PRECISELY PREDICTABLE DIRAC OBSERVABLES
CHAPTER (1 0 1) ??/?T + IH? = 0 , WITH THE “DIRAC HAMILTONIAN” (1 0 2) H = J THIS IMPOSES THE CONDITIONS (1 0 3) ?J?L + ?L?J = 2?JL , ?J? + ??J = 0 , ?2 = ON THE “DIRAC MATRICES” ?J, ? WHICH OTHERWISE MAY BE ARBITRARILY CHOSEN OUR POTENTIALS WILL BE ASSUMED AS C?-FUNCTIONS, AND (NORMALLY) INDEPENDENT OF TIME 1THE PHYSICAL CONSTANTS USUALLY FOUND IN THE DIRAC HAMILTONIAN HAVE BEEN ABSORBED BY CHOOS- ING PROPER UNITS: THE UNIT OF LENGHT IS THE COMPTON WAVE LENGTH OF THE ELECTRON ?/MC ? 3 861 × 10?13M THE UNIT OF TIME IS ?/MC2 ?1 287 × 10?21SEC THE UNIT OF ENERGY IS MC2 ?0 5MEV THIS WILL MAKE C = M = ?= E = 1 FURTHERMORE, WE MUST CHOOSE UNITS OF ELECTROMAGNETIC ?ELD STRENGHT TO ABSORB THE FACTOR E - RATHER |E| - THE ELEMENTARY CHARGE (WHILE E (OF COURSE) COUNTS AS A NEGATIVE CHARGE) NOTE THAT, WITH THESE UNITS, WE GET E = ?GRAD V ?A|T , B =CURL A AS ELECTROSTATIC AND MAGNETIC ?ELD STRENGTH, RESP ALSO, FOR THE COULOMB POTENTIAL WE GET V (X) = ? CF |X| WITH THE ?NE STRUCTURE CONSTANT CF ? 137