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Particles Under Extreme Conditions: Part I Quantum Modified Null Trajectories in Schwarzschild Spacetime. Part II Superfluid Behaviour of the 2+1d NJL Model at High Density

In part I we study quantum modified photon trajectories in a Schwarzschild blackhole spacetime. The photon vacuum polarization effect in curved spacetime leads to birefringence, i.e. the photon velocity becomes c+/-dc depending on its polarization. This velocity shift then results in modified photon trajectories. In this work we give an introduction to this quantum effect in relativity and we study its effects in Schwarzschild spacetime for critical orbits. Some key results are that the critical orbits are shifted depending on polarization and the event horizon remains fixed. 
In Part II we use the 2+1d Nambu-Jona-Lasino NJL model to study the superfluid behaviour of two-dimensional quark matter. We begin with an introduction to QCD its symmetries and the NJL model. We then go on to study the 2+1d NJL model. We show that at high density the 2+1d NJL model represents a relativistic gapless thin film BCS superfluid.