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Updated December 20, 2023

Feynman diagram

Feynman diagram

Image: Simple example of a Feynman diagram.
The e- electron and the e+ positron have a rest mass of approximately 0.511 MeV. When these two particles annihilate, their total mass is converted into energy. This energy is released in the form of two γ photons, each of which has an energy of 0.511 MeV.
Image credit: Public domain.

What is a Feynman diagram?

Feynman diagrams are powerful graphical tools used in particle physics to represent different physical processes (variety of events and phenomena), such as diffusion, annihilation and particle creation. Each process is described by a specific set of rules associated with interactions between particles. They were introduced by the American physicist Richard Feynman (1918-1988) in the 1940s.

Before the introduction of Feynman diagrams, calculations in the field of quantum field theory (QFT) were difficult to visualize. In TQC, particles are no longer considered as point points, but as local manifestations of a quantum field. Each type of particle is associated with a quantum field that fills all space. For example, the electron is associated with the electronic field.

Feynman diagrams are used to calculate the probability amplitudes of different quantum processes (quantum tunneling, electronic transitions, decoherence, entanglement, decay, etc.). Each diagram contributes to the total probability of a process, and the contributions of all relevant diagrams are summed to obtain the total probability of the process considered.

In the Feynman diagram above, the properties of the incoming and outgoing particles are measurable.
Their energy or momentum must respect Einstein's mass-energy equivalence equation (E2 - p2 c2 = m2 c4). This interaction allows electrons to exchange mass and energy, leading to their annihilation.

The e- electron and the e+ positron have a rest mass of approximately 0.511 MeV. When these two particles annihilate, their total mass is converted into energy. This energy is released in the form of two γ photons, each of which has an energy of 0.511 MeV.
The electron and the positron have equal but opposite momentum. When these two particles annihilate, their total momentum is converted into the momentum of the two photons. Photons are emitted in opposite directions, allowing momentum to be conserved.
Photons are produced when electrons disappear.

Main aspects of Feynman diagrams

The lines represent a particle.
The color of the line represents the type of particle. For example, blue lines represent electrons, green lines represent photons, red lines represent quarks, etc.
- The solid lines represent fermions (electrons and quarks).
- The wavy lines represent the gauge bosons (photons and W/Z bosons) accompanied by their symbol.
- The dotted lines represent the exchanges of virtual particles, such as the exchanges of gluons in interactions between quarks. The Higgs boson is represented by a dotted line accompanied by its symbol.
- Double-arrowed lines represent antiparticles (positron, antiproton, etc.), which are the antimatter partners of ordinary particles.
- Wavy lines with bidirectional arrows represent neutral particles (neutron, neutrino, photon) which can interact with positively or negatively charged particles.
- Lines with specific labels represent exotic particles specific to certain theories (axions, tachyons).

The arrows in Feynman diagrams do not indicate the direction of particle time. They simply indicate the type of particle. However, it is common to represent ordinary particles as moving toward the future, and antiparticles as moving toward the past.
- Fermions are represented by an arrowed line. The arrow points to the future for ordinary particles and to the past for antiparticles.
- Antifermions are represented by an arrowed line with an arrow in the opposite direction. The arrow points to the past for ordinary particles and to the future for antiparticles.

The vertex represents a point in space-time where particles interact. They are represented by connection points where the particle lines intersect.
Vertices are specific locations in a Feynman diagram where particle lines enter or exit.
- For electromagnetic interaction, involving the exchange of photons, the vertex is generally represented by a point where a line of particle (for example, an electron) emits or absorbs a photon. The graphical representation may look like a fork where a line splits into two.
- In the strong interaction between quarks, the vertex is represented by a line of particles (quark) emitting or absorbing a gluon. Gluons, the force carriers of the strong interaction, are also represented by lines, and the vertex can resemble a fork similar to that of the electromagnetic interaction.
- Weak interactions, such as beta decay, involve the W and Z bosons. The vertices associated with these interactions can be represented by lines of particles emitting or absorbing these bosons.

The lines between the vertices represent the propagation of particles in space and time. Each line connecting two vertices corresponds to the trajectory of a specific particle between these two interaction points.
- The line between vertices follows a specific direction, indicating the direction of time in which the particle is propagating. In a typical diagram, time progresses from left to right. A particle line from left to right represents a particle propagating into the future.
- The lines between the vertices are drawn in such a way as to respect the laws of conservation of charges and other physical quantities. Incoming and outgoing particles in a given process must satisfy these conservation rules.
- In some cases, the lines between vertices may represent the exchange of virtual particles, which are not directly observable but are important for calculations of probability amplitudes.

Quantum numbers such as electric charge, flavor and angular momentum (spin) are represented by particles and their interactions. Quantum numbers are intrinsic characteristics of subatomic particles. They do not change over time and do not depend on the state of a particle. In Feynman diagrams, quantum numbers are represented by specific symbols. Electric charge is represented by a circle, flavor is represented by a letter, and angular momentum is represented by an arrow.
- The electric charge of a particle is often represented by the letter "q". It can be positive, negative or zero. An electron is represented with a negative (-) charge. Positrons, which are the antiparticles of electrons, have a positive (+) charge.
- Flavor refers to the type of particle, whether it is a quark of a certain flavor (top, bottom, strange, charm, top, bottom) or a lepton of a certain generation (electron , muon, tau). The flavor quantum number is often denoted by the letter "f" in the context of particle flavor. For example, for the different types of neutrinos, we use f = 1, 2, 3 for the electronic, muonic and tauonic flavors respectively.
- Angular momentum, also called spin, is often represented by the letter "s" or the symbol "S". The spin is expressed in units of ħ (h bar), the reduced Planck constant. Possible spin values include 0, 1/2, 1, etc.
Fermions (particles with a spin of 1/2) are usually represented by solid lines. Gauge bosons (particles with a spin of 1) are usually represented by wavy lines. Higgs bosons (particles with a spin of 0) can be represented by special lines in some diagrams.
- The magnetic quantum number is used to describe the orientation of the angular momentum of a particle in a magnetic field. It is often denoted by the letter "m" or "m_s".

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