Aleksei V. Chechkin, Flavio Seno, Ralf Metzler, and Igor M. Sokolov Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany INFN, Padova Section, and Department of Physics and Astronomy “G. Galilei,” University of Padova, Via Marzolo 8 35131 Padova, Italy Akhiezer Institute for Theoretical Physics, Kharkov 61108, Ukraine Institute of Physics, Humboldt University Be...

We construct, for any given ` = 1 2 + N0, second-order nonlinear partial differential equations (PDEs) which are invariant under the transformations generated by the centrally extended conformal Galilei algebras. This is done for a particular realization of the algebras obtained by coset construction and we employ the standard Lie point symmetry technique for the construction of PDEs. It is obs...

Four hundred years ago Galileo Galilei aimed a telescope at the sky. He revolutionized astronomy. Equally revolutionary were his experiments in physics. Unlike his astronomical observations the experiments remain difficult to understand and replicate even today. Two centuries after Galileo, Augustin Coulomb demonstrated experimentally the law of electrostatic force. It has never been successful...

Quantum Mechanics in the non-commutative plane is shown to admit the “exotic” symmetry of the doubly-centrally-extended Galilei group. When coupled to a planar magnetic field whose strength is the inverse of the non-commutative parameter, the system becomes singular, and “Faddeev-Jackiw” reduction yields the “Chern-Simons” mechanics of Dunne, Jackiw, and Trugenberger. The reduced system moves a...

A non-relativistic plasma model endowed with an “exotic” structure associated with the two-parameter central extension of the planar Galilei group is constructed. Introducing a Chern-Simons statistical gauge field provides us with a self-consistent system; when the magnetic field takes a critical value determined by the extesion parameters, the fluid becomes incompressible and moves collectivel...

Suicide with One Cranial Gunshot by a .320 Caliber Pocket Revolver Lucia Tattoli1*, Saskia Sabrina Etzold2, Michael Tsokos2, Lars Oesterhelweg2, Sven Hartwig2 1 Section of Legal Medicine, Department of Public Health and Pediatrics, University of Turin, Corso Galileo Galilei 22, 10126, Torino, Italy 2 Institute of Legal Medicine and Forensic Sciences, University Medical Centre Charité, Universit...

Using the theory of fibre bundles, we provide several equivalent intrinsic descriptions for the Hilbert spaces of n “free” nonrelativistic and relativistic plektons in two space dimensions. These spaces carry a ray representation of the Galilei group and a unitary representation of the Poincaré group respectively. In the relativistic case we also discuss the situation where the braid group is r...

a Consiglio Nazionale delle Ricerche, Istituto di Cristallografia (IC-CNR) Campus Universitario c/o Dip.to Geomineralogico, Via Orabona 4, I-70125 Bari, Italy. E-mail [email protected]; Phone +39 080 5442624; Fax +39 080 5442591 b Università di Padova, Dipartimento di Fisica “G. Galilei” & Sez. INFM Via Marzolo 8, I-35131 Padova, Italy. E-mail [email protected]; Phone +3...

Kinematic algebras can be realised on geometric spaces and constrain the physical models that live these spaces. Different types of kinematic exist we consider interplay for non-relativistic limits a relativistic system, including both Galilei Carroll limit. We develop framework captures systematically corrections to strict limit by introducing new infinite-dimensional algebras, with emphasis c...