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nLab > Latest Changes: non-perturbative quantum field theory

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeDec 21st 2022

    added doi-link to

    diff, v14, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeNov 25th 2023

    added pointer to :

    diff, v19, current

    • CommentRowNumber3.
    • CommentAuthorDmitri Pavlov
    • CommentTimeNov 25th 2023

    Added:

    Open access PDF file of the second reissuing (2023): doi.

    diff, v20, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJan 7th 2024

    I have expanded the Idea-section (here) a fair bit, in reply to the questions in another thread (here).

    diff, v23, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeFeb 9th 2024

    added pointer to:

    diff, v26, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJun 5th 2024
    • (edited Jun 5th 2024)

    added pointer to:

    • Alvaro Ferraz, Kumar S. Gupta, Gordon W. Semenoff, Pasquale Sodano (eds.): Strongly Coupled Field Theories for Condensed Matter and Quantum Information Theory, Springer Proceedings in Physics 239, Springer (2020) [doi:10.1007/978-3-030-35473-2, pdf]

    diff, v27, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeDec 20th 2024

    added pointer to:

    diff, v34, current

    • CommentRowNumber8.
    • CommentAuthorDmitri Pavlov
    • CommentTime1 day ago

    The current version of the article says:

    Passage from the perturbative to the non-perturbative description of QFT involves taking account of non-perturbative effects invisible to perturbation theory. These arise notably from the presence of solitonic field configurations (instantonic, after Wick rotation): Such solitonic fields are invisible to perturbation theory because they are not continuously connected to the vacuum field configuration, since they are constituted by topologically non-trivial structures, e.g. gauge potentials which are connections on a topologically non-trivial principal bundle on spacetime (such as Dirac monopoles or Yang-Mills instantons, see at fiber bundles in physics).

    Suppose we are doing QFT on the spacetime R 4\mathbf{R}^4, which is contractible. Then there are no topologically nontrivial principal bundles on the spacetime. Does this mean that there are no nonperturbative effects to see in this case? (Probably the answer is “no”, but this is not clear in the current version of the article.)

    diff, v36, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTime1 day ago
    • (edited 1 day ago)

    Thanks for saying. I have added this paragraph:

    Beware that this is relevant even on Minkowski spacetime ℝ 1,d\mathbb{R}^{1,d}, and prominently so: While these spacetimes are contractible in themselves, solitons (instantons) are field configurations constrained to “vanish at infinity”, which means that they are classified by compactly supported cohomology, hence defined on the one-point compactification (−) ∪{∞}(-)_{\cup \{\infty\}} of space. For instance instantons on ℝ 4\mathbb{R}^4 are effectively bundles on ℝ ∪{∞} 4≃S 4\mathbb{R}^4_{\cup \{\infty\}} \simeq S^4 (see there).

    diff, v37, current

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