimensions

It is shown that Yang-Mills instantons in four dimensions can naturally be identified with the instantons of a two-dimensional theory with values in the loop group.     

Classical molecules in two dimensions

The ground-state configurations and spectrum of two parallel two-dimensional classical atoms are obtained as a function of the inter-atomic distance ( ). The classical particles are confined by parabolic potentials and repel each other through a Coulomb potential. As a function of we find several configurational transitions which are of first or second order. For first- (second-) order transitions the first (second) derivative of the energy with respect to is discontinuous, the radial position of the particles changes discontinuously (continuously) and the frequency of the eigenmodes exhibit a jump (softening of a mode). In the limit of an infinite number of electrons the Wigner bilayer system is recovered which moves through five different stable crystalline phases as a function of . For unequal strength of parabolic confinement we find that the number of configurational transitions increases.     

Quantum censorship in two dimensions

It is pointed out that increasingly attractive interactions, represented by partially concave local potential in the Lagrangian, may lead to the degeneracy of the blocked, renormalized action at the gliding cutoff scale by tree-level renormalization. A quantum counterpart of this mechanism is presented in the two-dimensional sine-Gordon model. The presence of Quantum Censorship is conjectured which makes the loop contributions pile up during the renormalization and thereby realize an approximate semiclassical effect.     

Non-translation-invariant states in two dimensions

We construct a class of models with translation-invariant interaction for which in dimension two there already exist non-periodic Gibbs states at low temperatures.     

Dilaton gravity in two dimensions

The study of general two-dimensional models of gravity allows to tackle basic questions of quantum gravity, bypassing important technical complications which make the treatment in higher dimensions difficult. As the physically important examples of spherically symmetric Black Holes, together with string inspired models, belong to this class, valuable knowledge can also be gained for these systems in the quantum case. In the last decade, new insights regarding the exact quantization of the geometric part of such theories have been obtained. They allow a systematic quantum field theoretical treatment, also in interactions with matter, without explicit introduction of a specific classical background geometry. The present review tries to assemble these results in a coherent manner, putting them at the same time into the perspective of the quite large literature on this subject.     

Critical interface in two dimensions

The interface separating two-dimensional phases close to a critical point is observed in the ferroelectric BaZr_xTi_1−xO₃ by transmission electron microscopy. The temperature dependence of the interfacial thickness is determined and compared with theoretical predictions.     

Supersymmetry anomally in two dimensions

In two dimensions we obtain a supersymmetric extension of a gauge anomaly, and find that this is the origin of a supersymmetry anomaly in the Wess-Zumino gauge. We also obtain an effective action whose variations give rise to the gauge and supersymmetry anomalies.     

Phase transitions in two dimensions

Recent developments - both theoretical and experimental - in the understanding of phase transitions in two-dimensional systems are reviewed. Topics discussed include the classification and characterization of order/disorder transitions in adsorbed monolayers, the breakdown of universality, superfluidity in helium films and the critical behaviour of the two-dimensional XY model, Abelian and non-Abelian symmetry and the analogies between the theory of phase transitions in two dimensions and quantum field theory, especially quark confinement, in four-dimensional space time.     

Inverse backscattering in two dimensions

We interpretN=2 superconformal field theories (SCFTs) formulated by Kazama and Suzuki via Goddard-Kent-Olive (GKO) construction from a viewpoint of the Lie algebra cohomology theory for the affine Lie algebra. We determine the cohomology group completely in terms of a certain subset of the affine Weyl group. We find that this subset describing the cohomology group can be obtained from its classical counterpart by the action of the Dynkin diagram automorphisms. Some algebra automorphisms of theN=2 superconformal algebra are also formulated. Utilizing the algebra automorphisms, we study the field identification problem for the branching coefficient modules in the GKO-construction. Also the structure of the Poincaré polynomial defined for eachN=2 theory is revealed.Dedicated to Professor Noboru Tanaka on his sixtieth birthday