Dear Jacques,

There is a large literature on coupling matter to loop quantum gravity and spin foam models as well as extensions to supergravity, higher dimensional gravity, branes, etc. All forms of matter have been coupled including fermions, Maxwell and Yang-Mills, scalars, supersymmetric extensions, p-form gauge fields.

These are all constructed by hand by adding degrees of freedom by enlarging the gauge group that defines the labelings on spin networks. There is also a new point of view about matter, which is that it is emergent from spin foam and some other background independent models of quantum spacetime, because there exist automatically coherent excitations that can be interpreted as chiral matter fields. This is work of Markopoulou and collaborators: F.Markopoulou hep-th/0604120, D. Krebs and F. Markopoulou gr-qc/0510052,, S. Bilson-Thompson, F. Markopoulou, LS hep-th/0603022. This is of course to be preferred if it works as it is much more restrictive, but there is much here to be done here.

Some references to the old approach of adding matter by hand are in my review paper hep-th/0408048, where there is also a list of open problems (not every important question has been solved!). Below are a small set of references found quickly, sorry for the sloppiness of the listing.

Also, as to what we mean by LQG and spin foam models being background independent, look at Rovelli’s book and my hep-th/0507235.

As to Georgi’s objection, there is a test case, which is 2+1 gravity coupled to matter. There are no gravitons but for any Feynman diagram of the matter theory there are gravitational degrees of freedom. The theory seems consistent for all forms of matter it is coupled to. As shown by Freidel and Livine, hep-th/0512113, one can also in this case integrate out the matter degrees of freedom to find an effective field theory on kappa-Minkowski spacetime.

Below are the references, broken up into categories.

For the Hamiltonian version of LQG the coupling to all matter fields was worked out in detail in several early papers, see for example, the following and references cited:

Ashtekar et. Al. Phys.Rev. D40 (1989) 2572

gr-qc/9705019 [abs, ps, pdf, other] :

Title: QSD V : Quantum Gravity as the Natural Regulator of Matter Quantum Field Theories

Authors: Thomas Thiemann

Comments: 34p, LATEX

Journal-ref: Class.Quant.Grav. 15 (1998) 1281-1314

Thomas Thiemann gr-qc/0110034 [abs, ps, pdf, other] :

Title: Introduction to Modern Canonical Quantum General Relativity

hep-th/9210110 [abs, ps, pdf, other] :

Title: Quantum Einstein-Maxwell Fields: A Unified Viewpoint from the Loop Representation

Authors: R. Gambini, J. Pullin

Comments: 13pp. no figures, Revtex, UU-HEP-92/9, IFFI 92-11

Journal-ref: Phys.Rev. D47 (1993) 5214

For coupling of the path integral or spin foam formulation to Yang-Mills fields:

gr-qc/0210051 [abs, ps, pdf, other] :

Title: Spin Foam Models of Yang-Mills Theory Coupled to Gravity

Authors: A. Mikovic

Comments: 10 pages

Journal-ref: Class.Quant.Grav. 20 (2003) 239-246

3. gr-qc/0207041 [abs, ps, pdf, other] :

Title: A spin foam model for pure gauge theory coupled to quantum gravity

Authors: Daniele Oriti, Hendryk Pfeiffer

Comments: 18 pages, LaTeX, 1 figure, v2: details clarified, references added

Journal-ref: Phys.Rev. D66 (2002) 124010

Coupling to fermions (see the above general papers and:)

gr-qc/9705021 [abs, ps, pdf, other] :

Title: Kinematical Hilbert Spaces for Fermionic and Higgs Quantum Field Theories

Authors: Thomas Thiemann

Comments: 26p, LATEX

Journal-ref: Class.Quant.Grav. 15 (1998) 1487-1512

gr-qc/9401011 [abs, ps, pdf, other] :

Title: Fermions in Quantum Gravity

Authors: H A Marales-Tecotl, C Rovelli

Comments: LaTeX file, 37 pages, no figures

Journal-ref: Phys.Rev.Lett. 72 (1994) 3642-3645

hep-th/9703112 [abs, ps, pdf, other] :

Title: Quantization of Diffeomorphism-Invariant Theories with Fermions

Authors: John C. Baez, Kirill V. Krasnov

Comments: 28 pages, latex, 7 ps-files (included) are needed to process the source file

Journal-ref: J.Math.Phys. 39 (1998) 1251-1271

SLAC-comments: Published in J.Math.Phys.39:1251-1271,1998

gr-qc/9506029 [abs, ps, pdf, other] :

Title: Quantum Loop Representation for Fermions coupled to Einstein-Maxwell field

Authors: Kirill V.Krasnov

Comments: 28 pages, REVTeX 3.0, 15 uuencoded ps-figures. The construction of the representation has been changed so that the representation space became irreducible. One part is removed because it developed into a separate paper; some corrections added

Journal-ref: Phys.Rev. D53 (1996) 1874-1888

SLAC-comments: Published in Phys.Rev.D53:1874-1888,1996

For general matter couplings to spin foams

gr-qc/0602010 [abs, ps, pdf, other] :

Title: Group field theory formulation of 3d quantum gravity coupled to matter fields

