Charges| Charges |
In General > s.a. G-parity;
Isospin; noether
charge; topology in physics.
* 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.
In a Gauge Theory > s.a. electromagnetism; gauge theory.
* Abelian electric charge: The electric charge of an isolated system
is
Q = 
S
Fab dsab =
S F 0b
dsb = S Ea
dsa ,
where S is any closed (N–1)-surface in N+1
spacetime dimensions enclosing the system, possibly a surface at infinity, Sinfty.
* Non-abelian theory:
The electric and magnetic charges Q and F have
internal indices; For a Yang-Mills theory they are, respectively,
Q ij
= (4
)–1 S Eaij
dsa and P = S *Fab dsab =
S Ba dsa ;
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-in].
@ Abelian, electric charge: Segers et al AJP(09)jan
[Einstein's "little machine" to measure small charges].
@ General references: Sniatycky & Schwartz RPMP(94)
[no local non-abelian charge density]; Marolf
ht/00-in;
Lyre IJMPD(00)gq [equivalence
principle for charge]; Barnich
CQG(03)ht [boundary
charges]; McMullan Sigma(07)ht;
> s.a. topology in physics.
Other Systems > s.a. particle
types.
@ In gravity: Hollands et al PRD(05)ht/05 [counter-term
subtraction definition]; > s.a.
Anti-de Sitter; 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: Staruszkiewicz AP(89);
Rañada & Trueba PLB(98)ht [topological];
Rañada ht/99;
Olive ht/01-in;
Allen et al ht/02;
Pérez-Lorenzana & Pires
MPLA(03)
[higher dimensions]; Barone & Helayel-Neto qp/04-in,
comment MacKenzie et al qp/05 [and
Aharonov-Bohm
effect]; Minguzzi et al JPA(06)
[from weak gauge principle]; > s.a. experiments, kaluza-klein.
@ Fractional charges: Wilczek cm/02-in;
Gies et al PRL(06)
[unquantized 'millicharged fermions', search]; > s.a. Hall
Effect [fractional]; Quarks.
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send feedback and suggestions to bombelli at olemiss.edu – modified
15 jun 2009