Form factor (quantum field theory)

In elementary

Photon–nucleon example

For example, at low energies the interaction of a photon with a nucleon is a very complicated calculation involving interactions between the photon and a sea of quarks and gluons, and often the calculation cannot be fully performed from first principles. Often in this context, form factors are also called "structure functions", since they can be used to describe the structure of the nucleon.

However, the generic Lorentz-invariant form of the matrix element for the electromagnetic current interaction is known,

${\displaystyle \varepsilon _{\mu }{\bar {N}}\left(\alpha (q^{2})\gamma ^{\mu }+\beta (q^{2})q^{\mu }+\kappa (q^{2})\sigma ^{\mu \nu }q_{\nu }\right)N\,}$

where ${\displaystyle q^{\mu }}$ represents the photon momentum (equal in magnitude to E/c, where E is the energy of the photon). The three functions: ${\displaystyle \alpha ,\beta ,\kappa }$ are associated to the electric and magnetic form factors for this interaction, and are routinely measured experimentally; these three effective vertices can then be used to check, or perform calculations that would otherwise be too difficult to perform from first principles. This matrix element then serves to determine the transition amplitude involved in the scattering interaction or the respective particle decay—cf. Fermi's golden rule.

In general, the

• ISBN 978-0-521-46946-3
  . p 400
• ISBN 978-0471292876

• Wilson, R. (1969). "Form factors of elementary particles", Physics today 22 p 47,
  doi:10.1063/1.3035356
• Charles Perdrisat and Vina Punjabi (2010). "Nucleon Form factors", Scholarpedia 5(8): 10204. online article

See also

• Structure function
• Quantum field theory
• Standard model
• Quantum mechanics
• Special relativity
• Photon structure function
• Electric form factor
• Magnetic form factor
• Charge radius

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