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#FeynmanPathIntegral

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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 an application in quantum field theory. Is there a way of meaningfully choosing a unique, finite average of a function whose graph matches the description in Wood&#39;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/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><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" target="_blank" rel="nofollow noopener noreferrer" translate="no"><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" target="_blank" rel="nofollow noopener noreferrer" translate="no"><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="tag">#<span>PathIntegral</span></a> <a href="https://mathstodon.xyz/tags/quantum" class="mention hashtag" rel="tag">#<span>quantum</span></a> <a href="https://mathstodon.xyz/tags/FeynmanPathIntegral" class="mention hashtag" rel="tag">#<span>FeynmanPathIntegral</span></a> <a href="https://mathstodon.xyz/tags/mean" class="mention hashtag" rel="tag">#<span>mean</span></a> <a href="https://mathstodon.xyz/tags/average" class="mention hashtag" rel="tag">#<span>average</span></a> <a href="https://mathstodon.xyz/tags/expectedvalue" class="mention hashtag" rel="tag">#<span>expectedvalue</span></a> <a href="https://mathstodon.xyz/tags/quantumfieldtheory" class="mention hashtag" rel="tag">#<span>quantumfieldtheory</span></a></p>
Ariadne<p>"The oracular formula is known as the Feynman path integral. As far as physicists can tell, it precisely predicts the behavior of any quantum system — an electron, a light ray or even a black hole. The path integral has racked up so many successes that many physicists believe it to be a direct window into the heart of reality.</p><p>“It’s how the world really is,” said Renate Loll, a theoretical physicist at Radboud University in the Netherlands.</p><p>But the equation, although it graces the pages of thousands of physics publications, is more of a philosophy than a rigorous recipe. It suggests that our reality is a sort of blending — a sum — of all imaginable possibilities. But it does not tell researchers exactly how to carry out the sum. So physicists have spent decades developing an arsenal of approximation schemes for constructing and computing the integral for different quantum systems."</p><p><a href="https://www.quantamagazine.org/how-our-reality-may-be-a-sum-of-all-possible-realities-20230206/?mc_cid=f0ed562e28&amp;mc_eid=6a152ea7f5" 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/?mc_cid=f0ed562e28&amp;mc_eid=6a152ea7f5</span></a></p><p><a href="https://kolektiva.social/tags/Physics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Physics</span></a> <a href="https://kolektiva.social/tags/QuantumPhysics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>QuantumPhysics</span></a> <a href="https://kolektiva.social/tags/Feynman" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Feynman</span></a> <a href="https://kolektiva.social/tags/FeynmanPathIntegral" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>FeynmanPathIntegral</span></a> <a href="https://kolektiva.social/tags/Philosophy" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Philosophy</span></a> <a href="https://kolektiva.social/tags/QuantumMechanics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>QuantumMechanics</span></a> <a href="https://kolektiva.social/tags/Quantum" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Quantum</span></a></p>
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