Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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|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.