1) How to prove that N×N matrix integral over complex matrices Z
∫dZdZ†e−TrZZ†x1deteZ−x2deteAZ†det(1−x1eZ)det(1−x2eAZ†)
does not depend on the external Hermitian matrix
A?
x1 and
x2 are numbers. The statement is trivial for
1×1 case.
2)The same for
∫dZdZ†e−TrZZ†x1deteZ−x2deteAZ†det(1−x1eZg)det(1−x2eAZ†g)
where g - arbitrary GL(N) matrix.
This post imported from StackExchange MathOverflow at 2014-07-29 11:48 (UCT), posted by SE-user Sasha