Time Evolution of Free-Field Spatial Moments in Relativistic Quantum Mechanics: (I) Massless Case

Y. A. Kanev；K. R. Brownstein

Chinese Journal of Physics

38卷3期（2000 / 06 / 01）

405 - 414

英文

The explicit solution for the time evolution of the Nth rank spatial moment (The equation is abbreviated)(rj is the jth cartesian component of the position vector →r) of some field (the symbol is abbreviated) (→r, t) has been obtained. (the symbol is abbreviated) can be any spatially bounded massless field satisfying a first order linear (”Dirac-like”) differential equation, such as the Dirac bi-spinor, and the electromagnetic fields (→E and →B). The solution for the Nth moment is a polynomial in time of degree N. The spin of the fields affects only the coefficients of the various powers of t. The general solution to the problem has been derived by using ”Dirac-like” field equations. For that reason, in order to apply this general result to electromagnetic fields, Maxwell's equations have also been recast into ”Dirac-like” form, i.e. (The equation is abbreviated) = 0, where Gμ are four 6-by-6 matrices (analogous to the Dirac γμ matrices) and (the symbol is abbreviated) = (Ex, Ey, Ez, Bx, By, Bz)^T .