[en] For local variational systems (like a charged particle in the field of a Dirac monopole) a quantum mechanically well-defined action (Q.M.W.D.A.) can be introduced if the system is prequantizable in the Kostant-Souriau sense. If the configuration space is multiply connected (as in the Bohm-Aharonov experiment), different expressions for the classical action may emerge; they are quantum mechanically equivalent (Q.M.E.) if the corresponding prequantizations are equivalent. In both cases the situation depends on the behaviour of the non integrable phase factor of Wu and Yang

[en] The phase of the wave function scattered by an Aharonov-Bohm solenoid containing the quantized flux (h/e).n where n is an integer is shown to be (-1)sup(n) times that of the free one. A two-solenoid experiment is proposed to observe the difference between the cases when n is even or odd

[en] The Landau problem is discussed in two similar but still different non-commutative frameworks. The 'standard' one, where the coupling to the gauge field is achieved using Poisson brackets, yields all Landau levels. The 'exotic' approach, where the coupling to the gauge field is achieved using the symplectic structure, only yields lowest-Landau level states, as advocated by Peierls and used in the description of the ground states of the fractional quantum Hall effect. The same reduced model also describes vortex dynamics in a superfluid ⁴He film. Remarkably, the spectrum depends crucially on the quantization scheme. The system is symmetric w.r.t. area-preserving diffeomorphisms

[en] The quantum mechanically admissible definitions of the factor exp [i/h S(γ)] -needed in Feynman's integral- are put in bijection with the prequantisations of Kostant and Souriau. The different allowed expressions of this factor -the inequivalent prequantisations- are classified in terms of algebraic topology

[en] A slight modification of Feynman's original method leads to the Maslov correction in the path integral formula of a harmonic oscillator. Caustics are treated in a direct geometry way

[en] Which gauge transformations are symmetries (in the sense of Schwarz, and Forgacs and Manton) of a given gauge field configuration. First, in topologically non-trivial gauge theories there may be an obstruction for implementing gauge transformations on the fields; next, even those which can be implemented may fail to be symmetries. For a test particle in such a background field, those gauge transformations which are symmetries generate ordinarily conserved Noether currents - one of which is the usual electric current. This sheds a new light on the problem of ''global color'' in monopole theory and explains why no conserved electric charge can be defined in general in the non-Abelian Aharonov-Bohm experiment proposed by Wu and Yang

[en] Exact time-dependent solutions of nonrelativistic noncommutative Chern-Simons gauge theory are presented in closed analytic form. They are different from (indeed orthogonal to) those discussed recently by Hadasz, Lindstroem, Rocek and von Unge. Unlike theirs, our solutions can move with an arbitrary constant velocity, and can be obtained from the previously known static solutions by the recently found 'exotic' boost symmetry

[en] Letting the mass depend on the spin-field coupling as M²=m²-(eg/2c²)F_αβS^αβ, we propose a new set of relativistic planar equations of motion for spinning anyons. Our model can accommodate any gyromagnetic ratio g and provides us with a novel version of the Bargmann-Michel-Telegdi equations in 2+1 dimensions. The system becomes singular when the field takes a critical value, and, for g≠2, the only allowed motions are those which satisfy the Hall law. For each g≠2,0 a secondary Hall effect arises also for another critical value of the field. The nonrelativistic limit of our equations yields new models which generalize our previous 'exotic' model, associated with the two-fold central extension of the planar Galilei group

[en] The topological invariants of monopoles are described for an arbitrary compact gauge group G and Higgs field PHI in any representation. The results generalize those obtained recently for compact and simply connected G and PHI in the adjoint representation. The cases when the residual symmetry group is H=U(1) or H=U(3) are worked out explicitly. This latter is needed to accomodate fractional electric charge with monopoles having one Dirac unit magnetic charge. The general theory is illustrated on the SU(5) monopole

[en] The topologically massive gauge theory of Deser, Jackiw and Templeton is understood from Souriau's Principle of General Covariance. The non-gauge invariant mass term corresponds to a non-trivial class in the first cohomology group of configuration space, generated by the Chern-Simons secondary characteristic class. Quantization requires this class to be integral