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location State College, PA
age 28
visits member for 1 year, 7 months
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I am a graduate student at the Physics department in Pennsylvania State University. I am a budding theoretical physicist with interests in application of representation theory in physics, supersymmetry, string theory and supersymmetric conformal field theories in general.


Jul
8
comment Defining the Moyal Product in Mathematica
@Jens Thanks a lot for the fix. It helps a lot!
Jul
8
comment Defining the Moyal Product in Mathematica
@Jens I was worried about those issues but the fact that MMA 8 seems to give the right results makes me wonder if these ConditionalExpressions are meaningful. Also I am doing the integration away from the pole i.e. x>0 so x^-n is well defined in which case integrals should give the correct expressions. Is that not correct?
Jul
8
comment Defining the Moyal Product in Mathematica
@Jens The MMA support guys replied and confirmed that it is a problem with the Integrate because it generates some ConditionalExpression which doesn't let it integrate. This is actually not polar coordinates but a type of nonlinear realization of noncompact Lie algebras which includes 1/x and 1/x^2 type terms. I am trying to see if the algebra defined by these nonlinear generators that closes under normal Lie bracket will also close under star bracket. Hence I need to use the star product between x and p normalized such that their star bracket is 1. I am not sure if x,p are correct variables.
Jul
8
comment Defining the Moyal Product in Mathematica
@Jens I reported the problem to Mathematica. However I am still getting the buggy behavior in 9.0.1. It does run fine on 8.0.4 as you mentioned.
Jul
7
comment Defining the Moyal Product in Mathematica
I get the correct result from star[(x + a)^-2, p] /. a :> 0.
Jul
7
comment Defining the Moyal Product in Mathematica
I am using Mathematica 9 and I set $Assumptions={x>0} at the beginning of the code as well. I tried quitting the kernel (and restarting MMA) and it still gives me the same results. Strange.
Jul
7
comment Defining the Moyal Product in Mathematica
Using the Fourier transform code, I tried to compute star[1/x,p] with Assumptions x>0 and it gives the correct answer but with star[1/x^2,p] I get FourierTransform[-2 I E^(1/2 I (kg lf - kf lg)) kf \[Pi]^2 DiracDelta[kg] DiracDelta[lf] Sign[kf] Derivative[1][DiracDelta][lg], {kf, lf, kg, lg}, {x, p, x, p}] whereas star[p,1/x^2] gives the correct answer. How can this be fixed?
Jul
2
awarded  Curious
Jun
30
awarded  Popular Question
Jan
7
accepted Memory leak issues
Jan
7
comment Memory leak issues
@Daniel The distributive rule didn't work till I put it at the top of the list in 'canonicalizeRules'. Could you tell me what caused that?
Jan
7
comment Memory leak issues
@DanielLichtblau I think there is some extra stuff in the canonicalizeRules2 definition. I tried to use your modifications to see the results but the product is not behaving distributively. Its strange because the answer that you computed for Cas2b is correct and same as what I had gotten previously. I exactly copied your rules but still I don't know what's going wrong in my notebook.
Jan
6
revised Memory leak issues
edited body
Jan
6
comment Memory leak issues
Jacob, I just noticed the changes and was in the process of changing things. It should be fine now.
Jan
6
revised Memory leak issues
edited body
Jan
6
comment Memory leak issues
Jacob, I agree this is neater looking and more efficient. I will replace this in my code on pastebin.
Jan
6
comment Memory leak issues
Jacob, I missed your updates before I posted my comments. I did try Block and everything went same as with Module. So I am not exactly sure what is the main difference in Block vs Module in this context.
Jan
6
revised Memory leak issues
added 94 characters in body
Jan
6
comment Memory leak issues
The suggestion that you made to use With and some other modifications does not work exactly how I want because of the way timesRules are written for now. I think you are right about NonCommutativeMultiply[] not getting replaced by 1 and I had made some quickfix to that by implementing CRule that I defined in the aliasing section.
Jan
6
comment Memory leak issues
I am putting a working example of my code on pastebin. The aliasing with CenterDot was meant to make input/output a little more intuitive (especially for my advisor who also likes to "play" around with the code).