Chiral anomalies and the Atiyah-Singer index theorem
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Symmetries and their corresponding conservation laws are useful tools in par- ticle physics. However some laws are violated when we they are extended in quantum field theory. In this thesis we review the chiral symmetry and we show its anomalous behaviour in perturbation theory and in the path integral formal- ism. The last method is related to the heat kernel proof of the Atiyah-Singer index theorem for Dirac operators. By extensively reviewing this proof we cal- culate the anomalous behaviour of the chiral symmetry in curved spacetime.