Sign up ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free.

Suppose I have a two dimensional classical Dirac Hamiltonian with $\Psi=(\psi_1,\psi_2)^T$: $$ H=\int \mathrm{d}x \mathrm{d}y \Psi^\dagger(\sigma^x i\partial_x+\sigma^y i\partial_y+m\sigma^z)\Psi. $$ The partition function is given by $$ Z=\int[\mathrm d\psi^\dagger][\mathrm d\psi]e^{-H}. $$ How can I relate it to a (1+1)-dim quantum system?

A simple replacement $x\rightarrow t$ seems to be wrong. Because in the standard (1+1)-dim Dirac action, the time derivative term must be $\Psi^\dagger\partial_\tau\Psi$, i.e. with identity matrix in front of the time derivative, to ensure the conjugate momenta of $\Psi$ is just $i\Psi^\dagger$.

share|cite|improve this question

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.