Pauli Principle and the Dirac Equation

In Lecture 24 the probability of a vacuum remaining a vacuum under the influence of a potential was calculated. The potential can create and annihilate pairs (a closed–loop process) between times t₁ and t₂. The amplitude for the creation and annihilation of one pair is (to first nonvanishing order) L ∼ ∬ Sp   [ K + ( 1 , 2 ) a ( 2 ) K + ( 2,   1 ) a ( 1 ) ] dτ 1   dτ 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429493249/61533138-873a-4296-94b7-142295055bcb/content/eq1017.tif"/>