Scalar Field Theories  

In General > s.a. Kemmer Equation.
* 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).
* Fields equations: They are usually taken to satisfy the Klein-Gordon equation, but a general field equation with self-interaction is

– V'() = 0 ,

and they can be described by the Kemmer equation.
* Massless: According to 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:= .

Specific Theories > s.a. black holes; Boson Stars; klein-gordon fields.
* 4 theory: In 1970 Kurt Symanzik proposed a 'precarious' 4-theory with a negative quartic coupling constant as a valid candidate for an asymptotically free theory of strong interactions; With positive , 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 3 theory: Bender et al PRL(04)ht [acceptable quantum field theory].
@ 4 theory: Al-Kuwari PLB(96) [interpretation]; Destri & de Vega PRD(06)hp/04 [thermalization]; Kleefeld JPA(06)ht/05 [Symanzik's theory]; Wreszinski & Jaekel AP(08)mp/06 [s+1 dimensions, non-relativistic limit]; Frasca IJMPA(07) [proof of triviality], IJMPA(07)ht [broken phase, spectrum]; Wolff PRD-a0902 [simulation and triviality check]; Kuppan et al IJMPA(09); Frasca a0907 [quartic theories, exact solutions]; Rodigast & Schuster a0908 [quantum-gravity corrections]; > s.a. lattice field theory; critical phenomena; quantum field theory techniques and types.
@ Special situations: Carrington et al PRD(00)ht/99 [1+1 in a box]; Mateos a0907-in [on a half-line].
@ Other theories: Klauder PRL(94), ht/98 [modified, non-trivial 4]; Harrivel mp/06 [p+1, Butcher series expansion of solutions].
> Other theories: see axions; Chameleon; dilaton; Galileon Field; Ghost Field; kaluza-klein models; quintessence; scalar-tensor.

References > s.a. modified electrodynamics [scalar].
@ Overview: Brans gq/97 [in gravity]; Kleinert & Schulte-Frohlinde 01 [4].
@ Types: Anco & Wald PRD(89) [Lie algebra-valued]; Unruh & Weiss PRD(89) [massless].
@ Massive: Helfer JMP(93) [and null infinity]; Garavaglia ht/01-in [Green function].
@ Massless: Frasca MPLA(09) [mapping to Yang-Mills theory].
@ Twisted fields: Isham PRS(78); Banach & Dowker JPA(79), JPA(79).
@ Coupled to general relativity: Christodoulou CMP(86), CMP(86), CMP(87) [dynamics]; Faraoni gq/98-in [value of coupling]; Ayón-Beato et al PRD(05)ht [non-linear fields that do not curve spacetime].
@ On generalized spacetime: Kosinski et al PRD(00) [-deformed Minkowski]; Schunck & Wainwright JMP(05) [supersphere]; Girelli & Livine a0910-in [with coset momentum space, and non-commutativity]; > s.a. 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]; Mota & Shaw PRD(07)ap/06 [light, in particle physics and cosmology].

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