For more information about this meeting, contact Mary Anne Raymond.
|Title:||The Campbell-Baker-Hausdorff Formula|
|Seminar:||Slow Pitch Seminar|
|Speaker:||Nigel Higson, Penn State|
|It is fundamental to nearly everything that if a and b are numbers, then exp ( a ) exp ( b ) = exp ( a + b ) ; that is, the exponential function converts addition into multiplication. If A and B are square matrices, then the corresponding formula is false, which is not surprising since multiplication of matrices is not commutative. In its place there is the Campbell-Baker-Hausdorff formula exp ( A ) exp ( B ) = exp ( C ) , where the matrix C is the sum of a series that begins
C = A + B + 1/2[A,B] + 1/12[A,[A,B]] + 1/12[B,[B,A]] + ...
where the brackets denote commutator: [X,Y] = XY - YX . I shall prove the formula and try to explain the foundational role it plays in Lie group theory.|
Room Reservation Information
|Date:||02 / 03 / 2009|
|Time:||05:00pm - 06:00pm|