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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeJun 30th 2013
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded a bit more text to the Idea-section at _[[Wick rotation]]_ and in particular added cross-links with _[[Osterwalder-Schrader theorem]]_.

   added a bit more text to the Idea-section at Wick rotation and in particular added cross-links with Osterwalder-Schrader theorem.

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeNov 9th 2018
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded an overview-diagram to the Idea section (copied over from _[[Euclidean field theory]]_) <a href="https://ncatlab.org/nlab/revision/diff/Wick+rotation/17">diff</a>, <a href="https://ncatlab.org/nlab/revision/Wick+rotation/17">v17</a>, <a href="https://ncatlab.org/nlab/show/Wick+rotation">current</a>

   added an overview-diagram to the Idea section (copied over from Euclidean field theory)

   diff, v17, current

3. • CommentRowNumber3.
   • CommentAuthorDavid_Corfield
   • CommentTimeNov 9th 2018
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexDoes this Wick rotation story 'lift' to some relation between stable cohomotopy spaces?

   Does this Wick rotation story ’lift’ to some relation between stable cohomotopy spaces?

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeNov 9th 2018
   • (edited Nov 9th 2018)
   • PermaLink
   Author: Urs
   Format: MarkdownItexRight, so by the discussion at [[stable splitting of mapping spaces]] we have that the real cohomology of the space of spatially compactly supported cocycles in degree-4 cohomotopy on Minkowski spacetime ("Lorentzian instantons") is equivalently correlators of Euclidean field theory on $R^3 \times S^1$, hence Is Wick-rotated n-point functions of relativistic field theory on Minkowski spacetime at finite temperature.

   Right, so by the discussion at stable splitting of mapping spaces we have that the real cohomology of the space of spatially compactly supported cocycles in degree-4 cohomotopy on Minkowski spacetime (“Lorentzian instantons”) is equivalently correlators of Euclidean field theory on $R^3 \times S^1$, hence Is Wick-rotated n-point functions of relativistic field theory on Minkowski spacetime at finite temperature.

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeNov 10th 2018
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded a few more words to the Idea-section, and pointed more prominently to [Fulling-Ruijsenaars 87](https://ncatlab.org/nlab/show/Wick+rotation#FullingRuijsenaars87) <a href="https://ncatlab.org/nlab/revision/diff/Wick+rotation/20">diff</a>, <a href="https://ncatlab.org/nlab/revision/Wick+rotation/20">v20</a>, <a href="https://ncatlab.org/nlab/show/Wick+rotation">current</a>

   added a few more words to the Idea-section, and pointed more prominently to Fulling-Ruijsenaars 87

   diff, v20, current

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeNov 10th 2018
   • (edited Nov 10th 2018)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded picture of the rotation doing it's thing <a href="https://ncatlab.org/nlab/revision/diff/Wick+rotation/21">diff</a>, <a href="https://ncatlab.org/nlab/revision/Wick+rotation/21">v21</a>, <a href="https://ncatlab.org/nlab/show/Wick+rotation">current</a>

   added picture of the rotation doing it’s thing

   diff, v21, current

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeApr 19th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded these pointers: *** On the (non-)existence of Wick rotation for [[quantum field theory on curved spacetimes]]: MathOverflow comments: * [[Igor Khavkine]] ([MO:a/165317](https://mathoverflow.net/a/165317/381)) * [[Robert Bryant]] ([MO:a/165345](https://mathoverflow.net/a/165345/381)) See also: * {#HollandsWald14} [[Stefan Hollands]], [[Robert Wald]], p. 7-8 in: _Quantum fields in curved spacetime_, Physics Reports Volume 574, 16 April 2015, Pages 1-35 ([arXiv:1401.2026](https://arxiv.org/abs/1401.2026), [doi:10.1016/j.physrep.2015.02.001](https://doi.org/10.1016/j.physrep.2015.02.001)) <a href="https://ncatlab.org/nlab/revision/diff/Wick+rotation/24">diff</a>, <a href="https://ncatlab.org/nlab/revision/Wick+rotation/24">v24</a>, <a href="https://ncatlab.org/nlab/show/Wick+rotation">current</a>

   added these pointers:

   ---

   On the (non-)existence of Wick rotation for quantum field theory on curved spacetimes:

   MathOverflow comments:

   • Igor Khavkine (MO:a/165317)

   • Robert Bryant (MO:a/165345)

   See also:

   • {#HollandsWald14} Stefan Hollands, Robert Wald, p. 7-8 in: Quantum fields in curved spacetime, Physics Reports Volume 574, 16 April 2015, Pages 1-35 (arXiv:1401.2026, doi:10.1016/j.physrep.2015.02.001)

   diff, v24, current

8. • CommentRowNumber8.
   • CommentAuthorUrs
   • CommentTimeDec 10th 2021
   • (edited Dec 10th 2021)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to the recent writeup: * [[Maxim Kontsevich]], [[Graeme Segal]], *Wick rotation and the positivity of energy in quantum field theory* ([arXiv:2105.10161](https://arxiv.org/abs/2105.10161)) and this recent talk: * [[Graeme Segal]], *Wick Rotation and the Positivity of Energy in Quantum Field Theory*, talk at IAS Physics Group Meeting, December 2021 ([video recording](https://www.ias.edu/video/wick-rotation-and-positivity-energy-quantum-field-theory)) following up on talks revolving around the same idea, such as * [[Graeme Segal]], _Wick rotation and the positivity of energy in quantum field theory_, talk at Institut des Hautes Études Scientifiques (IHÉS), June 2014 ([video recording](https://www.youtube.com/watch?feature=player_embedded&v=vTvXHL6ZJik)) which the entry already used to be linking to. <a href="https://ncatlab.org/nlab/revision/diff/Wick+rotation/25">diff</a>, <a href="https://ncatlab.org/nlab/revision/Wick+rotation/25">v25</a>, <a href="https://ncatlab.org/nlab/show/Wick+rotation">current</a>

   added pointer to the recent writeup:

   • Maxim Kontsevich, Graeme Segal, Wick rotation and the positivity of energy in quantum field theory (arXiv:2105.10161)

   and this recent talk:

   • Graeme Segal, Wick Rotation and the Positivity of Energy in Quantum Field Theory, talk at IAS Physics Group Meeting, December 2021 (video recording)

   following up on talks revolving around the same idea, such as

   • Graeme Segal, Wick rotation and the positivity of energy in quantum field theory, talk at Institut des Hautes Études Scientifiques (IHÉS), June 2014 (video recording)

   which the entry already used to be linking to.

   diff, v25, current

9. • CommentRowNumber9.
   • CommentAuthorUrs
   • CommentTimeNov 16th 2023
   • (edited Nov 16th 2023)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded publication data to this item: * [[Maxim Kontsevich]], [[Graeme Segal]], *Wick rotation and the positivity of energy in quantum field theory*, The Quarterly Journal of Mathematics **72** 1-2 (2021) 673–699 &lbrack;[arXiv:2105.10161](https://arxiv.org/abs/2105.10161), [doi:10.1093/qmath/haab027](https://doi.org/10.1093/qmath/haab027)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/Wick+rotation/26">diff</a>, <a href="https://ncatlab.org/nlab/revision/Wick+rotation/26">v26</a>, <a href="https://ncatlab.org/nlab/show/Wick+rotation">current</a>

   added publication data to this item:

   • Maxim Kontsevich, Graeme Segal, Wick rotation and the positivity of energy in quantum field theory, The Quarterly Journal of Mathematics 72 1-2 (2021) 673–699 [arXiv:2105.10161, doi:10.1093/qmath/haab027]

   diff, v26, current