Global anomaly

In theoretical physics, a global anomaly is a type of anomaly: in this particular case, it is a quantum effect that invalidates a large gauge transformation that would otherwise be preserved in the classical theory. This leads to an inconsistency in the theory because the space of configurations which is being integrated over in the functional integral involves both a configuration and the same configuration after a large gauge transformation has acted upon it and the sum of all such contributions is zero and the space of configurations cannot be split into connected components for which the integral is nonzero.

Alternatively, the existence of a global anomaly implies that the measure of Feynman's functional integral cannot be defined globally.

The adjective "global" refers to the properties of a group that are detectable via large gauge or diffeomorphism transformations, but are not detectable locally via infinitesimal transformations. For example, all features of a discrete group (as opposed to a Lie group) are global in character.

A famous example is an SU(2) Yang–Mills theory in 4D with an odd number of chiral fermions in the fundamental representation 2 or the isospin 1/2 of SU(2), transforming as doublets under SU(2). This is known as the Witten SU(2) anomaly.[1]

Another new but much more subtle example is found in 2018, also for the SU(2) gauge theory in 4D, with an odd number of chiral fermions in the representation 4 or the isospin 3/2 of SU(2). This is known as the new SU(2) anomaly.[2] The new SU(2) anomaly has an important application to rule out the existence of any global anomaly for the SO(10) grand unified theory. This new anomaly is a mixed gauge-gravitational anomaly and a nonperturbative global anomaly.[2][3]

Many types of global anomalies must cancel for a theory to be consistent. An example is modular invariance, the requirement of anomaly cancellation for a part of a gravitational anomaly that deals with the large diffeomorphisms over two dimensional worldsheets of genus 1 or more.

References

  1. ^ Witten, Edward (November 1982). "An SU(2) Anomaly". Phys. Lett. B. 117 (5): 324. Bibcode:1982PhLB..117..324W. doi:10.1016/0370-2693(82)90728-6.
  2. ^ a b Wang, Juven; Wen, Xiao-Gang; Witten, Edward (May 2019). "A New SU(2) Anomaly". Journal of Mathematical Physics. 60 (5): 052301. arXiv:1810.00844. Bibcode:2019JMP....60e2301W. doi:10.1063/1.5082852. ISSN 1089-7658. S2CID 85543591.
  3. ^ Wang, Juven; Wen, Xiao-Gang (1 June 2020). "Nonperturbative definition of the standard models". Physical Review Research. 2 (2): 023356. arXiv:1809.11171. Bibcode:2018arXiv180911171W. doi:10.1103/PhysRevResearch.2.023356. ISSN 2469-9896. S2CID 53346597.
Stub icon

This quantum mechanics-related article is a stub. You can help Wikipedia by expanding it.

Read other articles:

Turap

Ada usul agar Plamir digabungkan ke artikel ini. (Diskusikan) Diusulkan sejak Februari 2022. Peralatan untuk membuat turap. Seorang tukang sedang memoles plester pada dinding di awal abad ke-19, lukisan karya John Cranch (1751–1821). Plester atau turap[1] adalah bahan bangunan yang digunakan sebagai pelapis perlindungan atau dekoratif untuk dinding dan plafon serta untuk mencetak elemen-elemen dekoratif.[2] Dalam bahasa Inggris plester biasanya berarti bahan yang digunakan u...

 

Harold Godwinson

Harold GodwinsonRaja InggrisBerkuasa5 Januari – 14 Oktober 1066Penobatan6 Januari 1066PendahuluEdward sang PenasehatPenerusEdgar Ætheling (tidak dimahkotai)(lainnya) William sang PenaklukInformasi pribadiKelahiranc. 1022Wessex, InggrisKematian14 Oktober 1066 (aged 43/44)Pertempuran Hastings, SussexPemakamanWaltham Abbey, Essex, atau Bosham, Sussex (dipersengketakan)WangsaWangsa GodwinAyahGodwin, Earl of WessexIbuGytha ThorkelsdóttirPasanganEdith si AdilEdith dari MerciaAnakGodwinEdmu...

 

Pemilihan umum Bupati Ngada 2024

Pemilihan umum Bupati Ngada 20242020202927 November 2024Kandidat Peta persebaran suara Peta Provinsi Nusa Tenggara Timur yang menyoroti Kabupaten Ngada Bupati & Wakil Bupati petahanaAndreas Paru & Raymundus Bena Bupati & Wakil Bupati terpilih Belum diketahui Pemilihan umum Bupati Ngada 2024 dilaksanakan pada 27 November 2024 untuk memilih Bupati Ngada periode 2024–2029.[1] Pemilihan Bupati Ngada tahun tersebut akan diselenggarakan setelah Pemilihan umum Presiden Indones...

