A lecture is given on a paper by P Kulish and L. D. Faddeev Theor. Math. Phys. 4, 153 (1970). The motivations and results are briefly described. (JFP)

Asymptotic condition and infrared divergences in quantum electrodynamics

This article is divided in five parts, the first one having nothing to do with tachyons. In fact, to prepare the ground, in part I (sect.2) we shall merely show that special relativity - even without tachyons - can be given a form such to describe both particles and antiparticles. Part II is the largest one: initially, after some historical remarks and having revisited the postulates of special relativity, we presnt a review of the elegant ''model theory'' of tachyons in two dimensions; passing then to four dimensions, we review the main results of the classical theory of tachyons that do not depend on the existence of Superluminal reference frames (or that are at least independent of the explicit form of the Superluminal Lorentz ''transformations''). In particular, we discuss how tachyons would look like, i.e. their apparent ''shape''. Last but not least, all the common causality problems are thoroughly solved, on the basis of the previously reviewed tachyon kinematics. Part III deals with tachyons in general relativity; in particular the question of the apparent Superluminal expansions in astrophysics is reviewed. Part IV shows the interesting, possible role of tachyons in elementary-particle physcis and in quantum theory. In part V, the last one, we face the (still open) problem of the Superluminal Lorentz ''transformations'' in four dimensions, by introducing, for instance, an auxiliary six-dimensional space-time, and finally present the electromagnetic theory of tachyons: a theory that can be relevant also from the ''experimental'' point of view.

Classical tachyons and possible applications

In these notes we describe an analysis of the statistics problem in quantum field theory. It has been known for some time that in two space-time dimensions there is more to the problem of statistics of local fields than Bose- or Fermi statistics [1], In three-dimensional space-time, local quantum fields obey Bose- or Fermi statistics, but “extended particles”, coupled to the vacuum by fields localized on cones, may exhibit intermediate statistics, so called O-statistics [2].

Statistics of Fields, the Yang-Baxter Equation, and the Theory of Knots and Links

Quantum electrodynamics of particles on a plane and the Chern-Simons theory

We establish a direct link between massive Ising model and arbitrary massiveN=2 supersymmetric QFT's in two dimensions. This explains why the equations which appear in the computation of spin-correlations in the non-critical Ising model are the same as those describing the geometry of vacua inN=2 theories. The tau-function appearing in the Ising model (i.e., the spin correlation function) is reinterpreted in theN=2 context as a new “index”. In special cases this new index is related to the Ray-Singer analytic torsion, and can be viewed as a generalization of that to the loop space of Kahler manifolds.

J.A. Swieca

Papers

Euclidean functional integral approach for disorder variables and kinks

Order, disorder and generalized statistics

Spin and statistics of quantum kinks

Complex masses and acausal propagation in field theory

Comments on confinement criteria