sci.physics.research

On Feb 25, 2:03 pm, Ilja Schmelzer <...@>
wrote:
> On 23 Feb., 14:00, lek...@ wrote:
>
> > Sachs often refers to an "equal time commutation
> > relation." I remember studying commutation relations in Bransden &
> > Joachain's textbook when I took quantum mechanics, but I do not recall
> > any mention of 'equal time' commutation relations.
>
> > If any one could give me a quick definition of this form of
> > commutation relations, I would greatly appreciate it.
>
> You choose some system of coordinates, with a time coordinate t. You
> are in the Heisenberg picture, thus, your operators depend on t. Then,
> the commutation relations between operators with the same t are the
> equal time commutation relations. That's all.

It's a little more involved than that. One cannot maintain causality
unless the commutation relations for fields are imposed on a spacelike
initial hypersurface. The simplest such is t=const. in a given
referent.

-drl