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#pathintegral

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Bharath Krishnan<p>In a magazine article [1] on problems and progress in quantum field theory, Wood writes of Feynman path integrals, “No known mathematical procedure can meaningfully average an infinite number of objects covering an infinite expanse of space in general. The path integral is more of a physics philosophy than an exact mathematical recipe.”</p><p>This article [2] provides a method for averaging an arbitrary collection of objects; however, the average can be any number in the extension of the range of these objects. (Note, an arbitrary collection of these objects is a function.)</p><p>Question: Suppose anything meaningful has applications in quantum field theory. Is there a way to meaningfully choose a unique, finite average of a function whose graph matches the description in Wood's quote?</p><p>For more info, see this post [3].</p><p>[1]: <a href="https://www.quantamagazine.org/mathematicians-prove-2d-version-of-quantum-gravity-really-works-20210617/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://www.</span><span class="ellipsis">quantamagazine.org/mathematici</span><span class="invisible">ans-prove-2d-version-of-quantum-gravity-really-works-20210617/</span></a></p><p>[2]: <a href="https://arxiv.org/pdf/2004.09103" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="">arxiv.org/pdf/2004.09103</span><span class="invisible"></span></a></p><p>[3]: <a href="https://math.stackexchange.com/q/5052005/125918" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">math.stackexchange.com/q/50520</span><span class="invisible">05/125918</span></a></p><p><a href="https://mathstodon.xyz/tags/PathIntegral" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>PathIntegral</span></a> <a href="https://mathstodon.xyz/tags/quantum" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>quantum</span></a> <a href="https://mathstodon.xyz/tags/FeynmanPathIntegral" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>FeynmanPathIntegral</span></a> <a href="https://mathstodon.xyz/tags/mean" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>mean</span></a> <a href="https://mathstodon.xyz/tags/average" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>average</span></a> <a href="https://mathstodon.xyz/tags/expectedvalue" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>expectedvalue</span></a> <a href="https://mathstodon.xyz/tags/quantumfieldtheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>quantumfieldtheory</span></a></p>
Mark Hughes<p>How about some (theoretical) reality? </p><p><a href="https://mastodon.social/tags/Dirac" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Dirac</span></a>, <a href="https://mastodon.social/tags/Feynman" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Feynman</span></a> and what to put in the <a href="https://mastodon.social/tags/PathIntegral" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>PathIntegral</span></a>.</p><p>Very interesting and not too hard to follow.</p><p><a href="https://www.quantamagazine.org/how-our-reality-may-be-a-sum-of-all-possible-realities-20230206/" rel="nofollow noopener noreferrer" target="_blank"><span class="invisible">https://www.</span><span class="ellipsis">quantamagazine.org/how-our-rea</span><span class="invisible">lity-may-be-a-sum-of-all-possible-realities-20230206/</span></a></p><p><a href="https://mastodon.social/tags/Physics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Physics</span></a> <a href="https://mastodon.social/tags/QuantumPhysics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>QuantumPhysics</span></a> <a href="https://mastodon.social/tags/TheoreticalPhysics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>TheoreticalPhysics</span></a> <a href="https://mastodon.social/tags/QuantaMagazine" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>QuantaMagazine</span></a></p>
Jarvist Moore Frost<p><a href="https://mastodon.social/tags/Introduction" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Introduction</span></a></p><p>I’m a <a href="https://mastodon.social/tags/Physicist" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Physicist</span></a> working in a <a href="https://mastodon.social/tags/Chemistry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Chemistry</span></a> department, mostly <a href="https://mastodon.social/tags/CompChem" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>CompChem</span></a>. I try and understand functional materials (particularly <a href="https://mastodon.social/tags/semiconductor" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>semiconductor</span></a> s) with <a href="https://mastodon.social/tags/QuantumMechanics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>QuantumMechanics</span></a> and <a href="https://mastodon.social/tags/StatisticalMechanics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>StatisticalMechanics</span></a>, with a sprinkling of <a href="https://mastodon.social/tags/MachineLearning" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>MachineLearning</span></a>. I particularly like <a href="https://mastodon.social/tags/PathIntegral" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>PathIntegral</span></a> approaches. All my work is orientated towards <a href="https://mastodon.social/tags/RenewableEnergy" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>RenewableEnergy</span></a> materials.</p><p>My favourite programming languages are <a href="https://mastodon.social/tags/C" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>C</span></a> and <a href="https://mastodon.social/tags/JuliaLang" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>JuliaLang</span></a>. <a href="https://mastodon.social/tags/Unix" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Unix</span></a> <a href="https://mastodon.social/tags/CommandLine" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>CommandLine</span></a> <a href="https://mastodon.social/tags/HackThePlanet" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>HackThePlanet</span></a></p><p><a href="https://mastodon.social/tags/AcademicParent" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>AcademicParent</span></a> to a ~2 and ~4 year old.</p>
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