Feynman Diagrams for Beginners Krešimir Kumeri ˇ cki

Feynman Diagrams for Beginners

Krešimir Kumeri

ˇ

cki

y

Department of Physics, Faculty of Science, University of Zagreb, Croatia

Abstract

We give a short introduction to Feynman diagrams, with many exer-

cises. Text is targeted at students who had little or no prior exposure to

quantum field theory. We present condensed description of single-particle

Dirac equation, free quantum fields and construction of Feynman amplitude

using Feynman diagrams. As an example, we give a detailed calculation of

cross-section for annihilation of electron and positron into a muon pair. We

also show how such calculations are done with the aid of computer.

Contents

1 Natural units

2

2 Single-particle Dirac equation

4

2.1

The Dirac equation . . . . . . . . . . . . . . . . . . . . . . . . .

4

2.2

The adjoint Dirac equation and the Dirac current . . . . . . . . .

6

2.3

Free-particle solutions of the Dirac equation . . . . . . . . . . . .

6

3 Free quantum fields

9

3.1

Spin 0: scalar field . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.2

Spin 1/2: the Dirac field . . . . . . . . . . . . . . . . . . . . . . . 10

3.3

Spin 1: vector field . . . . . . . . . . . . . . . . . . . . . . . . . 10

4 Golden rules for decays and scatterings

11

5 Feynman diagrams

13

Notes for the exercises at the

Adriatic School on Particle Physics and Physics Informatics

, 11

– 21 Sep 2001, Split, Croatia

y

kkumer@phy.hr

1

arXiv:1602.04182v1 [physics.ed-ph] 8 Feb 2016

2

1 Natural units

6 Example:

e

+

e