Authors: Daniele Oriti, James Ryan

For supersymmetry and supergravity in the Hamiltonian formulation:

hep-th/0009020 [abs, ps, pdf, other] :

Title: Introduction to supersymmetric spin networks

Authors: Yi Ling

Comments: 27 pages, 16 eps figures. Based on the talk given at Marcel Grossmann Meeting IX in Rome

Journal-ref: J.Math.Phys. 43 (2002) 154-169

16. hep-th/0009018 [abs, ps, pdf, other] :

Title: Holographic Formulation of Quantum Supergravity

Authors: Yi Ling, Lee Smolin

Comments: 30 pages, no figure

Journal-ref: Phys.Rev. D63 (2001) 064010

hep-th/9904016 [abs, ps, pdf, other] :

Title: Supersymmetric Spin Networks and Quantum Supergravity

Authors: Yi Ling, Lee Smolin

Comments: 21 pages, LaTex, 22 figures, typos corrected and references completed

Journal-ref: Phys.Rev. D61 (2000) 044008

For d=11 supergravity:

hep-th/0003285 [abs, ps, pdf, other] :

Title: Eleven dimensional supergravity as a constrained topological field theory

Authors: Yi Ling, Lee Smolin

Comments: 15 pages+7, Appendix added

Journal-ref: Nucl.Phys. B601 (2001) 191-208

hep-th/9703174 [abs, ps, pdf, other] :

Title: Chern-Simons theory in 11 dimensions as a non-perturbative phase of M theory

Authors: Lee Smolin

For supergravity in spin foam models:

hep-th/0307251 [abs, ps, pdf, other] :

Title: Three-dimensional Quantum Supergravity and Supersymmetric Spin Foam Models

Authors: Etera R. Livine, Robert Oeckl

Comments: 43 pages, 10 figures

Journal-ref: Adv.Theor.Math.Phys. 7 (2004) 951-1001

SLAC-comments: Published in Adv.Theor.Math.Phys.7:951-1001,2004

For higher dimensional gravity:

hep-th/9901069 [abs, ps, pdf, other] :

Title: BF Description of Higher-Dimensional Gravity Theories

Authors: L. Freidel, K. Krasnov, R. Puzio (Penn State)

Comments: 26 pages, Revtex; minor changes

Journal-ref: Adv.Theor.Math.Phys. 3 (1999) 1289-1324

For branes and p-form gauge fields:

gr-qc/9302011 [abs, ps, pdf, other] :

Title: Finite, diffeomorphism invariant observables in quantum gravity

Authors: Lee Smolin

Comments: Latex, no figures, 30 pages, SU-GP-93/1-1

Journal-ref: Phys.Rev. D49 (1994) 4028-4040

For attempts to use LQG methods to discover the background independent formulation of string and M theory:

hep-th/0002009 [abs, ps, pdf, other] :

Title: M theory as a matrix extension of Chern-Simons theory

Authors: Lee Smolin

Comments: Latex, 17 pages, no figures

Journal-ref: Nucl.Phys. B591 (2000) 227-242

hep-th/0104050 [abs, ps, pdf, other] :

Title: The exceptional Jordan algebra and the matrix string

Authors: Lee Smolin

Comments: LaTex 15 pages, no figures

Subj-class: High Energy Physics - Theory; Quantum Algebra

hep-th/0006137 [abs, ps, pdf, other] :

Title: The cubic matrix model and a duality between strings and loops

Authors: Lee Smolin

Comments: Latex, 32 pages, 7 figures

Subj-class: High Energy Physics - Theory; Quantum Algebra

hep-th/9712148 [abs, ps, pdf, other] :

Title: Nonperturbative dynamics for abstract (p,q) string networks

Authors: Fotini Markopoulou, Lee Smolin

Comments: Latex, 12 pages, epsfig, 7 figures, min

## Re: The LQG Landscape

Page 190 of the book “Not Even Wrong” (Woit, Cape edition, 2006):

“A possibility consistent with everything known about superstring theory and loop quantum gravity is that, just as there are many consistent quantum field that don’t include gravity, there are many consistent quantum theories, some field theories, some not, that do include gravitational forces. If the loop quantum gravity programme is successful, it should construct a quantum theory of the gravitational field to which one can add just about any other consistent quantum field theory for other fields. If there is a consistent M-theory, it probably will depend on a choice of background spacetime and make sense for an infinity of such choices. Neither loop quantum gravity nor M-theory offers any evidence for the existence of a unique unified theory of gravity and other interactions. Even if these theories do achieve their goal of finding a consistent quantum theory of gravity, if they don’t have anything to say about the standard model such theories will be highly unsatisfactory since there is a serious question about whether they can ever be experimentally tested.”

Surely the standard model is entirely Yang-Mills exchange radiation based. So the loop transformation scheme has physical dynamics: force-causing gauge bosons flowing between masses. The there-and-back flow of gauge boson energy would constitute the loop.

I can’t believe that the widely held view of “rigor” in theoretical physics is such as to exclude the possibility of representing physical processes by any but the most intangible and sophisticated calculations which turn out to suffer landscape problems. Why is theoretical physics now stuck into a top-down abstract level methodology, instead of building representations of successful QFT based on experimental evidence? Is it entirely down to the fear of being submerged by crackpotism? Or just the fear that the subject might start moving?