Al-Mahdi (Abbasside)

Pour les articles homonymes, voir Al-Mahdi. Si ce bandeau n'est plus pertinent, retirez-le. Cliquez ici pour en savoir plus. Certaines informations figurant dans cet article ou cette section devraient être mieux reliées aux sources mentionnées dans les sections « Bibliographie », « Sources » ou « Liens externes » (janvier 2020). Vous pouvez améliorer la vérifiabilité en associant ces informations à des références à l'aide d'appels de notes. Al-Ma...

 

イスラームにおける結婚

イスラームにおける結婚（イスラームにおけるけっこん）とは、二者の間で行われる法的な契約である。新郎新婦は自身の自由な意思で結婚に同意する。口頭または紙面での規則に従った拘束的な契約は、イスラームの結婚で不可欠だと考えられており、新郎と新婦の権利と責任の概要を示している[1]。イスラームにおける離婚は様々な形をとることができ、個�...

 

Ido

Constructed international auxiliary language This article is about the language. For other uses, see Ido (disambiguation). Not to be confused with Edo language. IdoIdoPronunciationIPA: [ˈido]Created byDelegation for the Adoption of an International Auxiliary LanguageDate1907Setting and usageInternational auxiliary languageUsers100–200 (2000)[1]26 Native speakers in Finland (2022)[2]PurposeConstructed language International auxiliary languageProto-Esperanto...

Pennsylvania House of Representatives, District 97

American legislative district Pennsylvania's 97th StateHouse of RepresentativesdistrictRepresentative  Steven MentzerR–Manheim Township, Lancaster County Demographics93.8% White2.3%% Black3.9%% HispanicPopulation (2011) • Citizens of voting age66,45647,812 The 97th Pennsylvania House of Representatives District is located in Lancaster County. Steven Mentzer has represented the 97th district in the Pennsylvania House of Representatives since 2013. Dis...

 

South Shore, Chicago

Community area in Chicago Community area in Illinois, United StatesSouth ShoreCommunity areaCommunity Area 43 – South ShoreRainbow Beach along the shore of Lake Michigan.Location within the city of ChicagoCoordinates: 41°45.6′N 87°34.8′W / 41.7600°N 87.5800°W / 41.7600; -87.5800CountryUnited StatesStateIllinoisCountyCookCityChicagoNeighborhoods list Jackson Park HighlandsSouth Shore Area • Total2.99 sq mi (7.74 km2)Population (...

 

Encyclopedia of Camps and Ghettos, 1933–1945

American seven-part encyclopedia series Encyclopedia of Camps and Ghettos, 1933–1945 Cover art of Volume II of the EncyclopediaEditorGeoffrey P. MegargeeCountryUnited StatesLanguageEnglishGenreHistoryHolocaust studiesPublisherIndiana University PressUnited States Holocaust Memorial MuseumPublication date2009 (Volume I)2012 (Volume II)2018 (Volume III)Media typePrint, PDFAwards2009 National Jewish Book AwardWebsitewww.ushmm.org/research/publications/encyclopedia-camps-ghettos Encycloped...

Raffles Girls' School (Secondary)

artikel ini perlu dirapikan agar memenuhi standar Wikipedia. Tidak ada alasan yang diberikan. Silakan kembangkan artikel ini semampu Anda. Merapikan artikel dapat dilakukan dengan wikifikasi atau membagi artikel ke paragraf-paragraf. Jika sudah dirapikan, silakan hapus templat ini. (Pelajari cara dan kapan saatnya untuk menghapus pesan templat ini) Artikel atau bagian artikel ini diterjemahkan secara buruk. Kualitas terjemahannya masih kurang bagus. Bagian-bagian yang mungkin diterjemahkan da...

 

Аккад (город)

Эта статья о древнем городе; об одноимённом государстве и области см. Аккад. У этого термина существуют и другие значения, см. Аккад (значения). Эту страницу предлагается переименовать в «Аккаде».Пояснение причин и обсуждение — на странице Википедия:К переименованию/18 �...

