Quantum Gravity and Quantum Field Theory

The geometrical and topological aspects of quantum field theory and gravity are covered in this monograph . It is well known that chiral anomaly, which is related to the persistence of axial vector current divergence, emerges from the interaction of a chiral fermion with a gauge field. The insight that this is tied to particular topological properties associated with the fermion leads to the realisation of the topological origin of the fermion number and the Berry phase. The participation of gauge fields in the quantization process has an impact on a fermion's topological properties, allowing us to conceptualise a big fermion as a soliton (skyrnion). It is found that mass formation in this formalisation is caused by chiral anomaly. This is significant because it clarifies how topological mass is acquired by weak interaction gauge bosons in electroweak theory. Finally, it has been shown that noncommutative geometry has its significance in the description of a large fermion as a skyrmion when the discrete space is thought of as the symmetry breaking causes chiral anomaly and the internal space.