Author Archives: woit

Twistors and Unification

Posted on March 10, 2026 by woit

The last few postings here have been about rather technical problems with the conventional understanding of how spacetime symmetries and Wick rotation work in the Standard Model. These were written partly because I think these problems deserve to be better … Continue reading →

Posted in Euclidean Twistor Unification | 12 Comments

Twistors and Wick Rotation

Posted on March 9, 2026 by woit

In the last posting I explained how a fundamental problem shows up if you try to Wick rotate a Weyl spinor. Wick rotation is supposed to be analytic continuation in a four dimensional complex spacetime which, in terms of spinors, … Continue reading →

Posted in Euclidean Twistor Unification | 7 Comments

Weyl Spinor Fields and Right-handed Spacetime

Posted on March 5, 2026 by woit

In this post I’ll discuss Weyl spinor fields and explain why Wick-rotating a single Weyl spinor field appears to be impossible. This motivates a proposal for a different way of thinking about the relation between spinors and vectors, described by … Continue reading →

Posted in Euclidean Twistor Unification | Comments Off on Weyl Spinor Fields and Right-handed Spacetime

Lorentz versus Euclidean Symmetry

Posted on March 4, 2026 by woit

Wick rotation changes the spacetime symmetries of a quantum field theory, changing between The Lorentz group, by which I’ll mean either $SO(3,1)$ or $SL(2,\mathbf C)$, the double cover of the time orientation-preserving subgroup of $SO(3,1)$. The four-dimensional Euclidean signature rotation … Continue reading →

Posted in Euclidean Twistor Unification | Comments Off on Lorentz versus Euclidean Symmetry

Hyperfunctions

Posted on March 2, 2026 by woit

I’ve been trying to understand (not entirely successfully yet…) Wick rotation using hyperfunctions, which are a sort of distributions not as well-known as they should be. Some notes about them are in a separate pdf. What is well-known is that … Continue reading →

Posted in Uncategorized | 8 Comments

Osterwalder-Schrader and Euclidean Spinor Fields

Posted on February 28, 2026 by woit

If one tries to Wick rotate a quantum field theory with spinor fields, it’s well-known that problems arise, something first recognized in Schwinger’s earliest papers on the subject. I’ll try and outline here the 1972 proposal by Osterwalder and Schrader … Continue reading →

Posted in Uncategorized | 7 Comments

Harmonic Oscillators

Posted on February 27, 2026 by woit

This is related to the Osterwalder-Schrader posting, but is much, much more elementary. I’ll write up some basic facts about the quantum harmonic oscillator and explain what bothers me about the relation to Osterwalder-Schrader. Every quantum mechanics course covers the … Continue reading →

Posted in Uncategorized | 9 Comments

Looks Like it is Happening…

Posted on February 24, 2026 by woit

Update: Sorry, but a commenter points out that this may just be an artifact of counting based on when most recently modified, not on original submission date. Numbers using original, not most recent, submission dates For 12/1 to 12/31 the … Continue reading →

Posted in AI | 18 Comments

Osterwalder-Schrader

Posted on February 19, 2026 by woit

I’ve been trying to write up some new ideas about Wick rotation for a long time now, keep getting stuck as it becomes clear at various points that I haven’t gotten to the bottom of what is going on. To … Continue reading →

Posted in Uncategorized | 19 Comments

Weil Anima

Posted on February 10, 2026 by woit

Dustin Clausen is giving a course at the IHES starting today on “Weil Anima” (or maybe “Weil-Moore Anima”. They’ve already put up video of the talk here (also available on Youtube). For an earlier talk by Clausen on this material … Continue reading →

Posted in Langlands | 3 Comments