Is the Action Always a Minimum in the Principle of Least Action?

[BookWei]

Hello, When we applying the principle of least action, we require $\delta S=0$, which corresponding to the action S being an extremum. I am just wondering why do we say that the action is a minimum instead of a maximum for a physical path? Can I use the path integral to explain this problem?
Thanks for all responses.

 

[atyy]

It's conventional terminology.

http://www.eftaylor.com/pub/Gray&TaylorAJP.pdf
When action is not least
Gray and Taylor
Am. J. Phys., Vol. 75, No. 5, May 2007

 

[Helios]

I think that long ago, when Fermat's principle of least time came about, that people so liked the idea that they asked themselves why couldn't such a thing work for mechanics. The principle of least action was then made intentionally analogous to Fermat's principle. These optical considerations would then inspire others to develop wave mechanics.

 

[sweet springs]

If S is minimum , -S is maximum and anyway the both work. Stationary is more appropriate word to say.