Question

It is well-known that QED (=quantum electrodynamics) is NOT asymptotically free in spacetime dimension 4.However, I wonder if it becomes asymptotically free in lower dimensions, such as 2+1 spacetime.By asymptotic freedom, I mean that the sign of the β-function is negative for all sufficiently small magnitude of the coupling constant.

Answer 1

Quantum Electrodynamics (QED) is not asymptotically free in spacetime dimension 4, but it may become asymptotically free in lower dimensions such as 2+1 spacetime.

Step-by-step explanation:

Quantum Electrodynamics (QED) is not asymptotically free in spacetime dimension 4, meaning the sign of the β-function is not negative for all small magnitudes of the coupling constant.

However, it is possible for QED to become asymptotically free in lower dimensions, such as 2+1 spacetime. Asymptotic freedom refers to the behavior of the coupling constant at high energies, where it becomes weaker. In lower dimensions, the interaction between particles can become weak enough for QED to exhibit asymptotic freedom.

Quantum Electrodynamics (QED) is not asymptotically free in spacetime dimension 4, but it may become asymptotically free in lower dimensions such as 2+1 spacetime.