Galilei-invariant equations for massless fields are obtained via contractions of relativistic wave equations. It is shown that the collection of non-equivalent Galilei-invariant wave equations for massless fields with spin equal 1 and 0 is very reach and corresponds to various contractions of the representations of the Lorentz group to those of the Galilei one. It describes many physically consistent systems, e.g., those of electromagnetic fields in various media or Galilean Chern-Simon models. Finally, classification of all linear and a big group of non-linear Galilei-invariant equations for massless fields is presented.
Recently, a rich variety of the micro-phenomena of the superfluid passing an obstacle has been observed in the binary mixture of rotating Bose--Einstein condensates (BECs). Among such phenomena, the interaction of dark--bright solitons is one of the most important issues. In this work we investigate the semi-classical limit for a coupled system of Gross--Pitaevskii (GP) equations with rotating fields and trap potentials in a two-dimensional exterior domain, where the superfluid is non-vanishing at infinity. We establish a new Galilean type transformation and follow the argument of the modulate…
We study a class of Galilean-invariant one-dimensional Bethe ansatz solvable models in the thermodynamic limit. Their rapidity distribution obeys an integral equation with a difference kernel over a finite interval, which does not admit a closed-form solution. We develop a general formalism enabling one to study the moments of the rapidity distribution, showing that they satisfy a difference-differential equation. The derived equation is explicitly analyzed in the case of the Lieb-Liniger model and the moments are analytically calculated. In addition, we obtained the exact information about th…
An off-shell conformally invariant Galilean Weyl tensor
ens de Lyon, cral umr5574 , Université Claude Bernard Lyon 1, cnrs（里昂师范学院，CRAL UMR5574，克洛德·贝尔纳里昂大学，法国国家科学研究中心）；Institute of Theoretical Physics, Leibniz University Hannover（汉诺威莱布尼茨大学理论物理研究所）；Faculty of Philosophy, University of Oxford（牛津大学哲学系）
Exploring the concept of the extended Galilei group $\mathcal{G}$, a representation for the symplectic quantum mechanics in the manifold of $\mathcal{G}$, written in the light-cone of a five-dimensional De Sitter space-time, is derived consistently with the method of the Wigner function. A Hilbert space is constructed endowed with a simplectic structure, studying unitary operators describing rotations and translations, whose generators satisfy the Lie algebra of $\mathcal {G}$. This representation gives rise to the Schrödinger (Klein-Gordon-like) equation for the wave functions in phase-space,…
In this work, we derive from first principles the relativistic wave equation of massless particles of arbitrary helicity. We start from unitary projective irreducible representations of the restricted Poincaré group. We define a weaker notion of localization and find, in particular, a position operator for any massless particle of arbitrary helicity. Therefore, having the position representation for these particles, we obtain the wave equations in this representation. We compare our results with previous findings in the literature.
