current of space (time)

[AntonioLao]

Excerpt page 20 of A. Seiden’s Particle Physics: A Comprehensive Introduction: If the Lagrangian is invariant under a continuous group transformation, then there exist locally conserved quantities constructed from the fields and their derivatives. These quantities, like the electric charge, flow in space-time and are described in terms of currents.

This statement applies as well to the color charges of QCD. However, gluon currents are only indirectly observed from jets in high energy accelerators. On the other hand, theoretically, these local infinitesimal currents of local infinitesimal motion (LIM) are analogous to the existence of magnetic helicities, which are gauge invariant representations of the magnetic vector potential. When the whole of space-time is arranged according to a sieve of Diophantus then every arbitrary 2 by 2 matrix has its inverse as scalar multiples of Hadamard matrices. Since time is intimately related to magnetism, without these helicities time cannot be defined at the quantum level. On the other hand, quantized helicities create the continuous group transformation of dynamic quantized metric spaces as directional invariance of Hadamard matrices.

[sharon333]

Sounds like I need to read this book.

[AntonioLao]

I searched everywhere and then I found a copy at SMU's science and mathematics library.