Travelling waves and a fruitful `time' reparametrization in relativistic electrodynamics

We simplify the nonlinear equations of motion of charged particles in an external electromagnetic field that is the sum of a plane travelling wave F_t(ct-z) and a static part F_s(x,y,z): by adopting the light-like coordinate ct-z instead of time t as an independent variable in the Action, Lagrangian and Hamiltonian, and deriving the new Euler-Lagrange and Hamilton equations accordingly, we make the unknown z(t) disappear from the argument of F_t. We study and solve first the single particle equations in few significant cases of extreme accelerations. In particular we obtain a rigorous formulation of a Lawson-Woodward-type (no-final-acceleration) theorem and a compact derivation of cyclotron autoresonance, beside new solutions in the presence of uniform F_s. We then extend our method to plasmas in hydrodynamic conditions and apply it to plane problems: the system of partial differential equations may be partially solved and sometimes even completely reduced to a family of decoupled systems of ordinary ones; this occurs e.g. with the impact of the travelling wave on a vacuum-plasma interface (what may produce the slingshot effect). Since Fourier analysis plays no role in our general framework, the method can be applied to all kind of travelling waves, ranging from almost monochromatic to socalled "impulses", which contain few, one or even no complete cycle.Comment: Latex file, 35 pages, 6 figures. Final version to appear in J. Phys. A: Math. Theo

Noncommutative spaces with twisted symmetries and second quantization

In a minimalistic view, the use of noncommutative coordinates can be seen just as a way to better express non-local interactions of a special kind: 1-particle solutions (wavefunctions) of the equation of motion in the presence of an external field may look simpler as functions of noncommutative coordinates. It turns out that also the wave-mechanical description of a system of n such bosons/fermions and its second quantization is simplified if we translate them in terms of their deformed counterparts. The latter are obtained by a general twist-induced *-deformation procedure which deforms in a coordinated way not just the spacetime algebra, but the larger algebra generated by any number n of copies of the spacetime coordinates and by the particle creation and annihilation operators. On the deformed algebra the action of the original spacetime transformations looks twisted. In a non-conservative view, we thus obtain a twisted covariant framework for QFT on the corresponding noncommutative spacetime consistent with quantum mechanical axioms and Bose-Fermi statistics. One distinguishing feature is that the field commutation relations remain of the type "field (anti)commutator=a distribution". We illustrate the results by choosing as examples interacting non-relativistic and free relativistic QFT on Moyal space(time)s.Comment: Latex file 16 pages. Talk given at the conference "Noncommutative Structures in Mathematics and Physics" (Satellite Conference to the 5th European Congress of Mathematics), Brussels 22-26/7/2008. Appeared in the Proceedings, Ed. S. Caenepeel, J. Fuchs, S. Gutt, C. Schweigert, A. Stolin, F. Van Oystaeyen, Royal Flemish Academy of Belgium for Sciences and Arts, brussels, 2010, pp. 163-17

The q-Euclidean algebra Uq(eN)U_q(e^N) and the corresponding q-Euclidean lattice

We review the Euclidean Hopf algebra $U_q(e^N)$ dual of Fun(\rn_q^N\lcross SO_{q^{-1}}(N)) and describe its fundamental Hilbert space representations \cite{fioeu}, which turn out to be rather simple "lattice-regularized" versions of the classical ones, in the sense that the spectra of squared momentum components are discrete and the corresponding eigenfunctions normalizable.These representations can be regarded as describing a quantum system consisting of one free particle on the quantum Euclidean space. A suitable notion of classical limit is introduced, so that we recover the classical continuous spectra and generalized (non-normalizable) eigenfunctions in that limit.Comment: 19pages, latex. transmission error correcte

The spectrum of massive excitations of 3d 3-state Potts model and universality

We consider the mass spectrum of the 3$d$ 3-state Potts model in the broken phase (a) near the second order Ising critical point in the temperature - magnetic field plane and (b) near the weakly first order transition point at zero magnetic field. In the case (a), we compare the mass spectrum with the prediction from universality of mass ratios in the 3$d$ Ising class; in the case (b), we determine a mass ratio to be compared with the corresponding one in the spectrum of screening masses of the (3+1)$d$ SU(3) pure gauge theory at finite temperature in the deconfined phase near the transition. The agreement in the comparison in the case (a) would represent a non-trivial test of validity of the conjecture of spectrum universality. A positive answer to the comparison in the case (b) would suggest the possibility to extend this conjecture to weakly first order phase transitions.Comment: 20 pages, 12 figures; uses axodraw.st

