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

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• Jordan Moodie - University of Birmingham
• Monday 09 April 2018, 12:00-13:00
• Theory 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(e^X e^Y) = X + Y + ¹⁄₂ [X,Y] + ¹⁄₁₂[X,[X,Y] + ¹⁄₁₂[Y,[Y,X]] + ... , where it is not obvious what the dots represent. Considering the symmetric form of this formula, namely S(A,B) = log( e^A⁄₂ e^B e^A⁄₂ ), 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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