Scalar Field Theories  

In General > s.a. Kemmer Equation; laplacian operator.
* Examples: Dilatons in string theory; Nambu-Goldstone bosons; Higgs fields; Supersymmetric partners of spin-1/2 particles; Scalar component of gravity; Cosmologically motivated fields such as quintessence (> s.a. cosmological models).
* Field equations: They are often taken to satisfy the Klein-Gordon equation, but a more general field equation with self-interaction is

\[\square\,\phi - V'(\phi) = 0\;,\]

and they can be described by the Kemmer equation.
* Scalar components of gravity: Scalar fields may couple to gravity in such a way that they give rise to an effective metric that depends on both the true spacetime metric and on the scalar field and its derivatives; Such fields can be classified as conformal and disformal, where the disformal ones introduce gradient couplings between scalar fields and the energy momentum tensor of other matter fields.

Types of Scalar Fields > s.a. parametrized theories.
* Massless: In quantum gravity they cannot exist as elementary particles, because they would acquire a mass from interactions with topological fluctuations.
* 1+1 dimensions: There can be no massless scalar particle even without quantum gravity, because there could be arbitrarily long wavelength fluctuations, with an arbitrarily small energy cost – the energy cost, for fixed amplitude, would decrease as the size of the region increases; This does not happen in higher space dimensions because the volume integral grows faster with distance; What can exist in 1+1 dimensions is a theory of the gradient, B:= ∇φ.
@ Types: Anco & Wald PRD(89) [Lie algebra-valued]; Unruh & Weiss PRD(89) [massless].
@ Massive: Helfer JMP(93) [and null infinity]; Garavaglia ht/01-conf [Green function].
@ Massless: Frasca MPLA(09) [mapping to Yang-Mills theory].
@ Twisted fields: Isham PRS(78); Banach & Dowker JPA(79), JPA(79).

Specific Theories > s.a. black holes; Boson Stars; klein-gordon fields.
* λφ^4 theory: In 1970 Kurt Symanzik proposed a 'precarious' \(\lambda\phi^4\) theory with a negative quartic coupling constant as a valid candidate for an asymptotically free theory of strong interactions; With positive \(\lambda\), the potential is always positive, therefore it gives rise only to repulsive forces, and we can consider the theory not to have any bound states; The quantum theory is trivial.
* Chameleon field: A field whose mass depends on the local matter density.
@ i φ^3 theory: Bender et al PRL(04)ht [acceptable quantum field theory].
@ λφ^4 theory: Al-Kuwari PLB(96) [interpretation]; Destri & de Vega PRD(06)hp/04 [thermalization]; Kleefeld JPA(06)ht/05 [Symanzik's theory]; Wreszinski & Jäkel AP(08)mp/06 [s+1 dimensions, non-relativistic limit]; Frasca IJMPA(07) [proof of triviality], IJMPA(07)ht [broken phase, spectrum]; Wolff PRD(09)-a0902 [simulation and triviality check]; Kuppan et al IJMPA(09); Frasca JNMP(11)-a0907 [quartic theories, exact solutions]; Rodigast & Schuster PRL(10)-a0908 [quantum-gravity corrections]; Cattaruzza et al AP(11)-a1010 [diagrammatic perturbative expansion in path-integral approach]; > s.a. lattice field theory; critical phenomena; quantum field theory techniques and types.
@ Special situations: Carrington et al PRD(00)ht/99 [1+1 dimensional, in a box]; Mateos a0907-in [on a half-line]; Novello & Hartmann a1904 [fields acted on by the gravitational field that do not generate a gravitational field].
@ Light scalars: Mota & Shaw PRD(07)ap/06 [particle physics and cosmology]; Damour & Donoghue CQG(10)-a1007 [phenomenology and couplings].
@ Other theories: Klauder PRL(94), ht/98 [modified, non-trivial λφ4]; Harrivel mp/06 [φp+1, Butcher series expansion of solutions]; Ferrari a0912 [non-polynomial interactions]; Faraoni & Zambrano PRD(10)-a1006 [stealth fields, stability]; Saxena et al a1806 [higher-order field theories].
> Other theories: see axions; Chameleon; Cosmon; dark-energy models; dilaton; Galileon Field; Ghost Field; kaluza-klein models; modified electrodynamics [scalar]; quintessence; scalar-tensor gravity; Symmetron Field.

References > s.a. green functions; thermodynamic systems [thermodynamic quantities and speed of sound].
@ Overview: Brans gq/97-fs [in gravity]; Kleinert & Schulte-Frohlinde 01 [\(\lambda\phi^4\)]; in Franklin 10 [IIb].
@ In a curved background: Bernardini & Bertolami AP(13)-a1212 [cosmological background, Hamiltonian]; Wohlfarth PRD(18)-a1804 [tangent bundle formalism, and canonical quantization]; > s.a. critical phenomena; Geometrization; wave phenomena [tails].
@ Coupled to general relativity: Christodoulou CMP(86), CMP(86), CMP(87) [dynamics]; Faraoni gq/98-proc [value of coupling]; Ayón-Beato et al PRD(05)ht [non-linear fields that do not curve spacetime]; Esposito et al IJGMP(11)-a1009 [complex fields, and cosmology]; Vernov PoS-a1201 [non-local scalar field]; Brax et al JCAP(12)-a1206 [scalar components of gravity, experimental aspects]; Sotiriou ln(14)-a1404.
@ On generalized spacetime: Kosiński et al PRD(00) [κ-deformed Minkowski]; Schunck & Wainwright JMP(05) [supersphere]; Girelli & Livine AIP(09)-a0910-proc [with coset momentum space, and non-commutativity]; > s.a. fractals in physics; klein-gordon fields; non-commutative field theory.
@ Related topics: Derrick JMP(64), Adib ht/02 [no stable, \(t\)-independent solutions]; Gudder JMP(94) [non-standard]; Frommert IJTP(97)gq/96 [and relativistic particles]; Faraoni PRD(12)-a1201 [scalar fields and effective perfect fluids]; Ibort et al PLA(12)-a1202 [tomographic description]; Balondo & Govaerts a1906 [global symmetries].
> Online resources: see Wikipedia page.

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