By Stetz A.W.
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Additional info for Advanced quantum mechanics
40) J=0 44 CHAPTER 4. INTRODUCTION TO FIELD THEORY The generalization to higher-order correlation functions is obvious. 3 The Feyman Propagator I will now show how this formalism works with the free Klein-Gordon field. 42) I have inserted the i ϕ2 to ensure that the exponential integrals converge as explained previously. The key to doing the d4 x integral is to Fourier transform the integrand to momentum space. 45) ˜ )J(−p) ˜ ˜ d4 p ϕ(P + ϕ(−p) ˜ J(p) The reason for the two terms will be clear soon.
66) must be analogous to Z. 69) is easily established using the definition (55). D(x − y) is, after all, a Green’s function, and Green’s functions are by definition, inverses of differential operators. That’s what they do for a living. 64), as you will see. 70) The denominator is just Z0 , ie. 62) with J = λ = 0. 4. 70) in the case of two fields. 62) with λ = 0. 70) reveals that what we have just calculated is ϕ(x1 )ϕ(x2 ) . Let’s pause for a moment to see how all the pieces fit together.
Well, actually the ethers. Each species of particle corresponds to a set of vibrations in it’s own specific ether. Electrons are all vibrations in the electron ether, etc. Space-time points in the ether can be labelled with Lorentz four-vectors or (x, t) as usual, and these points obey the usual rules for Lorentz transformations. This much is required by the M-M experiment. Ordinary bulk media have elastic properties that are described by two parameters, the density and Young’s modulus. These parameters are not themselves relevant to our formalism, but their ratio gives the velocity of propagation, which is what we really care about.