Editing Scalar field (section)

=== Examples in quantum theory and relativity ===
* In [[quantum field theory]], a [[Bosonic field|scalar field]] is associated with spin-0 particles. The scalar field may be real or complex valued. Complex scalar fields represent charged particles. These include the [[Higgs field]] of the [[Standard Model]], as well as the charged [[pions]] mediating the [[strong nuclear interaction]].<ref>Technically, pions are actually examples of [[pseudoscalar meson]]s, which fail to be invariant under spatial inversion, but are otherwise invariant under Lorentz transformations.</ref>
* In the [[Standard Model]] of elementary particles, a scalar [[Higgs field]] is used to give the [[lepton]]s and [[W and Z bosons|massive vector bosons]] their mass, via a combination of the [[Yukawa interaction]] and the [[spontaneous symmetry breaking]]. This mechanism is known as the [[Higgs mechanism]].<ref>{{cite journal|author=P.W. Higgs|journal=Phys. Rev. Lett.|volume=13|issue=16|pages=508–509|date=Oct 1964|title=Broken Symmetries and the Masses of Gauge Bosons|doi=10.1103/PhysRevLett.13.508|bibcode = 1964PhRvL..13..508H |doi-access=free}}</ref> A candidate for the [[Higgs boson]] was first detected at CERN in 2012.
* In [[scalar theories of gravitation]] scalar fields are used to describe the gravitational field.
* [[Scalar–tensor theory|Scalar–tensor theories]] represent the gravitational interaction through both a tensor and a scalar. Such attempts are for example the [[Pascual Jordan|Jordan]] theory<ref>{{cite book |first=P. |last=Jordan |title=Schwerkraft und Weltall |publisher=Vieweg |location=Braunschweig |year=1955 |url=https://books.google.com/books?id=snJTcgAACAAJ }}</ref> as a generalization of the [[Kaluza–Klein theory]] and the [[Brans–Dicke theory]].<ref>{{cite journal |first1=C. |last1=Brans |first2=R. |last2=Dicke |title=Mach's Principle and a Relativistic Theory of Gravitation |journal=Phys. Rev. |volume=124 |issue=3 |pages=925 |year=1961 |doi=10.1103/PhysRev.124.925 |bibcode=1961PhRv..124..925B }}</ref>
** Scalar fields like the Higgs field can be found within scalar–tensor theories, using as scalar field the Higgs field of the [[Standard Model]].<ref>{{cite journal |first=A. |last=Zee |title=Broken-Symmetric Theory of Gravity |journal=Phys. Rev. Lett. |volume=42 |issue=7 |pages=417–421 |year=1979 |doi=10.1103/PhysRevLett.42.417 |bibcode=1979PhRvL..42..417Z }}</ref><ref>{{cite journal |first1=H. |last1=Dehnen |first2=H. |last2=Frommert |first3=F. |last3=Ghaboussi |title=Higgs field and a new scalar–tensor theory of gravity |journal=Int. J. Theor. Phys. |volume=31 |issue=1 |pages=109 |year=1992 |doi=10.1007/BF00674344 |bibcode=1992IJTP...31..109D |s2cid=121308053 }}</ref> This field interacts gravitationally and [[Yukawa interaction|Yukawa]]-like (short-ranged) with the particles that get mass through it.<ref>{{cite journal |first1=H. |last1=Dehnen |first2=H. |last2=Frommmert |title=Higgs-field gravity within the standard model |journal=Int. J. Theor. Phys. |volume=30 |issue=7 |pages=985–998 [p. 987] |year=1991 |doi=10.1007/BF00673991 |bibcode=1991IJTP...30..985D |s2cid=120164928 }}</ref>
* Scalar fields are found within superstring theories as [[dilaton]] fields, breaking the conformal symmetry of the string, though balancing the quantum anomalies of this tensor.<ref>{{cite arXiv |first=C. H. |last=Brans |title=The Roots of scalar–tensor theory |eprint=gr-qc/0506063 |year=2005 }}</ref>
* Scalar fields are hypothesized to have caused the high accelerated expansion of the early universe ([[Inflation (cosmology)|inflation]]),<ref>{{cite journal |first=A. |last=Guth |title=Inflationary universe: A possible solution to the horizon and flatness problems |journal=Phys. Rev. D |volume=23 |pages=347–356 |year=1981 |issue=2 |doi=10.1103/PhysRevD.23.347 |bibcode=1981PhRvD..23..347G |doi-access=free }}</ref> helping to solve the [[horizon problem]] and giving a hypothetical reason for the non-vanishing [[cosmological constant]] of cosmology. Massless (i.e. long-ranged) scalar fields in this context are known as [[inflaton]]s. Massive (i.e. short-ranged) scalar fields are proposed, too, using for example Higgs-like fields.<ref>{{cite journal |first1=J. L. |last1=Cervantes-Cota |first2=H. |last2=Dehnen |title=Induced gravity inflation in the SU(5) GUT |journal=Phys. Rev. D |volume=51 |pages=395–404 |year=1995 |issue=2 |doi=10.1103/PhysRevD.51.395 |pmid=10018493 |arxiv=astro-ph/9412032 |bibcode=1995PhRvD..51..395C |s2cid=11077875 }}</ref>