In the present paper, we study rotational surfaces in the three dimensional pseudo-Galilean space G3. Also, we classify linear Weingarten rotational surfaces in G3. A linear Weingarten surface is the surface having a linear equation between the Gaussian curvature and the mean curvature of a surface. In last section, we construct isotropic rotational surfaces in G3 with prescribed mean curvature...

The Souriau massless Galilean particle of “colour” k and spin s is shown to be the Galilean limit of the Souriau tachyon of mass m = ik and spin s. We compare and contrast this result with the Galilean limit of the Nambu-Goto string and GreenSchwarz superstring.

Galilean invariance is a fundamental property; however, although the lattice Boltzmann equation itself is Galilean invariant, this property is usually not taken into account in the treatment of the fluid-solid interface. Here, we show that consideration of Galilean invariance in fluid-solid interfacial dynamics can greatly enhance the computational accuracy and robustness in a numerical simulat...

The six-dimensional exotic Galilean algebra in (2+1) dimensions with two central charges m and θ, is extended when m = 0, to a tendimensional Galilean conformal algebra with dilatation, expansion, two acceleration generators and the central charge θ. A realisation of such a symmetry is provided by a model with higher derivatives recently discussed in [1]. We consider also a realisation of the G...

This paper undertakes a study of the nature of the force associated with the local U (1) gauge symmetry of a non-relativistic quantum particle. To ensure invariance under local U (1) symmetry, a matter field must couple to a gauge field. We show that such a gauge field necessarily satisfies Maxwell's equations, whether the matter field coupled to it is relativistic or non-relativistic. This res...

This article examines the relationship between geometric Poisson brackets and integrable systems in flat Galilean, and Lorentz manifolds. First, moving frames are used to calculate differential invariants of curves and to write invariant evolution equations. The moving frames are created to ensure that the Galilean moving frame is the limit of the Lorentz one as c → ∞. Then, associated integrab...

We construct a Galilean invariant non-gravitational closed string theory whose excitations satisfy a non-relativistic dispersion relation. This theory can be obtained by taking a consistent low energy limit of any of the conventional string theories, including the heterotic string. We give a finite first order worldsheet Hamiltonian for this theory and show that this string theory has a sensibl...

We argue that correct account of the quantum properties of macroscopic objects which form reference frames (RF) demand the change of the standard space-time picture accepted in Quantum Mechanics. Galilean or Lorentz space-time transformations are shown to become incorrect in this case and for the description of transformations between different RF the special quantum space-time transformations ...