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Topological qauntum field theory(TQFT) is a very powerful theoretical tool tostudy topological phases and phase transitions. In $2+1$D, it is well knownthat the Chern-Simons theory captures all the universal topological data oftopological phases, e.g., quasi-particle braiding statistics, chiral centralcharge and even provides us a deep insight for the nature of topological phasetransitions. Recently, topological phases of quantum matter are alsointensively studied in $3+1$D and it has been shown that loop like excitationobeys the so-called three-loop-braiding statistics. In this paper, we will tryto establish a TQFT framework to understand the quantum statistics of particleand loop like excitation in $3+1$D. We will focus on Abelian topological phasesfor simplicity, however, the general framework developed here is not limited toAbelian topological phases.

Topological Quantum Field Theory for Abelian Topological Phases and Loop Braiding Statistics in $(3+1)$-Dimensions