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seen Aug 18 '11 at 0:17

Aug
14
comment Can the following be integrated?
@mixedmath thanks. I can't seem to do it numerically because when integrating the whole thing (including extra functions of y and z) over x, y and z, mathematica can't figure out where the singularities are.
Aug
14
comment Can the following be integrated?
I don't, but sometimes an integral that looks more complicated is actually simpler, and I wanted to make sure I wasn't missing something like that.
Apr
27
comment Can you differentiate with respect to a sum?
And I'll think some more about the ordering - thank you.
Apr
27
comment Can you differentiate with respect to a sum?
@joriki Ahh so it should be $(\delta /\delta x(\tau')) Exp[\int_0^p d\tau (x(\tau) \alpha (\tau) - y(\tau) \beta (\tau))] = \alpha (\tau') Exp[\int_0^p d\tau (x(\tau) \alpha (\tau) - y(\tau) \beta (\tau))]$ ? (But possibly with the $\alpha$ after the integral rather than before).
Apr
27
comment Can you differentiate with respect to a sum?
@joriki since $x$ is in front of $\alpha$, I don't think it should matter that they're Grassmann numbers.. Should it?
Apr
27
comment Can you differentiate with respect to a sum?
@joriki I used to write the same $\tau$ for all, but have been told the way I wrote it above is the correct way since when they are all tau, it looks like you're differentiating wrt the integration variable.
Apr
27
comment Can you differentiate with respect to a sum?
And sorry, i'm not sure why I said operators! Must be a lack of sleep. I meant Grassmann numbers!
Apr
27
comment Can you differentiate with respect to a sum?
@joriki I'm not sure what you mean by that there's no need for the Integrating variables to be different...
Apr
27
comment Can you differentiate with respect to a sum?
@joriki thanks. I tried to simplify the problem to much I think. I've edited my question again to hopefully make it clearer.
Apr
26
comment Can you differentiate with respect to a sum?
$a$, $b$, $\alpha$ and $\beta$ are also operators rather than just variables. Does this make any difference?
Apr
26
comment Can you differentiate with respect to a sum?
@joriki thanks. So since what I want is to find $\alpha Exp[(5a+3b)\alpha−(3a+5b)\beta]$ (or $\alpha Exp[x\alpha−y\beta]$ is fine too), the useful meaning for me of $\partial / \partial x$ is $\partial / \partial (5a+3b)$?
Apr
26
comment Can you differentiate with respect to a sum?
@Christian thanks for your reply .. I've edited my question a bit to clarify a few things. Is it ok to label $x=5a+3b$ and $y=3a+5b$ or like J.M. said, do I need to write $3a+5b$ in terms of $x$?
Apr
26
comment Can you differentiate with respect to a sum?
Thanks @J.M. @Henry @Jim and @david. I've edited my question a bit to clarify that $a$ and $b$ are not dependent on $\alpha$ or $\beta$. So is it ok to label $x=5a+3b$ and $y=3a+5b$ or like J.M. said, do I need to write $3a+5b$ in terms of $x$?