User talk:Vasilii Tiorkin

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Your submission at Articles for creation: Supersymmetric Theory of Stochastic Dynamics has been accepted

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» Shadowowl | talk 20:04, 26 May 2017 (UTC)[reply]

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Supersymmetric theory of stochastic dynamics

Hi, it looks like you are sometimes active on wikipedia. I wanted to talk about Supersymmetric theory of stochastic dynamics, and ideally, have you explain it to me. FWIW, I do know supersymmetry, and once upon a time, I studied BRST but kind of forgotten it (I could learn it again.) Here's why I ask. That article makes some very dramatic and broad claims that I find surprising. I want to understand if they are as broad as they seem to be, or if they are narrower. And thus .. I'd like to talk to you directly, to straighten things out.

Let me start with the basics: so, for example, the article starts with a ${\mathcal {W}}=...$ but then doesn't "do anything" with it. It's rewritten in several different forms, but ... its not obvious how to use it to "solve" anything. Say, given some specific diffeq, its not clear how to obtain solutions using this, or how to actually calculate specific "useful" quantities/invariants/averages, etc. (perhaps I'm being stupid and impatient)

Right now, I'm not even sure what to ask or how to ask it; but the first step was to try to contact you. We can continue this conversation ... here, or on my talk page, or on the article talk page, or by private email. The conversation will probably be very very slow, because I have many other things to worry about, and the quantity of material here is so large, it will take me a while to absorb it. But I'd be thrilled if you could wave a magic wand and make me instantly smart. 67.198.37.16 (talk) 07:20, 23 May 2024 (UTC)[reply]

Hi, thank you for your message !

Regarding the Witten index, it is a subtle, fundamental and very common mistake in the Literature to use W as if it was a partition function of the SDE. In reality, it is a partition function of the noise (up to a topological factor) and it is not responsive to, say, the perturbation of the SDE. Accordingly, it cannot be used to study the response of the system to the perturbation - the response of W is identically zero. This is why I tried to stress it in the article that W cannot be used to "solve anything".

To address various interesting characteristics, one should turn to the partition function by switching from the periodic to antiperiodic boundary conditions for the ghosts. Unlike the Witten index, the partition function is not a topological invariant. This does not mean, however, that the topological supersymmetry is gone -- the topological supersymmetry is the property of the evolution operator and it is still there.

Let us use conventional email. My email is in this paper

https://www.sciencedirect.com/science/article/abs/pii/S0960077924001620

Vasilii Tiorkin (talk) 14:36, 23 May 2024 (UTC)[reply]