Henri Poincaré formulated the mathematics of Lorentz transformations, known as the Poincaré group. He also formulated the Poincaré sphere for polarization optics. It is shown that these two mathematical instruments can be derived from the two-by-two representations of the Lorentz group. Wigner’s little groups for internal space-time symmetries are studied in detail. While the particle mass is a...

A great advance in physics came when it was realized that it was better to think about motion in empty space rather than starting with what happen in the “real world” with gravity pulling things downwards, friction slowing things down, etc. First, that the laws of physics should be the same at one point as at another, i.e. that they are translation invariant, and also from one day to another, i...

A great advance in physics came when it was realized that it was better to think about motion in empty space rather than starting with what happen in the “real world” with gravity pulling things downwards, friction slowing things down, etc. First, that the laws of physics should be the same at one point as at another, i.e. that they are translation invariant, and also from one day to another, i...

Mesonic baryon resonance decays are calclulated from constituent quark models along a Poincaré-invariant generalization of the elementary emission model. Covariant results of pionic decay widths are presented for the Goldstone-boson-exchange constituent quark model.

A new fully numerical method is presented which employs multiple Poincaré sections to find quasiperiodic orbits of the Restricted Three-Body Problem (RTBP). The main advantages of this method are the small overhead cost of programming and very fast execution times, robust behavior near chaotic regions that leads to full convergence for given family of quasiperiodic orbits and the minimal memory...

Abstract. Linear statistics of eigenvalues in many familiar classes of random matrices are known to obey gaussian central limit theorems. The proofs of such results are usually rather difficult, involving hard computations specific to the model in question. In this article we attempt to formulate a unified technique for deriving such results via relatively soft arguments. In the process, we int...

A great advance in physics came when it was realized that it was better to think about motion in empty space rather than starting with what happen in the “real world” with gravity pulling things downwards, friction slowing things down, etc. First, that the laws of physics should be the same at one point as at another, i.e. that they are translation invariant, and also from one day to another, i...

This paper provides a complete list of Krajewski diagrams representing the standard model of particle physics. We will give the possible representations of the algebra and the anomaly free lifts which provide the representation of the standard model gauge group on the fermionic Hilbert space. The algebra representations following from the Krajewski diagrams are not complete in the sense that th...