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A-R-Q
 Post subject: Evaluate the integral (13) - Attempt Shown
PostPosted: Sat, 17 Mar 2012 18:27:14 UTC 
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What did I do wrong?
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outermeasure
 Post subject: Re: Evaluate the integral (13) - Attempt Shown
PostPosted: Sat, 17 Mar 2012 18:40:35 UTC 
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A-R-Q wrote:
What did I do wrong?
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Why do you think it is wrong?

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\begin{aligned} Spin(1)&=O(1)=\mathbb{Z}/2&\quad&\text{and}\\ Spin(2)&=U(1)=SO(2)&&\text{are obvious}\\ Spin(3)&=Sp(1)=SU(2)&&\text{by }q\mapsto(\mathop{\mathrm{Im}}\mathbb{H}\ni p\mapsto qp\bar{q})\\ Spin(4)&=Sp(1)\times Sp(1)&&\text{by }(q_1,q_2)\mapsto(\mathbb{H}\ni p\mapsto q_1p\bar{q_2})\\ Spin(5)&=Sp(2)&&\text{by }\mathbb{HP}^1\cong S^4_{round}\hookrightarrow\mathbb{R}^5\\ Spin(6)&=SU(4)&&\text{by the irrep }\Lambda_+\mathbb{C}^4 \end{aligned}
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Shadow
 Post subject: Re: Evaluate the integral (13) - Attempt Shown
PostPosted: Sun, 18 Mar 2012 01:12:05 UTC 
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Indeed, if you just want to check it, use the integrator or WolframAlpha, we're here if you cannot figure out how to do the problem or if you did it but have some reason to believe the answer is incorrect (i.e. it disagrees with a CAS or similar device).

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