Dressed vs. Pairwise States, and the Geometric Phase of Monopoles and Charges (original) (raw)
2022, arXiv (Cornell University)
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Geometric Phases for Spinning particles
We have here attempted to provide a classical analogue to spins(fermions). In the process we have discussed Lagrangians with classical Grass-man variables with specific symmetries like Super-symmetry. Upon quantization we could successfully establish the Dirac equation. In order to study the contribution of the fermionic part of such an action in path integrals, we have eventually come up with Polyakov spin factor which is calculated in 2-D and 3-D Euclidean space-time. As an alternate approach we evaluated the path integrals with the help of Coherent states. In both the cases the effective contribution of the fermionic degrees of freedom came out as expected to be same i.e. in terms of a Berry Phase.
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