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...

In this paper we derive two rigorous properties of residence-time distributions for flows in pipes and mixers motivated by computational results of Khakhar et al. [Chem. Eng. Sci. 42, 2909 (1987)], using some concepts from ergodic theory. First, a curious similarity between the isoresidence-time plots and Poincare maps of the flow observed in Khakhar et al. is resolved. It is shown that in long...

A model potential for two-particle relativistic systems is investigated in the framework of Poincare-invariant quantum mechanics (or relativistic Hamiltonian dynamics). The potential considered allows to reduce the main integro-differential equation of Poincare-invariant quantum mechanics to the equation analogous to the radial equation and have analytical solution for relativistic bound system...

Sculpting various 3D facial expressions from a static 3D face model is a process with intensive manual tuning efforts. In this paper, we present an interactive 3D facial expression posing system through 2D portrait manipulation, where a manipulated 2D portrait serves a metaphor for automatically inferring its corresponding 3D facial expression with fine details. Users either rapidly assemble a ...

The paper looks at the digital portrait used in the form of avatars in various online worlds and communication networks. It describes an ongoing modal shift from an ontological understanding of the portrait towards the portrait as performative