Editing Lorentz covariance (section)

==Lorentz violating models==
{{See also|Modern searches for Lorentz violation}}

In standard field theory, there are very strict and severe constraints on [[Renormalization group#Relevant and irrelevant operators and universality classes|marginal and relevant]] Lorentz violating operators within both [[Quantum electrodynamics|QED]] and the [[Standard Model]]. Irrelevant Lorentz violating operators may be suppressed by a high [[cutoff (physics)|cutoff]] scale, but they typically induce marginal and relevant Lorentz violating operators via radiative corrections. So, we also have very strict and severe constraints on irrelevant Lorentz violating operators.

Since some approaches to [[quantum gravity]] lead to violations of Lorentz invariance,<ref name="Mattingly">{{Cite journal|doi=10.12942/lrr-2005-5|pmid=28163649|pmc=5253993|title=Modern Tests of Lorentz Invariance|year=2005|last1=Mattingly|first1=David|journal=Living Reviews in Relativity|volume=8|issue=1|pages=5|doi-access=free |arxiv = gr-qc/0502097 |bibcode = 2005LRR.....8....5M }}</ref> these studies are part of [[phenomenological quantum gravity]]. Lorentz violations are allowed in [[string theory]], [[supersymmetry]] and [[Hořava–Lifshitz gravity]].<ref>{{Cite journal |arxiv = 1709.03434|doi = 10.1038/s41567-018-0172-2|title = Neutrino interferometry for high-precision tests of Lorentz symmetry with Ice ''Cube''|journal = Nature Physics|volume = 14|issue = 9|pages = 961–966|year = 2018|last1 = Collaboration|first1 = IceCube|last2 = Aartsen|first2 = M. G.|last3 = Ackermann|first3 = M.|last4 = Adams|first4 = J.|last5 = Aguilar|first5 = J. A.|last6 = Ahlers|first6 = M.|last7 = Ahrens|first7 = M.|last8 = Al Samarai|first8 = I.|last9 = Altmann|first9 = D.|last10 = Andeen|first10 = K.|last11 = Anderson|first11 = T.|last12 = Ansseau|first12 = I.|last13 = Anton|first13 = G.|last14 = Argüelles|first14 = C.|last15 = Auffenberg|first15 = J.|last16 = Axani|first16 = S.|last17 = Bagherpour|first17 = H.|last18 = Bai|first18 = X.|last19 = Barron|first19 = J. P.|last20 = Barwick|first20 = S. W.|last21 = Baum|first21 = V.|last22 = Bay|first22 = R.|last23 = Beatty|first23 = J. J.|last24 = Becker Tjus|first24 = J.|last25 = Becker|first25 = K. -H.|last26 = BenZvi|first26 = S.|last27 = Berley|first27 = D.|last28 = Bernardini|first28 = E.|last29 = Besson|first29 = D. Z.|last30 = Binder|first30 = G.|bibcode = 2018NatPh..14..961I|s2cid = 59497861|display-authors = 29}}</ref>

Lorentz violating models typically fall into four classes:{{Citation needed|date=October 2011}}

* The laws of physics are exactly [[Lorentz covariant]] but this symmetry is [[spontaneously broken]]. In [[special relativity|special relativistic]] theories, this leads to [[phonon]]s, which are the [[Goldstone boson]]s. The phonons travel at ''less'' than the [[speed of light]].
* Similar to the approximate Lorentz symmetry of phonons in a lattice (where the speed of sound plays the role of the critical speed), the Lorentz symmetry of special relativity (with the speed of light as the critical speed in vacuum) is only a low-energy limit of the laws of physics, which involve new phenomena at some fundamental scale. Bare conventional "elementary" particles are not point-like field-theoretical objects at very small distance scales, and a nonzero fundamental length must be taken into account. Lorentz symmetry violation is governed by an energy-dependent parameter which tends to zero as momentum decreases.<ref name="Gonzalez-MestresMoriond1995">{{Cite journal|title=Properties of a possible class of particles able to travel faster than light |url=https://archive.org/details/arxiv-astro-ph9505117 |journal=Dark Matter in Cosmology |pages=645 |author=Luis Gonzalez-Mestres |date=1995-05-25 |arxiv=astro-ph/9505117 |bibcode=1995dmcc.conf..645G }}</ref> Such patterns require the existence of a [[preferred frame|privileged local inertial frame]] (the "vacuum rest frame"). They can be tested, at least partially, by ultra-high energy cosmic ray experiments like the [[Pierre Auger Observatory]].<ref name="Gonzalez-MestresICRC97">{{Cite journal|title=Absence of Greisen-Zatsepin-Kuzmin Cutoff and Stability of Unstable Particles at Very High Energy, as a Consequence of Lorentz Symmetry Violation |journal=Proceedings of the 25th International Cosmic Ray Conference (Held 30 July - 6 August) |author=Luis Gonzalez-Mestres |volume = 6|pages=113 |date=1997-05-26 |bibcode = 1997ICRC....6..113G|arxiv=physics/9705031}}</ref>
* The laws of physics are symmetric under a [[deformation theory|deformation]] of the Lorentz or more generally, the [[Poincaré group]], and this deformed symmetry is exact and unbroken. This deformed symmetry is also typically a [[quantum group]] symmetry, which is a generalization of a group symmetry. [[Deformed special relativity]] is an example of this class of models. The deformation is scale dependent, meaning that at length scales much larger than the Planck scale, the symmetry looks pretty much like the Poincaré group. Ultra-high energy cosmic ray experiments cannot test such models.
* [[Very special relativity]] forms a class of its own; if [[CP symmetry|charge-parity]] (CP) is an exact symmetry, a subgroup of the Lorentz group is sufficient to give us all the standard predictions. This is, however, not the case.

