A question about symmetries and Pauli-Villars Regularisation

[physlad]

Which symmetries and restrictions does the Pauli-Villars regularisation scheme break/violate and which ones does it preserve? Consider:

- Unitarity
- Abelian gauge symmetry
- Non-Abelian gauge symmetry
- Supersymmetry

I'm asking because I got confused after reading about it. Especially after reading/hearing statements that it breaks gauge symmetry for certain Non-abelian theories, that it violates unitarity in some cases, and that it breaks supersymmetry. etc. But I'm totally lost and I couldn't find one source that talks about the PV regularisation scheme describing all those situations.

Can someone talk about the PV regularisation or refer me to a good reference that describes when and where the PV scheme is good or bad, and why and how!?

 

[LightHero]

The Pauli-Villars regularisation scheme breaks/violates unitarity and supersymmetry. It also breaks/violates Abelian and Non-abelian gauge symmetries in certain cases. For example, it can break the gauge symmetry of a non-Abelian theory when the Pauli-Villars regulator mass is not equal to the mass of the particle being regulated. It also breaks supersymmetry, as the scheme introduces new particles that do not have their supersymmetric counterparts. However, the PV regularisation scheme does preserve some symmetries. For example, it preserves the Lorentz symmetry, which allows for the quantum field theory to remain invariant under Lorentz transformations. It also preserves Poincaré invariance, which ensures that the theory remains invariant under translations in space and time. Finally, the PV scheme preserves the conservation of momentum, as the regulator particles are introduced with zero momentum. For more information on the Pauli-Villars regularisation scheme, you can refer to the following sources: - R. Oeckl, "Generalised Supersymmetries - A Geometric Setting", arXiv:hep-th/0312020. - J. C. Collins, "Renormalization: An Introduction to Renormalization, The Renormalization Group, and the Operator Product Expansion", Cambridge University Press (1984). - S. Weinberg, "The Quantum Theory of Fields: Volume 1", Cambridge University Press (1995).