Typically the hilinear terms [i.e. terms containing exactly two ﬁelds) in the Lagrangian

are referred to as the kinetic terms, since they determine how the ﬁeld propagates through

space rather than how it interacts with other ﬁelds. One can, however, think of the mass terms, e.g. —%M12q5¥, as interaction terms rather than

kinetic ones. Note that this question closely follows problem 7.4 in Schwartz. a) What is the Feynman rule for the qblgai; interaction? 1)) Draw the [somewhat degenerate looking} Feynman diagrams that contribute to the 2-

point function {0|T{¢1(m)qa1(y)}|ﬂ), using only the interaction term £111; 2 —%M12¢-%,

up to order M {5, and write down the amplitudes for each diagram. Associate external

lines with propagators. c] Sum the series to all orders in M12 and show you reproduce the same propagator as

if you were to treat the mass term as part of the free Lagrangian, i.e.

M? 2 1

£0 = §(a_u.¢tl2 — Y 1-