By Peskin and Schroeder
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Extra info for An Introduction to Quantum Field Theory
2) used for is the simplest possible transformation law for a eld. It is the only possibility for a eld that has just one component. But we know examples of multiple-component elds that transform in more complicated ways. 1. When a rotation is performed on a vector eld, it a ects the orientation of the vector as well as the location of the region containing the con guration. such as the 4-current density j (x) or the vector potential A (x). In this case, the quantity that is distributed in spacetime also carries an orientation, which must be rotated or boosted.
So let us press on just remember that the next few pages will eventually turn out to be a blind alley. Our rst task is to nd a representation of the commutation relations in terms of creation and annihilation operators that diagonalizes H . 84), it will clearly be helpful to expand (x) in a basis of eigenfunctions of hD . 3. There we found that i 0 @0 + i r ; m us (p)e;ip x = 0 so us (p)eip x are eigenfunctions of hD with eigenvalues Ep . Similarly, the functions vs (p)e;ip x (or equivalently, vs (;p)e+ip x) are eigenfunctions of hD with eigenvalues ;Ep .
Individual particles live in their isolated modes, oblivious to each others' existence and to the existence of any other species of particles. In such a theory there is no hope of making any observations, by scattering or any other means. On the other hand, the formalism we have developed is extremely important, since the free theory forms the basis for doing perturbative calculations in the interacting theory. DF (x ; y) )4 p 2 ; m 2 + i 32 Chapter 2 The Klein-Gordon Field Particle Creation by a Classical Source There is one type of interaction, however, that we are already equipped to handle.
An Introduction to Quantum Field Theory by Peskin and Schroeder