arXiv subjects
Publications and source records attributed to C. Montonen.
The validity of the tree-unitarity criterion for scattering amplitudes on the noncommutative space-time is considered, as a condition that can be used to shed light on the problem of unitarity violation in noncommutative quantum field theories when time is noncommutative. The unitarity constraints on the partial wave amplitudes in the noncommutative space-time are also derived.
Recently, developments in the understanding of low-energy N=1 supersymmetric gauge theory have revealed two important phenomena: the appearance of new four-dimensional superconformal field theories and a non-Abelian generalization of electric-magnetic duality at the IR fixed point. This report is a pedagogical introduction to these phenomena. After presenting some necessary background material, a detailed introduction to the low-energy non-perturbative dynamics of N=1 supersymmetric $SU(N_c)$ QCD is given. The emergence of new four-dimensional superconformal field theories and non-Abelian duality is explained. New non-perturbative phenomena in supersymmetric $SO(N_c)$ and $Sp(N_c=2n_c)$ gauge theories, such as the two inequivalent branches, oblique confinement and electric-magnetic-dyonic triality, are presented. Finally, some new features of these four-dimensional superconformal field theories are exhibited: the universal operator product expansion, evidence for a possible $c$-theorem in four dimensions and the critical behaviour of anomalous currents. The concluding remarks contain a brief history of electric-magnetic duality and a discussion on the possible applications of duality to ordinary QCD.
We study the thermodynamics of degenerate electron and charged vector boson gases in very intense magnetic fields. In degenerate conditions of the electron gas, the pressure transverse to the magnetic field $B$ may vanish, leading to a transverse collapse. For W-bosons an instability arises because the magnetization diverges at the critical field B_c = M_W^2/e. If the magnetic field is self-consistently maintained, the maximum value it can take is of the order of $2B_c/3$, but in any case the system becomes unstable and collapses.
We review a detailed investigation of the perturbative part of the low-energy effective action of N=2 supersymmetric Yang-Mills theory in a conventional effective field theory approach. With the restriction that the effective action should contain at most two derivatives and not more than four-fermion couplings, the features of the low-energy effective action obtained by Seiberg based on $U(1)_R$ anomaly and non-perturbative $β$-function arguments are shown to emerge.
We investigate the perturbative part of Seiberg's low-energy effective action of N=2 supersymmetric Yang-Mills theory in Wess-Zumino gauge in the conventional effective field theory technique. Using the method of constant field approximation and restricting the effective action with at most two derivatives and not more than four-fermion couplings, we show some features of the low-energy effective action given by Seiberg based on $U(1)_R$ anomaly and non-perturbative $β$-function arguments.
Renormalization in quantum statistics in the presence of a charge associated to a spontaneously broken symmetry is discussed for the scalar field model. In contrast to the case of non-broken symmetry, the renormalization mass counterterm depends on the chemical potential. We argue that this is connected to the ill-defined character of the charge operator.
We find a class of nonlocal operators constructed by attaching a disorder operator to fermionic degrees of freedom, which can be used to generate q-deformed algebras following the Schwinger approach. This class includes the recently proposed anyonic operators defined on a lattice.
The statistics of $q$-oscillators, quons and to some extent, of anyons are studied and the basic differences among these objects are pointed out. In particular, the statistical distributions for different bosonic and fermionic $q$-oscillators are found for their corresponding Fock space representations in the case when the hamiltonian is identified with the number operator. In this case and for nonrelativistic particles, the single-particle temperature Green function is defined with $q$-deformed periodicity conditions. The equations of state for nonrelativistic and ultrarelativistic bosonic $q$-gases in an arbitrary space dimension are found near Bose statistics, as well as the one for an anyonic gas near Bose and Fermi statistics. The first corrections to the second virial coefficients are also evaluated. The phenomenon of Bose-Einstein condensation in the $q$-deformed gases is also discussed.