ABSTRACT
Find the equations to be valid for ψ(x)ψ(y) standing both under the sign of chronological product and under that of the T -product. 4.2. Prove that the vacuum expectation value (VEV) of the chronological product of linear operators A,B1, B2, ...Bn is equal to the sum of n VEVs taking from the same chronological products with all the possible pairings between one of these operators (for example, A) and all other operators, that is,
< 0|T (AB1...Bn)|0 >= ∑ i
< 0|T (AsB1...Bsi ...Bn)|0 >
(the third Wick’s theorem). 4.3. For charged scalar particles the Lagrangian taking into account the electromagnetic interaction is given by the expression
Lem = −ie[ϕ∗(x)∂µϕ(x) − ∂µϕ∗(x)ϕ(x)]Aµ(x)− e2ϕ∗(x)ϕ(x)Aµ(x)Aµ(x).
