Charges |

**In General**
> s.a. G-parity; Isospin; noether
charge; topology in physics [topological charges].

* __Idea__: Loosely speaking,
a charge is a conserved quantity other than energy-momentum.

* __And conserved currents__:
When a charge is conserved because it is associated with a conserved
current, it can be calculated as a surface integral (see examples below);
> s.a. conservation laws.

> __Online resources__:
see Wikipedia page.

**In a Gauge Theory**
> s.a. electromagnetism; gauge theory.

* __Abelian electric charge__:
The electric charge of an isolated system is

*Q* = \(1\over2\)\(\displaystyle\oint_S\)
*F*^{ab} d*s*_{ab}
= \(\displaystyle\oint_S\) *F*^{ 0b}
d*s*_{b}
= \(\displaystyle\oint_S\) *E*_{a}
d*s*^{a} ,

where *S* is any closed (*N*−1)-surface in *N*+1
spacetime dimensions enclosing the system, possibly a surface at infinity,
*S*_{∞}.

* __Non-abelian theory__:
The electric and magnetic charges *Q* and *F* have
internal indices; For a Yang-Mills theory they are, respectively,

*Q*^{ i}_{j}
= \(1\over4\pi\)\(\displaystyle\oint_S\)
*E*_{a}^{i}_{j}
d*s*^{a} and *P*
= \(1\over2\)\(\displaystyle\oint_S\) **F*^{ab}
d*s*_{ab}
= \(\displaystyle\oint_S\) *B*_{a}
d*s*^{a} ;

Several electric and magnetic charges can actually be defined; 'Brane source
charge' is gauge invariant and localized but not conserved or quantized, 'Maxwell
charge' is gauge invariant and conserved but not localized or quantized, while
'Page charge' conserved, localized, and quantized but not gauge invariant
[@ Marolf ht/00-proc].

@ __Abelian, electric charge__: Segers et al AJP(09)jan [Einstein's "little machine" to measure small charges];
Dzhunushaliev a1002
[non-perturbative, finite quantum field theory corrections];
Gratus et al FP(19)-a1904 [on possible non-conservation].

@ __General references__: Sniatycky & Schwartz RPMP(94) [no local non-abelian charge density];
Marolf ht/00-proc;
Lyre IJMPD(00)gq [equivalence principle for charge];
Barnich CQG(03)ht [boundary charges];
McMullan Sigma(07)ht;
Altas et al a2105 [Einstein-Yang-Mills theory];
> s.a. topology in physics.

**Specific Systems and Particles**
> s.a. electron [decay]; particle types.

@ __In gravity__: Hollands et al PRD(05)ht/05 [counter-term subtraction definition];
Bousso et al PRD(18)-a1709 [asymptotic charges cannot be observed in finite retarded time];
Frodden & Hidalgo IJMPD(20)-a1911 [surface charges, different theories];
Godazgar et al PRL(20)-a2007 [asymptotic, method],
JHEP(20)-a2007 [dual, Hamiltonian derivation];
Oliveri & Speziale a2009 [dual];
> s.a. anti-de sitter space;
gravitational energy.

**References** > s.a. renormalization.

@ __General__: Klauder & Wheeler RMP(57) [re neutrinos];
Toussaint GRG(00)gq/99 [general relativity / gauge theory];
Hofer qp/00 [origin?].

@ __Quantization__: Rosen IJTP(79);
Staruszkiewicz AP(89);
Rañada & Trueba PLB(98)ht [topological];
Rañada ht/99;
Olive ht/01-conf;
Allen et al ht/02;
Pérez-Lorenzana & Pires MPLA(03) [higher dimensions];
Barone & Helayël-Neto qp/04-proc,
comment MacKenzie et al qp/05 [and Aharonov-Bohm effect];
Minguzzi et al JPA(06) [from weak gauge principle];
Buitrago a1404 [from 2-spinor approach to U(1) gauge theory];
Solha JGP(16)-a1409 [topological argument, without magnetic monopoles];
> s.a. experiments in physics; kaluza-klein theory;
monopoles [Dirac's argument].

@ __Fractional charges__: Wilczek in(02)cm;
Gies et al PRL(06) [unquantized 'millicharged fermions', search];
Semenoff a2003;
> s.a. Hall Effect [fractional]; Quarks;
types of dark matter.

main page
– abbreviations
– journals – comments
– other sites – acknowledgements

send feedback and suggestions to bombelli at olemiss.edu – modified 26 may 2021