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A mathematical construct quantifying the difference in effect of applying two operators in two alternate successions. It is the defining product of a Lie algebra, the efficient underlying description of Lie groups, of use in several areas of physics, most notably quantum field theory.

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Looking at equation 10.191, 10.192 was just the operator multiplication and taking the expectation value, and equation 10.191 was given and derived from the previous cases.
answered May 24 by user9976437