Models belonging to the first two classes can be consistent with experiment if Lorentz breaking happens at Planck scale or beyond it, or even before it in suitable [[preon]]ic models,<ref name="Gonzalez-MestresCrete2013">{{Cite journal|doi=10.1051/epjconf/20147100062|title=Ultra-high energy physics and standard basic principles. Do Planck units really make sense?|journal=EPJ Web of Conferences|volume=71|pages=00062|year=2014|author=Luis Gonzalez-Mestres|url=http://www.epj-conferences.org/articles/epjconf/pdf/2014/08/epjconf_icnfp2013_00062.pdf|bibcode=2014EPJWC..7100062G|doi-access=free}}</ref> and if Lorentz symmetry violation is governed by a suitable energy-dependent parameter. One then has a class of models which deviate from Poincaré symmetry near the Planck scale but still flows towards an exact Poincaré group at very large length scales.  This is also true for the third class, which is furthermore protected from radiative corrections as one still has an exact (quantum) symmetry.

Even though there is no evidence of the violation of Lorentz invariance, several experimental searches for such violations have been performed during recent years. A detailed summary of the results of these searches is given in the Data Tables for Lorentz and CPT Violation.<ref name="DataTables">
{{cite arXiv
 |first1=V.A. |last1=Kostelecky |first2=N. |last2=Russell
 |title=Data Tables for Lorentz and CPT Violation
 |year=2010
 |eprint=0801.0287v3
 |class=hep-ph
}}</ref>

Lorentz invariance is also violated in QFT assuming non-zero temperature.<ref>{{Cite book|last1=Laine|first1=Mikko|last2=Vuorinen|first2=Aleksi|date=2016|title=Basics of Thermal Field Theory|series=Lecture Notes in Physics|volume=925|language=en-gb|doi=10.1007/978-3-319-31933-9|issn=0075-8450|arxiv=1701.01554|bibcode=2016LNP...925.....L|isbn=978-3-319-31932-2|s2cid=119067016}}</ref><ref>{{Cite journal|last=Ojima|first=Izumi|date=January 1986|title=Lorentz invariance vs. temperature in QFT|journal=Letters in Mathematical Physics|language=en|volume=11|issue=1|pages=73–80|doi=10.1007/bf00417467|issn=0377-9017|bibcode=1986LMaPh..11...73O|s2cid=122316546}}</ref><ref>{{Cite web|url=https://physics.stackexchange.com/q/131197|title=Proof of Loss of Lorentz Invariance in Finite Temperature Quantum Field Theory|website=Physics Stack Exchange|access-date=2018-06-18}}</ref>

