PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

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
Abstract:
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

Room Number:MB106
Date:02 / 03 / 2009
Time:05:00pm - 06:00pm