sci.physics.research

On Aug 13, 4:38 pm, "Jay R. Yablon" wrote:
> "Igor Khavkine" wrote in message
> news: @ ...

[...examples of quantum Hamilton's principle function observables...]

> Now, how do you go from these examples to S = int_{-oo to +oo} L (t,x)
> d^4x? Is there some general rule here? Do +oo and -oo lend themselves
> to imposing boundary conditions that can give us a general answer?

To answer this question, you first need to find what is the field
theory quantity analogous to x(t) in my earlier examples. Then, follow
the steps I already outlined.

> Also, perhaps as stepping stones to answer this, permit me please to ask
> the following:
>
> 1) can you come up with a classical example that yields a discrete
> spectrum?

No, impossible. Classical observables are either constant or take on
continuous ranges of values.

> 2) can you come up with a quantum theory example that yields a discrete
> spectrum?

Not off hand.

> 3) can you articulate a general rule which will tell us when we will
> obtain a continuous spectrum and when we will obtain a discrete
> spectrum?

Not off hand.

Igor