There is also growing evidence of Lorentz violation in [[Weyl semimetal]]s and [[Dirac semimetal]]s.<ref>{{Cite journal |doi = 10.1126/sciadv.1603266|title = Discovery of Lorentz-violating type II Weyl fermions in LaAl ''Ge''|journal = Science Advances|volume = 3|issue = 6|pages = e1603266|year = 2017|last1 = Xu|first1 = Su-Yang|last2 = Alidoust|first2 = Nasser|last3 = Chang|first3 = Guoqing|last4 = Lu|first4 = Hong|last5 = Singh|first5 = Bahadur|last6 = Belopolski|first6 = Ilya|last7 = Sanchez|first7 = Daniel S.|last8 = Zhang|first8 = Xiao|last9 = Bian|first9 = Guang|last10 = Zheng|first10 = Hao|last11 = Husanu|first11 = Marious-Adrian|last12 = Bian|first12 = Yi|last13 = Huang|first13 = Shin-Ming|last14 = Hsu|first14 = Chuang-Han|last15 = Chang|first15 = Tay-Rong|last16 = Jeng|first16 = Horng-Tay|last17 = Bansil|first17 = Arun|last18 = Neupert|first18 = Titus|last19 = Strocov|first19 = Vladimir N.|last20 = Lin|first20 = Hsin|last21 = Jia|first21 = Shuang|last22 = Hasan|first22 = M. Zahid|pmid = 28630919|pmc = 5457030|bibcode = 2017SciA....3E3266X|doi-access = free}}</ref><ref>{{Cite journal | doi=10.1038/s41467-017-00280-6| pmid=28811465| pmc=5557853| title=Lorentz-violating type-II Dirac fermions in transition metal dichalcogenide PtTe2| journal=Nature Communications| volume=8| issue=1| pages=257| year=2017| last1=Yan| first1=Mingzhe| last2=Huang| first2=Huaqing| last3=Zhang| first3=Kenan| last4=Wang| first4=Eryin| last5=Yao| first5=Wei| last6=Deng| first6=Ke| last7=Wan| first7=Guoliang| last8=Zhang| first8=Hongyun| last9=Arita| first9=Masashi| last10=Yang| first10=Haitao| last11=Sun| first11=Zhe| last12=Yao| first12=Hong| last13=Wu| first13=Yang| last14=Fan| first14=Shoushan| last15=Duan| first15=Wenhui| last16=Zhou| first16=Shuyun| author-link16= Shuyun Zhou|bibcode=2017NatCo...8..257Y| arxiv=1607.03643}}</ref><ref>{{cite journal | arxiv=1603.08508| doi=10.1038/nphys3871| title=Experimental observation of topological Fermi arcs in type-II Weyl semimetal MoTe2| journal=Nature Physics| volume=12| issue=12| pages=1105–1110| year=2016| last1=Deng| first1=Ke| last2=Wan| first2=Guoliang| last3=Deng| first3=Peng| last4=Zhang| first4=Kenan| last5=Ding| first5=Shijie| last6=Wang| first6=Eryin| last7=Yan| first7=Mingzhe| last8=Huang| first8=Huaqing| last9=Zhang| first9=Hongyun| last10=Xu| first10=Zhilin| last11=Denlinger| first11=Jonathan| last12=Fedorov| first12=Alexei| last13=Yang| first13=Haitao| last14=Duan| first14=Wenhui| last15=Yao| first15=Hong| last16=Wu| first16=Yang| last17=Fan| first17=Shoushan| last18=Zhang| first18=Haijun| last19=Chen| first19=Xi| last20=Zhou| first20=Shuyun| bibcode=2016NatPh..12.1105D| s2cid=118474909}}</ref><ref>{{Cite journal | doi=10.1038/nmat4685 |pmid = 27400386|title = Spectroscopic evidence for a type II Weyl semimetallic state in MoTe2|journal = Nature Materials|volume = 15|issue = 11|pages = 1155–1160|year = 2016|last1 = Huang|first1 = Lunan|last2 = McCormick|first2 = Timothy M.|last3 = Ochi|first3 = Masayuki|last4 = Zhao|first4 = Zhiying|last5 = Suzuki|first5 = Michi-To|last6 = Arita|first6 = Ryotaro|last7 = Wu|first7 = Yun|last8 = Mou|first8 = Daixiang|last9 = Cao|first9 = Huibo|last10 = Yan|first10 = Jiaqiang|last11 = Trivedi|first11 = Nandini|last12 = Kaminski|first12 = Adam|bibcode = 2016NatMa..15.1155H|arxiv = 1603.06482|s2cid = 2762780}}</ref><ref>{{Cite journal |doi = 10.1038/ncomms13643|pmid = 27917858|pmc = 5150217|title = Discovery of a new type of topological Weyl fermion semimetal state in MoxW1−xTe2|journal = Nature Communications|volume = 7|pages = 13643|year = 2016|last1 = Belopolski|first1 = Ilya|last2 = Sanchez|first2 = Daniel S.|last3 = Ishida|first3 = Yukiaki|last4 = Pan|first4 = Xingchen|last5 = Yu|first5 = Peng|last6 = Xu|first6 = Su-Yang|last7 = Chang|first7 = Guoqing|last8 = Chang|first8 = Tay-Rong|last9 = Zheng|first9 = Hao|last10 = Alidoust|first10 = Nasser|last11 = Bian|first11 = Guang|last12 = Neupane|first12 = Madhab|last13 = Huang|first13 = Shin-Ming|last14 = Lee|first14 = Chi-Cheng|last15 = Song|first15 = You|last16 = Bu|first16 = Haijun|last17 = Wang|first17 = Guanghou|last18 = Li|first18 = Shisheng|last19 = Eda|first19 = Goki|last20 = Jeng|first20 = Horng-Tay|last21 = Kondo|first21 = Takeshi|last22 = Lin|first22 = Hsin|last23 = Liu|first23 = Zheng|last24 = Song|first24 = Fengqi|last25 = Shin|first25 = Shik|last26 = Hasan|first26 = M. Zahid|bibcode = 2016NatCo...713643B|arxiv = 1612.05990}}</ref>