Review of spin operators, Pauli matrices, and Pauli matrix identities. Reading: Review your old notes and texts on spin and Pauli matrices. Lecture 2: January 9, 2020. The five quantum operator identities: (i) Leibnitz, (ii) Hadamard, (iii) Baker-Campbell-Hausdorff, (iv) exponential reordering (braiding) and (v) exponential disentangling.
Motivated by the importance of the Campbell, Baker, Hausdorff, Dynkin Theorem in many different branches of Mathematics and Physics (Lie group-Lie algebra theory, linear PDEs, Quantum and Statistical Mechanics, Numerical Analysis, Theoretical Physics, Control Theory, sub-Riemannian Geometry), this monograph is intended to: fully enable readers (graduates or specialists, mathematicians ...
A Baker-Campbell-Hausdorff relation is derived which expresses the group parameters of the product (written as an exponential) in terms of the parameters of the exponential factors. This requires the eigenvalues of three.N N/matrices.
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