Take the 2-minute tour ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.

The Euler-Lagrange equations follow from minimizing the action. Usually this is done with fixed (e.g. vanishing) boundary conditions such that we do not have to worry about any boundary terms. However, it's also possible to obtain boundary conditions which follow from the action itself, the so-called natural boundary conditions. In terms of some Lagrangian $L$ they take on the form $$ \frac{\delta L}{\delta x'(t)}\Bigg|_{x=a} = 0 $$ or for fields $$ \frac{\delta \mathcal{L}}{\delta \partial_x\phi}\Bigg|_{x=a} = 0~. $$

These boundary conditions minimize the action for a system with variable end-points.

But what happen with these boundary conditions when we quantize the theory? Specifically, do states in the Hilbert space satisfy the natural boundary conditions automatically or is this something that needs to be imposed "by hand"?

share|improve this question
add comment

Your Answer

 
discard

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

Browse other questions tagged or ask your own question.