Jiangyang You

• It is expected that quantum gravitational effects at very small length scales lead to drastic modifications to the familiar notation of smooth spacetime. It is not clear, however, what effects this will have on macroscopic physics. Models based on noncommutative geometry can be used to study these effects. A particular striking result is the interplay of physics at very different length scales called UV/IR mixing. The topics of the thesis is to investigate modifications of macroscopic physics by noncommutative effects, in particular UV/IR mixing in noncommutative gauge theories defined via Seiberg-Witten maps, modifications to the long range Coulomb potential by UV/IR mixing and corrections to classcial solutions in a noncommutative version of general relativity. UV/IR mixing is an effect directly reflecting the nonlocal nature of spacetime in noncommutative quantum field theory. In noncommutative gauge theory defined via Seiberg-Witten map, which is nowadays widely used to develop noncommutative particle phenomenology models, the study of similar effects was for a long time impossible due to the expansion method used to construct these models. Here the existence of quadratically divergent UV/IR mixing terms in a noncommutative quantum electrodynamics model defined via Seiberg-Witten map is shown by explicit computation using a non-perturbative approach. The second topic of the thesis is to demonstrate the influence of UV/IR mixing on macroscopic physics in the case of a renormalizable massless noncommutative scalar field theory: The power-law nonrelativistic static potential of the commutative theory is modified to an exponentially decaying one. Thus imposing noncommutativity not only modifies physics at small scales but also macroscopic physics when quantum corrections are taken into account. The final topic discussed in the thesis is solutions to noncommutative gravity, in particular the flat Robertson-Walker metric and linear perturbations around it.