Create accountLogin

Recent searches

No recent searches

Search options

Only available when logged in.
universeodon.com is part of the decentralized social network powered by Mastodon.
Be one with the #fediverse. Join millions of humans building, creating, and collaborating on Mastodon Social Network. Supports 1000 character posts.

Administered by:

Server stats:

3.5K
active users
Learn more

universeodon.com: AboutStatusProfiles directoryPrivacy policy

Mastodon: AboutGet the appKeyboard shortcutsView source codev4.2.17

#feynmanintegral

0 posts0 participants0 posts today
Paul Balduf<p>Currently, I'm working on a problem in <a href="https://mathstodon.xyz/tags/quantum" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>quantum</span></a> field theory where we use <a href="https://mathstodon.xyz/tags/FeynmanIntegral" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>FeynmanIntegral</span></a> s. These integrals are depicted by graphs, and they can be divergent when a graph has too many edges for a given number of vertices. The task is to identify all subgraphs that are divergent. This is a coproduct: It produces multiple terms, and each term is a list of 2 elements. The first element is one or multiple divergent subgraphs, and the second element is the remainder. It is surprising how many terms the coproduct has even for small graphs. For my example, even if the red graph is rather small, there are already 15 combinations of divergent subgraphs. To compute a physically sensible result, one needs to sum over all original graphs, and subtract all these combinations of subgraphs. <a href="https://mathstodon.xyz/tags/physics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>physics</span></a> <a href="https://mathstodon.xyz/tags/research" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>research</span></a></p>
Paul Balduf<p>At the <a href="https://mathstodon.xyz/tags/CAP" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>CAP</span></a> <a href="https://mathstodon.xyz/tags/Physics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Physics</span></a> Congress and the Theory Canada meeting, I gave two talks about the statistical distribution of <a href="https://mathstodon.xyz/tags/FeynmanIntegral" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>FeynmanIntegral</span></a> s and how their correlations can be used for efficient sampling at high loop order. The slides are now available from my website!<br><a href="https://paulbalduf.com/research/statistics-periods/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">paulbalduf.com/research/statis</span><span class="invisible">tics-periods/</span></a></p>
Paul Balduf<p>In <a href="https://mathstodon.xyz/tags/QuantumFieldTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>QuantumFieldTheory</span></a>, scattering amplitudes can be computed as sums of (very many) <a href="https://mathstodon.xyz/tags/FeynmanIntegral" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>FeynmanIntegral</span></a> s. They contribute differently much, with most integrals contributing near the average (scaled to 1.0 in the plots), but a "long tail" of integrals that are larger by a significant factor. <br>We looked at patterns in these distributions, and one particularly striking one is that if instead of the Feynman integral P itself, you consider 1 divided by root of P, the distribution is almost Gaussian! To my knowledge, this is the first time anything like this has been observed. We only looked at one quantum field theory, the "phi^4 theory in 4 dimensions". It would be interesting to see if this is coincidence for this particular theory and class of Feynman integrals, or if it persists universally. <br>More background and relevant papers at <a href="https://paulbalduf.com/research/statistics-periods/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">paulbalduf.com/research/statis</span><span class="invisible">tics-periods/</span></a><br><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/physics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>physics</span></a> <a href="https://mathstodon.xyz/tags/statistics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>statistics</span></a></p>
ExploreLive feeds
About