BF
Theory| BF
Theory |
In General > s.a. branes; lattice
gauge theory; yang-mills gauge theory.
* Idea: A topological
gauge theory, used as model for gravity, with variables
Aai and B,
and action
S = 
M
tr(B 
F)
.
@ General references: Broda ht/05-in
[summary].
@ Spin foam: Baez LMP(96)qa/95; Baez LNP(00)gq/99;
Maran gq/03, gq/03,
PRD(04)gq.
@ Discretized: Kawamoto et al NPB(00)ht/99 [4D];
Oriti & Williams PRD(01)gq/00 [and
Barrett-Crane model]; Mnev ht/06 [simplicial].
@ Connections: Cattaneo et al JMP(95),
CMP(99)m.DG/98;
Cattaneo et al LMP(00)m.QA [Wilson
loops].
@ Canonical-symplectic form: Mondragón & Montesinos JMP(06)gq/04,
Montesinos CQG(06)gq [4D, covariant].
@ Related topics: Waelbroeck CMP(95)gq/93 [flat
spacetimes]; Cattaneo et al JMP(95), NPB(95)
[knots]; Freidel & Krasnov CQG(99)ht/98 [volume].
@ Massive: Landim & Almeida PLB(01)ht/00 [topological
mass, D dimensions];
Landim PLB(02)
[D dimensions].
@ With other fields: Leitgeb et al NPB(99)ht [2D
with matter]; Bizdadea et al IJMPA(06)-a0704 [3-form
gauge fields]; Fairbairn & Pérez a0709 [extended matter].
@ Other versions: Husain & Major NPB(97)gq,
Momen PLB(97)ht/96 [bounded
regions]; Ikeda JHEP(00)ht,
JHEP(01)ht [deformation];
Barbero & Villaseñor
PRD(01)gq/00 [for
Husain-Kuchar model]; Diakonov & Petrov G&C(02)ht/01 [Yang-Mills
and
string theory]; Blasi et al NPB(06)
[non-commutative, 2D]; Borowiec et al IJGMP(06)
[covariant, Lagrangian].
And Gravity > s.a. first-order
actions; 3D
gravity; canonical
general relativity, connection and other
formulations; gravity
theories.
* Idea: Gravity is
not a topological theory, but one can write down its action as that of a
BF theory (B F,
with B = e e)
with an added term of the type *B F,
with a coefficient that corresponds to the Immirzi parameter.
* Motivation: It
is taken as a starting point for spin-foam formulations of quantum gravity.
* Plebanski action:
For
complex general relativity one can write down a modified BF action,
S(A,B,
)
= M (B F + 
b abcd Bab Bcd)
d4x .
@ Plebanski action: Reisenberger CQG(99)gq/98 [complex
general relativity]; Buffenoir et al CQG(04)
[Hamiltonian analysis].
@ With arbitrary
Immirzi parameter: Holst PRD(96)gq/95 [for
Barbero Hamiltonian]; Capovilla et al CQG(01)gq.
@ Related topics: Constantinidis et al JHEP(02)ht/01 [symmetries
and gravity]; in Maran gq/05 [modified
SO(4,C) Plebanski theory]; Canfora NPB(05)ht [and
large-N expansion]; Mikovic gq/05-in
[with cosmological constant, as deformed SO(4,1)
theory], ht/06-in
[quantum gravity as broken phase of BF theory]; Cuesta & Montesinos PRD(07).
> Related topics: see holography; spherical
symmetry.
Quantized > s.a. 2D quantum
gravity; Feynman Diagram.
* Idea: The transition
amplitude for the 3D BF theory with cosmological constant is given by the Turaev-Viro
state-sum invariant.
@ References: Bi & Gegenberg CQG(94)gq/93 [loop/connection];
Cattaneo & Rossi CMP(01)m.QA/00 [n-dimensional,
Batalin-Vilkovisky].
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Send feedback and suggestions to bombelli at olemiss.edu – Modified
18 jun 2008