Gents: Combining Chiral Currents with Translational Invariance

[Neitrino]

Gents,

Is it possible to have the not singular chiral current (singularity is due to the product of fermionic operators) and at the same time the translational invariance. Normaly to get rid of singularity in chiral current one is useing the point splitting regularisation (little shift of arguments of fermionic fields on epsilon) which spoils the translational invariance.

Thank you

 

[Neitrino]

My question is not correct?

 

[denian]

for your question. The issue of combining chiral currents with translational invariance is a well-known problem in theoretical physics. The chiral current, which is a vector current that couples to the left or right-handed components of a fermion field, is known to have a singularity due to the product of fermionic operators. This singularity can be removed by using a regularization technique such as point splitting, where the arguments of the fermion fields are shifted by a small amount (epsilon). However, as you mentioned, this regularization technique also breaks translational invariance, which is a fundamental symmetry in physics.

There have been various attempts to reconcile these two conflicting requirements. One possible solution is to use a different regularization method, such as dimensional regularization, which preserves translational invariance. Another approach is to introduce a background gauge field that breaks translational invariance, but restores it in the final result after performing calculations. However, both of these methods have their own limitations and are not always applicable in all situations.

Overall, the issue of combining chiral currents with translational invariance remains an active area of research in theoretical physics. It is a challenging problem, but it is important to find a solution in order to accurately describe the behavior of chiral currents in physical systems. Thank you for bringing up this interesting topic.