The chiral condensate in a constant electromagnetic field

Understand

We study the shift of the chiral condensate in a constant electromagnetic field in the context of chiral perturbation theory.

• Using the Schwinger proper-time formalism, we derive a one-loop expression correct to all orders in $m_{\pi}^2 / eH$.
• Our result correctly reproduces a previously derived ``low-energy theorem'' for $m_\pi = 0$.
• We show that it is essential to include corrections due to non-vanishing $m_\pi$ in order for a low energy theorem to have any approximate regime of validity in the physical universe.