The Euclidean Hopf algebra Uq(eN)U_q(e^N) and its fundamental Hilbert space representations

We construct the Euclidean Hopf algebra $U_q(e^N)$ dual of Fun(\rn_q^N\lcross SO_{q^{-1}}(N)) by realizing it as a subalgebra of the differential algebra \DFR on the quantum Euclidean space \rn_q^N; in fact, we extend our previous realization \cite{fio4} of $U_{q^{-1}}(so(N))$ within \DFR through the introduction of q-derivatives as generators of q-translations. The fundamental Hilbert space representations of $U_q(e^N)$ turn out to be of highest weight type and rather simple `` lattice-regularized '' versions of the classical ones. The vectors of a basis of the singlet (i.e. zero-spin) irrep can be realized as normalizable functions on \rn_q^N, going to distributions in the limit $q\rightarrow 1$.Comment: 67 pages, 1 figures. Revised version: Format changed, typos amended, some citations adde

The SOq(N,R)SO_q(N,{\bf R})-Symmetric Harmonic Oscillator on the Quantum Euclidean Space RqN{\bf R}_q^N and its Hilbert Space Structure

We show that the isotropic harmonic oscillator in the ordinary euclidean space ${\bf R}^N$ ($N\ge 3$) admits a natural q-deformation into a new quantum mechanical model having a q-deformed symmetry (in the sense of quantum groups), $SO_q(N,{\bf R})$. The q-deformation is the consequence of replacing $R^N$ by ${\bf R}^N_q$ (the corresponding quantum space). This provides an example of quantum mechanics on a noncommutative geometrical space. To reach the goal, we also have to deal with a sensible definition of integration over ${\bf R}^N_q$, which we use for the definition of the scalar product of states.Comment: 55 pages, tex, to appear in the Int. J Mod. Phys. A, 1993. Revised Feb. 199

Multiwavelength perspective of AGN evolution

Discovering and studying obscured AGN at z>1-3 is important not only to complete the AGN census, but also because they can pinpoint galaxies where nuclear accretion and star-formation are coeval, and mark the onset of AGN feedback. We present the latest results on the characterization of z=1-3 galaxies selected for their high mid-infrared to optical flux ratio, showing that they are massive and strongly star-forming galaxies, and that many do host highly obscured AGN. We present a pilot program to push the search of moderately obscured AGN up to z=5-6 and discuss the perspectives of this line of research.Comment: Invited talk at the conference: X-Ray Astronomy 2009, Present Status, multiwavelength approach and future perspectives, September 2009, Bologn

On Bose-Fermi Statistics, Quantum Group Symmetry, and Second Quantization

Can one represent quantum group covariant q-commuting "creators, annihilators" $A^+_i,A^j$ as operators acting on standard bosonic/fermionic Fock spaces? We briefly address this general problem and show that the answer is positive (at least) in some simplest cases.Comment: 9 pages, latex file, no figures. Talk presented at Group2

q-Quaternions and deformed su(2) instantons on the quantum Euclidean space R_q^4

We briefly report on our recent results regarding the introduction of a notion of a q-quaternion and the construction of instanton solutions of a would-be deformed su(2) Yang-Mills theory on the corresponding SO_q(4)-covariant quantum space. As the solutions depend on some noncommuting parameters, this indicates that the moduli space of a complete theory will be a noncommutative manifold.Comment: Latex file, 13 pages. Talk given at the 4-th International Symposium "Quantum Theories and Phsysics", Varna, Bulgaria, August 2005. This is a slightly improved version of the contribution which will appear in the proceedings of the conferenc

Quantum group covariant (anti)symmetrizers, epsilon-tensors, vielbein, Hodge map and Laplacian

GL_q(N)- and SO_q(N)-covariant deformations of the completely symmetric/antisymmetric projectors with an arbitrary number of indices are explicitly constructed as polynomials in the braid matrices. The precise relation between the completely antisymmetric projectors and the completely antisymmetric tensor is determined. Adopting the GL_q(N)- and SO_q(N)-covariant differential calculi on the corresponding quantum group covariant noncommutative spaces C_q^N, R_q^N, we introduce a generalized notion of vielbein basis (or "frame"), based on differential-operator-valued 1-forms. We then give a thorough definition of a SO_q(N)-covariant R_q^N-bilinear Hodge map acting on the bimodule of differential forms on R_q^N, introduce the exterior coderivative and show that the Laplacian acts on differential forms exactly as in the undeformed case, namely it acts on each component as it does on functions.Comment: latex file, 24 pages. Some citations added and misprints corrected. Final version to appear in J. Phys. A Math. and Ge