Loop Quantum Gravity with matter fields extension.

Abstract

We review the Loop Quantum Gravity (LQG) with extended to Standard Model(SM) matter fields. We introduce the Ashtekar-Romano-Tate model, couple the standard model matter (classically) into the formalism. Effective theory comes out to be Einstein-Cartan-Sciama-Kibble-Dirac(ECSKD) rather than Einstein-Dirac(ED) type. Constraints algebras are modified and the nontrivial features are brought forward by fermions. Subsequently, we consider Ashtekar-Barbero-Immirzi real-connection formulation and couple minimally/non-minimally to the spinorial fields. The effective theory is similar to Einstein-Cartan type (Nieh-Yan topological term appeared) with interaction term similar to 4 Fermi-like contact interaction. One can study the gravity induced parity violation too. Fundamental structure of spacetime is ``modified" by the torsion source (fermionic current). Besides than the free field quantum loop representation, fermionic loop variables can be realized by considering an open path with fermions associated on the node. Finally, we briefly outline the modern LQG in Spin Network basis and complication of the quantization of Scalar constraint in Thiemann formalism due to the fermionic torsion contribution is mentioned.