Canonical quantization promotes Poisson brackets in classical mechanics to commutators in quantum mechanics. Is there any classical counterpart similar to the Poisson bracket for the anticommutator?


FWIW, in classical Hamiltonian formalism, the phase space is a supermanifold with a super-Poisson bracket $\{\cdot,\cdot\}_{SPB}$. The super-Poisson bracket corresponds to a super-commutator $\frac{1}{i\hbar}[\cdot,\cdot]_{SC}$ upon quantization. The super-commutator is a commutator (an anticommutator) in the Grassmann-even (Grassmann-odd) sector, respectively.

See also my Phys.SE answer here.

  • $\begingroup$ As a person who just started learning QFT, are there some gentle introductions to supersymmetry such that I can understand your answer? $\endgroup$ – Leo L. Jan 16 '20 at 17:46

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.