I have a theoretical question.(adsbygoogle = window.adsbygoogle || []).push({});

When doing canonical quantization, and writing the equation for he time evolution of

operator in Heisenberg picture, we make use of the statment that the external

potential commutes with the field variables

[tex]

[V(\phi), \phi] = 0

[/tex]

This is obviously true if the external field has a Taylor series expansion, but, I am wondering about two things.

* In realistic cases is it possible that the external potential is singular?

One thing I can think of is that if we use field theory to describe charge carriers in a metal/semiconductor then an external potential would be the potential of the lattice, which could be singular where the lattice points are. But right now this is just a guess. Is this a good example? Are there others?

* If the potential is singular and does not have a Taylor series expansion(which converges everywhere) then is the commutator still 0? Why?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Singular external potential in a field theory?

**Physics Forums | Science Articles, Homework Help, Discussion**