On Tue, Feb 3, 2015 at 1:52 PM, Francesco Bonazzi <franz.bona...@gmail.com>
wrote:

>
> On Tuesday, February 3, 2015 at 8:18:58 PM UTC+1, Aaron Meurer wrote:
>
>> Do physics applications actually use summation notation with noninteger
>> limits? If so, what convention do they use?
>>
>
> Summing over the states of fermions. But that's a convention.
>
>
>> @asmeurer. I only know they are used in summing the "half-integer" spins.
>> But i have no idea regarding the rules used.
>>
>
> Spins are usually half-integers in spacetime, but I know of some special
> cases, like propagation on waves on 2D surfaces, where one may build a
> theory with any rational spin quasi-particles, or something like that.
>
> Sometimes people with a background in mathematics get really scared when
> they see how mathematics is used in physics. The funniest I can think of is
> that multiple summations and integrals are often silently assumed to
> commute, even if they sum over to infinity.
>

But do they actually use summation convention, as if i=0.5..2.5 meant i =
0.5, 1.5, 2.5?

I guess you make a good point, in that I wouldn't completely trust it even
if they did, because I doubt physicists would have thought through all the
mathematical implications of choosing that convention, which is something
that we do need to care about.

Aaron Meurer


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