Question: Grassmannians in the Physics package

January 03 2014 John Fredsted 1259

1

In order to get a little acquainted with the Grassmannian capabilities of the Physics package, I presently consider the following simple setup:

with(Physics):
Setup(
   mathematicalnotation = true,
   anticommutativepre   = theta
):
A := Matrix(2,(i,j) -> theta||i||j);
B := A . A;
C := Expand(B);

producing for A, B, and C the following results:

To me the [2,2]-entry of B seems erroneous: the first addend has the wrong ordering of the theta's, or, equivalently, the wrong sign. Not so surprisingly, this error is then present also in the [2,2]-entry of C. But in C, the [1,2]- and [2,1]-entries seem erroneous as well: the sign of theta11 in the [1,2]-entry is wrong, and so, too, is the sign of theta22 in the [2,1]-entry.

Have I fundamentally misunderstood something?

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