✍ Scribed by Mario Schönberg
No coin nor oath required. For personal study only.
The analysis of the commutation rules between field variables at different times, begun in the first part of this paper ~), is extended to more general cases, in connection with the Heisenberg-Pauli quantum theory of wave fields 2). This theory is discussed in connection with the wave equations of the classical field. The theory involves difficulties in the case of first order e.quations of motion. It is shown that the commutation rules between field quantities at different times can be determined by means of the commutation rules at the same time and the equations of motion, when these equations are linear .The case of second order wave equations is explicitely treated, the commutation rules for the same time being known from the Heisenberg-Pau]i theory. The study of the functions involved in the relativistic rules shows that the knowledge of these functions is equivalent to the complete solution of the wave equations, any solution being calculable by integrations involving the initial values. ,962 _V.(r, 0 Qa,(r', 0 --Q~,(r, t) _Va(r, 0 = ~aa, ~(r --r') (8) P.(r, t) P~,(r', t) --Pa,(r, t) P~(r, t) = 0 (?.(r, 0 (A,(r', 0 --(2a,(r', t) Oa(r, 0 = 0 *) The partial tunctional derivatives of a functional 0 M(u~(P') ; -~ u~(P'); u~(P'), taken with respect to the variable ua(P) is given by the formula: ~M .. M(u[3(P') +~afl~(P--P')Au; ~-~ [ufl(P ) +~a[3~(P--P )Au]; u[3(P'))--M(u~(P'); ~ ufl(P'); ;~fl(P' ~.a(P),~.,5% " ~.
📜 SIMILAR VOLUMES
We derive the relativistic field equation of the A@84 quantum field theory using the techniques of Euclidean quantum field theory. Next we derive the relativistic field equation using the techniques of renormalized perturbation theory and we show that the equations coincide.
The gauge independence of transition rates as opposed to the gauge invariance of the equations of motion and gauge dependence of operators and state vectors is critically examined and explicitly demonstrated, both in nonrelativistic quantum mechanics and quantum field theory. Time independent as wel