Naturally light Dirac neutrinos in gauge theories

Motivated by recent experimental results, we discuss the possibility of generating small Dirac neutrino masses in a natural way. We give a mechanism based on symmetry arguments which works in the SU(2) × U(1) and SU(5) models, but fails in left-right symmetric theories. We conclude that in these models Dirac masses can only be made small by a fine tuning.     

Virtual black holes in generalized dilaton theories

The virtual black hole phenomenon, which has been observed previously in specific models, is established for generic 2D dilaton gravity theories with scalar matter. The ensuing effective line element can become asymptotically flat only for two classes of models; among them spherically reduced theories and the string inspired dilaton black hole. We present simple expressions for the lowest order scalar field vertices of the effective theory which one obtains after integrating out geometry exactly. Treating the boundary in a natural and simple way, asymptotic states, tree-level vertices and the tree-level S-matrix are conformally invariant. Examples are provided pinpointing the physical consequences of virtual black holes on the (CPT-invariant) S-matrix for gravitational scattering of scalar particles. For minimally coupled scalars the evaluation of the S-matrix in closed form is straightforward. For a class of theories including the string inspired dilation black hole all tree-graph vertices vanish, which explains the particular simplicity of that model and at the same time shows yet another essential difference to the Schwarzschild case.Received: 7 August 2002, Revised: 2 June 2003, Published online: 11 July 2003D.V. Vassilevich: On leave from V. Fock Institute of Physics, St. Petersburg University, 198904 St. Petersburg, Russia     

The problems in quantum foundations in the light of gauge theories

We review the issues of nonseparability and seemingly acausal propagation of information in EPR, as displayed by experiments and the failure of Bell's inequalities. We show that global effects are in the very nature of the geometric structure of modern physical theories, occurring even at the classical level. The Aharonov-Bohm effect, magnetic monopoles, instantons, etc. result from the topology and homotopy features of the fiber bundle manifolds of gauge theories. The conservation of probabilities, a supposedly highly quantum effect, is also achieved through global geometry equations. The EPR observables all fit in such geometries, and space-time is a truncated representation and is not the correct arena for their understanding. Relativistic quantum field theory represents the global action of the measurement operators as the zero-momentum (and therefore spatially infinitely spread) limit of their wave functions (form factors). We also analyze the collapse of the state vector as a case of spontaneous symmetry breakdown in the apparatus-observed state interaction.Work supported in part by U.S. DOE Grant DE-FG05-85ER40200.Wolfson Chair Extraordinary in Theoretical Physics, TAUP N-161-85.     

Nonconservation of gauge singlet charge operators in light cone field theories

A light cone gauge theory is considered which possesses one or more conserved currents. It is shown quite generally that the usual associated charge operator is not conserved whenever the current transforms as a vector in Minkowski space. This includes the case of a conserved current which is a singlet under the operations of any group associated with a coupling to a non-abelian gauge field. As one application of this result one infers that there are no conserved flavor charge operators in the light cone formulation of quantum chromodynamics.     

Charges in gauge theories

In this article we investigate charged particles in gauge theories. After reviewing the physical and theoretical problems, a method to construct charged particles is presented. Explicit solutions are found in the abelian theory and a physical interpretation is given. These solutions and our interpretation of these variables as the true degrees of freedom for charged particles, are then tested in the perturbative domain and are demonstrated to yield infra-red finite, on-shell Green’s functions at all orders of perturbation theory. The extension to collinear divergences is studied and it is shown that this method applies to the case of massless charged particles. The application of these constructions to the charged sectors of the standard model is reviewed and we conclude with a discussion of the successes achieved so far in this programme and a list of open questions. An erratum to this article is available at .     

Potentials of pointlike particles in gauge theory with a dilaton

I examine the potential of a pointlike particle carrying SU (N _c) charge in a gauge theory with a dilaton. The potential depends on boundary conditions imposed on the dilaton: For a dilaton that vanishes at infinity the resulting potential is a regulatized Coulomb potential of the form (r+r _ϕ)⁻¹, withr _ϕ, inversely proportional to the decay constant of the dilaton. Another natural constraint on the dialaton ϕ is independence of (1/g ²) exp(ϕ/f_ϕ) from the gauge couplingg. This requirement yields a confining potential proportional tor.     

Non-abelian gauge couplings in thermal gauge field theories

Properties of the effective gauge couplings renormalized at finite temperature and density in thermal non-abelian gauge field theories are studied within one-loop approximations. Strong and severe vertex dependence is shown to come out both in the temperature and chemical potential dependences. Difficulties appearing in the perturbative calculation of physical quantities, indicated by the above disaster, are discussed. Also discussed is what insight might be gained from the present analysis into the “magnetic” screening of effective charge.     

Phase transition in gauge theories

In this short review we present the consequences of the spontaneously broken gauge theories will lead to when describing matter at high temperature and density. It appears various phase transitions should occur leading to the restoration of symmetry at high temperature of the originally broken one. Symmetry behaviour in external magnetic fields and in the early universe has been briefly mentioned.     

Electric-charge quantization in gauge theories

The electric-charge quantization and fixing conditions of particles are found using a number of gauge theories, and it is shown that the presence of Higgs fields is a necessary condition for the electric-charge quantization in the considered models.     

Physical variables in gauge theories

The symplectic method is applied to obtain the physical variables and the physical Hamiltonian in two examples of gauge theories: the electrodynamics in the Coulomb gauge and the two-dimensional bosonic Schwinger model.     

Vacuum stability in gauge theories

The vacuum behaviour in a quantum SU(2) gauge theory is investigated by calculating the one-loop contributions to the effective action in a covariant constant background field. It is found that the vacuum is stable against decay, for a particular nonzero value of the electric field, indicating a dynamical symmetry breaking.     

Quadratic divergences in gauge theories

Quadratic divergences are analysed using dimensional regularisation in gauge theories in general and the standard model in particular. We give a prediction (under dubious assumptions) thatm _t ≈115 GeV andm _H ≈180 GeV.     

Tumbling in two-dimensional gauge theories

The ideas of tumbling and most attractive channel condensation are confronted in two-dimensional chiral gauge theories. We first demonstrate how to perform a gauge-invariant regularization. We then proceed to find exact results about the spectra in both abelian and non-abelian cases. These conflict with the predictions of tumbling and MAC.     

Quark fragmentation in gauge theories

A theory of quark fragmentation is based on the phenomenon of spontaneous pair creation in a strong Coulomb field, applied to the color field surrounding the leading quarks.     

Soliton quantization in gauge theories

We study the quantization of the SO₃ gauge theory which possesses the 't Hooft-Polyakov monopole as a classical solution. The one-monopole sector of this model is constructed in lowest-order perturbation theory, with \(\sqrt \hbar \) as expansion parameter. Explicit expressions for the fields are given and their properties discussed. We use a manifestly covariant formalism.     

Space-time symmetries in gauge theories

A general definition of symmetries of gauge fields is proposed and a method developed for constructing symmetric fields for an arbitrary gauge group. Scalar fields occur naturally in the formalism and the pure gauge theory reduces to a Higgs model in lower dimensions.Laboratoire propre du C.N.R.S. associé à l'Ecole Normale Supérieure et à l'Université de Paris Sud