University of Birmingham > Talks@bham > Theoretical Physics Journal Club and Group Meeting > An exact power series representation of the Baker-Campbell-Hausdorff formula

An exact power series representation of the Baker-Campbell-Hausdorff formula

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  • UserJordan Moodie - University of Birmingham
  • ClockMonday 09 April 2018, 12:00-13:00
  • HouseTheory Library.

If you have a question about this talk, please contact Manjinder Kainth.

The Baker-Campbell-Hausdorff formula is well known and given by Z = log(eX eY) = X + Y + 12 [X,Y] + 112[X,[X,Y] + 112[Y,[Y,X]] + ... , where it is not obvious what the dots represent. Considering the symmetric form of this formula, namely S(A,B) = log( eA2 eB eA2 ), we find an exact power series representation in the matrix B. We find closed form A-dependent coefficients in the form of hyperbolic functions for all orders of B. Each of these coefficients represent an infinite number of terms in the original expansion, making truncation of the series much more controllable for small B but arbitrary A.

This talk is part of the Theoretical Physics Journal Club and Group Meeting series.

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