Interaction |

**In General**
> s.a. causality [action at a distance]; classical
field theory; force; particles;
particle physics; quantum field theory.

* __Idea__: Generalizes the concept of force,
and it is important to clarify in what sense it generalizes it, if one wants to understand,
for example, what the ordinary concept of force and weak processes have in common.

* __Remark__: In non-relativistic mechanics
an interaction is represented by a local force, transmitted by action at a distance; In
relativistic mechanics, an interaction is described by a classical or quantum field theory.

* __Hope__: Be able to derive the existing
interactions from a self-consistency argument using effective theory ideas and phase
transitions for steady states far from equilibrium, which may exhibit universality;
Something like this has worked for ergodicity and equilibrium steady states.

**Static Forces**

* __Idea__: One can derive the
form of the potential for the static interaction between two field sources
by using properties of the field itself; In Minkowski space,

*V*(**x** − **x***'*)
~ ∫_{ \(\mathbb R\)}
Δ_{F}(*t* − *t'*,
**x** − **x***'*) d*t* ,

or by some other procedure involving the Schwinger propagator.

* __Result__: If a force is
transmitted by a quantum of mass *m*, the static force is

*F* = *β* e^{−mr}
/ *r*^{2} ,

where *β* depends on the interacting particles and the way they couple;
For a quantum of odd spin, or *s* > 2, *β* = 0, so there can
be no static force, e.g., from neutrinos.

* __And spin__: For a force transmitted by
a boson of spin *s* between two charges *Q*_{1}
and *Q*_{2}, the coefficient that tells the strength
and sign of the force is (−1)^{s}
*Q*_{2}*Q*_{2};
This comes from the static limit of an integral with currents and boson propagators,
which depend on *s*, in quantum field theory; Thus, the graviton must have
*s* = 0 (Newtonian theory) or *s* = 2 (general relativity).

@ __And spin__: Deser AJP(05)aug-gq/04.

**Specific Interactions** > s.a. force [exchange
interaction]; higher-spin fields; types
of field theories and quantum field theories.

@ __Overview__: Chamseddine ht/05-ln
[and representations of Poincaré Lie algebra, supersymmetry].

@ __Strong__: Vigier PLA(03) [in terms of electromagnetism];
> s.a. QCD.

> __Weak__: see electroweak
theory; standard model.

> __Gravitational__: see general relativity;
theories of gravity.

> __Electromagnetic__: see electromagnetism.

> __Unified__: see GUTS;
unified theories [including geometric aspects].

**Other References** > s.a. category theory.

@ __Consistent interactions__: Kaparulin et al JHEP(13)-a1210 [identifying all consistent interactions from involution of field equations];
Lyakhovich & Sharapov MPLA(14)-a1402;
Kaparulin et al JPA(16)-a1510 [compatible with global symmetries and conservation laws of a given free theory];
> s.a. types of gauge theories.

@ __Effective interactions__: Holstein AJP(99)may [and Rayleigh scattering],
AJP(04)mar [and H atom];
> s.a. effective quantum field theory.

@ __Non-locality in time__: Gainutdinov et al PLA(02) [atom-surroundings].

@ __Instantaneous interactions__: Bebronne PLB(08)-a0806 [in massive gravity].
@ __Other models and related topics__: Bastin et al IJTP(79) [combinatorial hierarchy model and "Schnurs"];
Jenkins ht/04-proc
[composite mediators and Lorentz symmetry breaking];
Dean PS(12) [fluctuation-induced interactions, non-equilibrium aspects];
Edwards JHEP(16)-a1507 [contact interactions between particle worldlines];
Roederer a1512
[pragmatic information and interaction between material bodies as a primary concept];
Laudato a1703
[geometric description of interactions, and non-commutative geometry];
> s.a. Three-Body Forces [ternary].

@ __Other interactions__:
Slad a1811 [proposal, and phenomenology];
Fayet PRD(19)-a1809 [bounds on the strength of a new force];
Fabbrichesi & Urbano a1902 [dark force weaker than gravity?];
Metsaev a2005 [3D, cubic interactions of arbitrary spin fields].

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