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| <header id="title-block-header"> | ||
| <h1 class="title">FeynCalc manual (development version)</h1> | ||
| </header> | ||
| <h2 id="fcloopglilowerdimension">FCLoopGLILowerDimension</h2> | ||
| <p><code>FCLoopGLILowerDimension[gli, topo]</code> lowers the dimension | ||
| of the given <code>GLI</code> from <code>D</code> to <code>D-2</code> | ||
| and expresses it in terms of <code>D</code>-dimensional loop integrals | ||
| returned in the output.</p> | ||
| <p>The algorithm is based on the code of the function | ||
| <code>RaisingDRR</code> from R. Lee’s LiteRed</p> | ||
| <h3 id="see-also">See also</h3> | ||
| <p><a href="Extra/FeynCalc.html">Overview</a>, <a | ||
| href="FCLoopGLIRaiseDimension.html">FCLoopGLIRaiseDimension</a>.</p> | ||
| <h3 id="examples">Examples</h3> | ||
| <div class="sourceCode" id="cb1"><pre | ||
| class="sourceCode mathematica"><code class="sourceCode mathematica"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a>topo <span class="ex">=</span> FCTopology<span class="op">[</span></span> | ||
| <span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a> topo1<span class="op">,</span> <span class="op">{</span>SFAD<span class="op">[</span>p1<span class="op">],</span> SFAD<span class="op">[</span>p2<span class="op">],</span> SFAD<span class="op">[</span><span class="fu">Q</span> <span class="sc">-</span> p1 <span class="sc">-</span> p2<span class="op">],</span> SFAD<span class="op">[</span><span class="fu">Q</span> <span class="sc">-</span> p2<span class="op">],</span> </span> | ||
| <span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a> SFAD<span class="op">[</span><span class="fu">Q</span> <span class="sc">-</span> p1<span class="op">]},</span> <span class="op">{</span>p1<span class="op">,</span> p2<span class="op">},</span> <span class="op">{</span><span class="fu">Q</span><span class="op">},</span> <span class="op">{</span><span class="fu">Hold</span><span class="op">[</span>SPD<span class="op">[</span><span class="fu">Q</span><span class="op">]]</span> <span class="ot">-></span> qq<span class="op">},</span> <span class="op">{}]</span></span></code></pre></div> | ||
| <p><span | ||
| class="math display">\text{FCTopology}\left(\text{topo1},\left\{\frac{1}{(\text{p1}^2+i | ||
| \eta )},\frac{1}{(\text{p2}^2+i \eta | ||
| )},\frac{1}{((-\text{p1}-\text{p2}+Q)^2+i \eta | ||
| )},\frac{1}{((Q-\text{p2})^2+i \eta )},\frac{1}{((Q-\text{p1})^2+i \eta | ||
| )}\right\},\{\text{p1},\text{p2}\},\{Q\},\{\text{Hold}[\text{SPD}(Q)]\to | ||
| \;\text{qq}\},\{\}\right)</span></p> | ||
| <div class="sourceCode" id="cb2"><pre | ||
| class="sourceCode mathematica"><code class="sourceCode mathematica"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a>FCLoopGLILowerDimension<span class="op">[</span>GLI<span class="op">[</span>topo1<span class="op">,</span> <span class="op">{</span><span class="dv">1</span><span class="op">,</span> <span class="dv">1</span><span class="op">,</span> <span class="dv">1</span><span class="op">,</span> <span class="dv">1</span><span class="op">,</span> <span class="dv">1</span><span class="op">}],</span> topo<span class="op">]</span></span></code></pre></div> | ||
| <p><span | ||
| class="math display">G^{\text{topo1}}(1,1,1,2,2)+G^{\text{topo1}}(1,1,2,1,2)+G^{\text{topo1}}(1,1,2,2,1)+G^{\text{topo1}}(1,2,1,1,2)+G^{\text{topo1}}(1,2,2,1,1)+G^{\text{topo1}}(2,1,1,2,1)+G^{\text{topo1}}(2,1,2,1,1)+G^{\text{topo1}}(2,2,1,1,1)</span></p> | ||
| <div class="sourceCode" id="cb3"><pre | ||
| class="sourceCode mathematica"><code class="sourceCode mathematica"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a>FCLoopGLILowerDimension<span class="op">[</span>GLI<span class="op">[</span>topo1<span class="op">,</span> <span class="op">{</span>n1<span class="op">,</span> n2<span class="op">,</span> n3<span class="op">,</span> <span class="dv">1</span><span class="op">,</span> <span class="dv">1</span><span class="op">}],</span> topo<span class="op">]</span></span></code></pre></div> | ||
| <p><span | ||
| class="math display">G^{\text{topo1}}(\text{n1},\text{n2},\text{n3},2,2)+\text{n3} | ||
| G^{\text{topo1}}(\text{n1},\text{n2},\text{n3}+1,1,2)+\text{n3} | ||
| G^{\text{topo1}}(\text{n1},\text{n2},\text{n3}+1,2,1)+\text{n2} | ||
| G^{\text{topo1}}(\text{n1},\text{n2}+1,\text{n3},1,2)+\text{n2} | ||
| \;\text{n3} | ||
| G^{\text{topo1}}(\text{n1},\text{n2}+1,\text{n3}+1,1,1)+\text{n1} | ||
| G^{\text{topo1}}(\text{n1}+1,\text{n2},\text{n3},2,1)+\text{n1} | ||
| \;\text{n3} | ||
| G^{\text{topo1}}(\text{n1}+1,\text{n2},\text{n3}+1,1,1)+\text{n1} | ||
| \;\text{n2} | ||
| G^{\text{topo1}}(\text{n1}+1,\text{n2}+1,\text{n3},1,1)</span></p> | ||
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