 

美国众议院

此條目需要补充更多来源。 (2021年7月4日)请协助補充多方面可靠来源以改善这篇条目，无法查证的内容可能會因為异议提出而被移除。致使用者：请搜索一下条目的标题（来源搜索：美国众议院 — 网页、新闻、书籍、学术、图像），以检查网络上是否存在该主题的更多可靠来源（判定指引）。 美國眾議院 United States House of Representatives第118届美国国会众议院徽章 众议院旗...

Gennady Khripel

Russian politician (1949–2024) Gennady KhripelГеннадий ХрипельKhripel in 2005Member of the Federation Council of RussiaIn officeJanuary 1996 – May 2007Succeeded byYuri VorobyovChairman of the Legislative Assembly of Vologda OblastIn officeFebruary 1996 – December 2001Preceded byG. V. Sudakov [ru]Succeeded byNikolai Tikhomirov [ru]In officeApril 1994 – September 1995Preceded byposition establishedSucceeded byG. V. Suda...

 

彼得一世岛

此條目需要补充更多来源。 (2023年1月22日)请协助補充多方面可靠来源以改善这篇条目，无法查证的内容可能會因為异议提出而被移除。致使用者：请搜索一下条目的标题（来源搜索：彼得一世岛 — 网页、新闻、书籍、学术、图像），以检查网络上是否存在该主题的更多可靠来源（判定指引）。 彼得一世島Peter I Øy1931年—1961年 國旗 國徽 彼得一世島位置(紅色)、南極洲(�...

 

Cleaver (Stone Age tool)

Biface stone tool This article includes a list of general references, but it lacks sufficient corresponding inline citations. Please help to improve this article by introducing more precise citations. (November 2022) (Learn how and when to remove this message) You can help expand this article with text translated from the corresponding article in Spanish. (January 2024) Click [show] for important translation instructions. View a machine-translated version of the Spanish article. Machine ...

Nabor and Felix

Saints Nabor and FelixSaints Nabor and Felix (foreground), with the Virgin Mary, Saint Francis, Saint Claire, Saint John the Baptist, Saint Mary Magdalene, and Saint Catherine. Orazio Samacchini, ca. 1570.MartyrsBorn3rd centuryMauretania Caesariensis (modern-day Algeria)Diedc. 303Laus Pompeia, ItalyVenerated inRoman Catholic ChurchEastern Orthodox ChurchMajor shrineMilan, ItalyFeastJuly 12Attributestwo young men in military attire; palms Nabor and Felix (d. c. AD 303) were Chr...

 

Wikipedia talk:WikiProject National Football League/Archive 24

This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. Archive 20 ← Archive 22 Archive 23 Archive 24 Article for the cowboys-lions game? Should an article be made for the referee debacle in the cowboys-Lions game? It could be called Decker Reported Eligible, similar to the Dez Caught It article, or the Fail Mary article. It did receive coverage 8 days after the inci...

 

Ralph Linton

American anthropologist Ralph LintonFrontispiece of 1958's Ralph Linton, 1893–1953: A Biographical MemoirBorn(1893-02-27)February 27, 1893Philadelphia, Pennsylvania, U.S.DiedDecember 24, 1953(1953-12-24) (aged 60)New Haven, Connecticut, U.S.Alma materUniversity of PennsylvaniaColumbia UniversityKnown forThe Study of Man (1936)The Tree of Culture (1955)AwardsViking Fund Medal (1951)Scientific careerFieldsCultural anthropologyInstitutionsField Museum, University of Wisconsin–...

フィリップス・アウフスティン・イメンラート

フィリップス・A・イメンラートPhilips Augustijn Immenraet 人物のいる風景画(1666/1679)誕生日 (1627-02-21) 1627年2月21日出生地 アントウェルペン死没年 1679年9月25日(1679-09-25)（52歳没）死没地 アントウェルペンテンプレートを表示 フィリップス・アウフスティン・イメンラート（Philips Augustijn Immenraet[1]、1627年2月21日 - 1679年9月25日）は、フランドルの画家である。風景画を描�...

 

Georges Catroux

Si ce bandeau n'est plus pertinent, retirez-le. Cliquez ici pour en savoir plus. Certaines informations figurant dans cet article ou cette section devraient être mieux reliées aux sources mentionnées dans les sections « Bibliographie », « Sources » ou « Liens externes » (mai 2019). Vous pouvez améliorer la vérifiabilité en associant ces informations à des références à l'aide d'appels de notes. Pour les articles homonymes, voir Catroux. Georges Cat...