data/mathoid/252.mml
<math
xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="upper H Subscript normal upper G Superscript normal p normal h normal e normal n Baseline left-bracket upper N right-bracket equals StartFraction 1 Over 16 pi upper G EndFraction integral Underscript normal upper Sigma Endscripts normal d cubed x upper N overbar left-bracket minus 6 StartRoot p overbar EndRoot left-parenthesis StartFraction sine mu overbar gamma k overbar Over mu overbar gamma EndFraction right-parenthesis squared minus StartFraction 1 Over 2 p overbar Superscript 3 slash 2 Baseline EndFraction left-parenthesis StartFraction sine mu overbar gamma k overbar Over mu overbar gamma EndFraction right-parenthesis squared left-parenthesis delta upper E Subscript j Superscript c Baseline delta upper E Subscript k Superscript d Baseline delta Subscript c Superscript k Baseline delta Subscript d Superscript j Baseline right-parenthesis plus StartRoot p overbar EndRoot left-parenthesis delta upper K Subscript c Superscript j Baseline delta upper K Subscript d Superscript k Baseline delta Subscript k Superscript c Baseline delta Subscript j Superscript d Baseline right-parenthesis minus StartFraction 2 Over StartRoot p overbar EndRoot EndFraction left-parenthesis StartFraction sine m mu overbar gamma k overbar Over m mu overbar gamma EndFraction right-parenthesis left-parenthesis delta upper E Subscript j Superscript c Baseline delta upper K Subscript c Superscript j Baseline right-parenthesis plus StartFraction 1 Over p overbar Superscript 3 slash 2 Baseline EndFraction left-parenthesis delta Subscript c d Baseline delta Superscript j k Baseline delta Superscript e f Baseline partial-differential Subscript e Baseline upper E Subscript j Superscript c Baseline partial-differential Subscript f Baseline upper E Subscript k Superscript d Baseline right-parenthesis right-bracket">
<semantics>
<mrow>
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<mrow data-semantic-type="relseq" data-semantic-role="equality" data-semantic-id="318" data-semantic-children="315,317" data-semantic-content="15" data-semantic-parent="320">
<mrow data-semantic-type="appl" data-semantic-role="simple function" data-semantic-id="315" data-semantic-children="11,307" data-semantic-content="314,0" data-semantic-parent="318">
<msubsup data-semantic-type="subsup" data-semantic-role="simple function" data-semantic-id="11" data-semantic-children="0,1,9" data-semantic-parent="315" data-semantic-collapsed="(11 (10 0 1) 9)">
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<mi mathvariant="normal" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="normal" data-semantic-id="1" data-semantic-parent="11">G</mi>
</mrow>
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<mrow class="MJX-TeXAtom-ORD" data-semantic-parent="11">
<mrow class="MJX-TeXAtom-ORD" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="9" data-semantic-children="2,3,4,5" data-semantic-content="6,7,8" data-semantic-parent="11">
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<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="6" data-semantic-parent="9" data-semantic-added="true" data-semantic-operator="infixop,"></mo>
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</mrow>
</msubsup>
<mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-id="314" data-semantic-parent="315" data-semantic-added="true" data-semantic-operator="appl"></mo>
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<mfrac data-semantic-type="fraction" data-semantic-role="division" data-semantic-id="23" data-semantic-children="16,22" data-semantic-parent="317">
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<msup data-semantic-type="superscript" data-semantic-role="latinletter" data-semantic-id="29" data-semantic-children="27,28" data-semantic-parent="311">
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<mi mathvariant="normal" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="normal" data-semantic-id="27" data-semantic-parent="29">d</mi>
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<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="28" data-semantic-parent="29">3</mn>
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<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="308" data-semantic-parent="311" data-semantic-added="true" data-semantic-operator="infixop,"></mo>
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<mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="305" data-semantic-children="303" data-semantic-content="34,304" data-semantic-parent="311">
<mo data-semantic-type="fence" data-semantic-role="open" data-semantic-id="34" data-semantic-parent="305" data-semantic-operator="fenced">[</mo>
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<mrow data-semantic-type="infixop" data-semantic-role="subtraction" data-semantic-id="300" data-semantic-children="296,299" data-semantic-content="160" data-semantic-parent="303">
<mrow data-semantic-type="infixop" data-semantic-role="addition" data-semantic-id="296" data-semantic-children="293,295" data-semantic-content="131" data-semantic-parent="300">
<mrow data-semantic-type="infixop" data-semantic-role="subtraction" data-semantic-id="293" data-semantic-children="289,292" data-semantic-content="67" data-semantic-parent="296">
<mrow data-semantic-type="prefixop" data-semantic-role="negative" data-semantic-id="289" data-semantic-children="288" data-semantic-content="35" data-semantic-parent="293">
<mo data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-id="35" data-semantic-parent="289" data-semantic-operator="prefixop,−">−
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<mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="288" data-semantic-children="36,40,66" data-semantic-content="286,287" data-semantic-parent="289">
<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="36" data-semantic-parent="288">6</mn>
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<mover data-semantic-type="overscore" data-semantic-role="latinletter" data-semantic-id="39" data-semantic-children="37,38" data-semantic-parent="40">
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<msup data-semantic-type="superscript" data-semantic-role="leftright" data-semantic-id="66" data-semantic-children="64,65" data-semantic-parent="288">
<mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="64" data-semantic-children="62" data-semantic-content="41,63" data-semantic-parent="66">
<mo data-semantic-type="fence" data-semantic-role="open" data-semantic-id="41" data-semantic-parent="64" data-semantic-operator="fenced">(</mo>
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<mrow data-semantic-type="appl" data-semantic-role="prefix function" data-semantic-id="55" data-semantic-children="42,53" data-semantic-content="54,42" data-semantic-parent="62">
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<mover data-semantic-type="overscore" data-semantic-role="greekletter" data-semantic-id="46" data-semantic-children="44,45" data-semantic-parent="53">
<mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="44" data-semantic-parent="46">μ
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<mfrac data-semantic-type="fraction" data-semantic-role="division" data-semantic-id="80" data-semantic-children="68,79" data-semantic-parent="292">
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<annotation encoding="application/x-tex">H_{\rm {G}}^{\rm {phen}}[N]={\frac {1}{16\pi G}}\int _{\Sigma }\mathrm {d} ^{3}x{\bar {N}}\left[-6{\sqrt {\bar {p}}}\left({\frac {\sin {\bar {\mu }}\gamma {\bar {k}}}{{\bar {\mu }}\gamma }}\right)^{2}-{\frac {1}{2{\bar {p}}^{3/2}}}\left({\frac {\sin {\bar {\mu }}\gamma {\bar {k}}}{{\bar {\mu }}\gamma }}\right)^{2}(\delta E_{j}^{c}\delta E_{k}^{d}\delta _{c}^{k}\delta _{d}^{j})+{\sqrt {\bar {p}}}(\delta K_{c}^{j}\delta K_{d}^{k}\delta _{k}^{c}\delta _{j}^{d})-{\frac {2}{\sqrt {\bar {p}}}}\left({\frac {\sin m{\bar {\mu }}\gamma {\bar {k}}}{m{\bar {\mu }}\gamma }}\right)(\delta E_{j}^{c}\delta K_{c}^{j})+{\frac {1}{{\bar {p}}^{3/2}}}(\delta _{cd}\delta ^{jk}\delta ^{ef}\partial _{e}E_{j}^{c}\partial _{f}E_{k}^{d})\right]~{}</annotation>
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</math>