We do a study of the real representations of the Poincare group, motivated by the following: i) the classical electromagnetic field —from which the Poincare group was originally defined— transforms as a real representation of the Poincare group; ii) the localization of complex unitary representations of the Poincare group is incompatible with causality, Poincare covariance and energy positivity...

The concept of Diff 4 invariant Poincare transformations is a cornerstone of T(opological) G(eometro)D(ynamics). This concept makes it possible to understand the concept of subjective time and irreversibelity as well as nontriviality of S-matrix at quantum level. In this paper the possibility of identifying Diff 4 invariant Poincare transformations as the recently discovered Lorentz invariant d...

Near the vicinity of 308 latitude, the coincidence of the period of sea breeze and the inertial period of the ocean leads to a maximum near-inertial ocean response to sea breeze. This produces a propagating inertial internal (Poincare) wave response that transfers energy laterally away from the coast and provides significant vertical mixing. In this paper, the latitudinal dependence of this wav...

Chaotic dynamics of a classical prey-predator-superpredator ecological model are considered. Although much is known about the behavior of the model numerically, very few results have been proven analytically. A new analytical result is obtained. It is demonstrated that there exists a subset on which a singular Poincare map generated by the model is conjugate to the shift map on two symbols. The...

It is well known that the Galilei algebra is a sub algebra of Poincare algebra in one space dimension more. 1 This fact allows us to relate relativistic Poincare and Galilean theories. An interesting point is that Galilei transformations in two space dimensions are contained in the usual Poincare transformations? This enables us to present Poincare spin zero wavefunctions as Fourier transforms ...

There are Poincare group representations on complex Hilbert spaces, like the Dirac spinor field, or real Hilbert spaces, like the electromagnetic field tensor. The Majorana spinor is an element of a 4 dimensional real vector space. The Majorana spinor field is a space-time dependent Majorana spinor, solution of the free Dirac equation. The Majorana-Fourier and Majorana-Hankel transforms of Majo...

The Poincare invariance in the temporal gauge canonical quantization of QCD is shown manifestly by verifying the energy-momentumvector and angular-momentum-tensor satisfy the Poincare algebra in the physical Hilbert space. Two different values of θ for the θ-term in QCD lagrangian lead to different representations of the Poincare group, which are, however, connected by an unitary transformation...

ECG data sequences are classical and most reliable clinical data for patients to provide complex physiological and pathological information diagnosing various heart diseases. Extracting dynamic information from ECG signal time sequences, Poincare maps have developed as classical assistant tools using two dimension maps as important basis for medical doctors to diagnose multiple cardiovascular d...