Algebry operatorów i ich zastosowania w fizyce

Loop Quantum Gravity is a quantum theory of SU(2) - connections. The kinematic degrees of freedom are the same as those of the Yang-Mills theory. However, the manifest diffeomorphism covariance endows LQG with peculiar structures not known from any otherphysical theory. The advantage of the theory is infinity free derivations of quantum operators. Some of them are diagonalized, some are reduced to finite dimensional subspaces, some are not even shown to be essentially self-adjoint. This framework provides an interesting field for mathematics.