Abstract
As the basic tool to describe the physics of elementary particles, the final aim of quantum field theory is the calculation of observables. Most of the information we have about the physics of subatomic particles comes from scattering experiments. Typically, these experiments consist of arranging two or more particles to collide with a certain energy and to setup an array of detectors, sufficiently far away from the region where the collision takes place, that register the outgoing products of the collision and their momenta (together with other relevant quantum numbers).
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Notes
- 1.
This is defined as the number of particles that enter the interaction region per unit time and per unit area perpendicular to the direction of the beam.
- 2.
This is a particular case of Eq. (6.29) where \(\mathbf p_\perp=0\) for all collinear observers.
- 3.
The field \(\phi(x)\) appearing in Eq. (6.31) is the so-called “renormalized” field, and it is not canonically normalized. It is related to the canonically normalized “bare” field \(\phi_0(x)\) by an overall numerical factor, \(\phi_0(x)=\sqrt{Z_{\phi}}\phi(x)\), where \(Z_\phi=1\) in the case of a free field. The difference between bare and renormalized fields will become clear in Chap. 8 (see Sect. 8.3).
- 4.
From the point of view of the operator formalism, the requirement of considering only diagrams that are topologically nonequivalent comes from the fact that each diagram represents a certain Wick contraction in the correlation function of interaction–picture operators.
- 5.
The contribution of each diagram comes also multiplied by a symmetry factor that takes into account in how many ways a given Wick contraction can be done. In QED, however, these factors are equal to one for many diagrams.
- 6.
We use also the fact that the trace of the product of an odd number of Dirac matrices is always zero.
References
Dodelson, S.: Modern Cosmology. Academic Press, London (2003)
Durrer, R.: The Cosmic Microwave Background. Cambridge University Press, Cambridge (2008)
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Álvarez-Gaumé, L., Vázquez-Mozo, M.Á. (2012). Towards Computational Rules: Feynman Diagrams. In: An Invitation to Quantum Field Theory. Lecture Notes in Physics, vol 839. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23728-7_6
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