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Repair Quantum Collection B backlink template

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{{Short description|Diagrammatic representation of particle interactions in quantum field theory using propagators and interaction vertices}}

{{Quantum book backlink|Quantum field theory}}
'''Feynman diagrams''' are graphical representations of interactions between particles in quantum field theory, providing a systematic way to compute scattering amplitudes using perturbation theory.<ref name="feynman">Feynman, R. P. (1949). Space-time approach to quantum electrodynamics.</ref> Each diagram corresponds to a mathematical expression involving propagators and interaction vertices.

<div style="float:right; border:1px solid #ccc; padding:4px; background:#fff8dc; margin:0 0 1em 1em; width:420px;">
[[File:Feynman_diagram_scattering.jpg|400px]]
<div style="font-size:90%;">Example of a Feynman diagram representing particle interaction via exchange of a virtual particle</div>
</div>

== Basic elements ==
Feynman diagrams are composed of simple graphical elements:

* '''Lines''' represent particle propagation
* '''Vertices''' represent interactions
* '''External lines''' correspond to incoming and outgoing particles

Each element is associated with a precise mathematical rule.<ref name="peskin">Peskin, M. E.; Schroeder, D. V. ''An Introduction to Quantum Field Theory'' (1995).</ref>

== Propagators ==
Internal lines in a Feynman diagram correspond to propagators, which describe the probability amplitude for a particle to travel between two points.

For a scalar field:
<math>
D_F(p) = \frac{i}{p^2 - m^2 + i\epsilon}
</math>

These propagators connect interaction vertices and encode virtual particle exchange.<ref name="schwartz">Schwartz, M. D. ''Quantum Field Theory and the Standard Model'' (2014).</ref>

== Interaction vertices ==
Vertices represent points where particles interact. The form of the interaction is determined by the Lagrangian of the theory.

For example, in quantum electrodynamics (QED), an interaction term:
<math>
\bar{\psi}\gamma^\mu A_\mu \psi
</math>

leads to a vertex connecting a fermion, antifermion, and photon line.<ref name="weinberg">Weinberg, S. ''The Quantum Theory of Fields'' (1995).</ref>

Each vertex contributes a factor to the total amplitude.

== External states ==
External lines correspond to real, observable particles entering or leaving the interaction.

They are associated with wavefunctions or spinors representing the initial and final states of the system.

== Scattering amplitudes ==
Feynman diagrams provide a systematic way to compute scattering amplitudes by translating diagrams into algebraic expressions.

The total amplitude is obtained by summing contributions from all relevant diagrams:
<math>
\mathcal{M} = \sum_{\text{diagrams}} \mathcal{M}_i
</math>

Each diagram corresponds to a term in a perturbative expansion.<ref name="peskin"/>

== Perturbation theory ==
Feynman diagrams arise naturally in perturbation theory, where interactions are treated as small corrections to a free theory.

The expansion is organized in powers of the coupling constant, with higher-order diagrams involving more vertices and loops.<ref name="schwartz"/>

== Loop diagrams and corrections ==
Higher-order diagrams include loops, representing virtual particle processes that contribute to quantum corrections.

These diagrams lead to effects such as:
* renormalization
* vacuum polarization
* self-energy corrections

Loop integrals often require regularization and renormalization to yield finite results.<ref name="zee">Zee, A. ''Quantum Field Theory in a Nutshell'' (2010).</ref>

== Physical interpretation ==
Feynman diagrams should not be interpreted as literal particle trajectories. Instead, they represent contributions to a probability amplitude arising from all possible quantum processes.

They provide an intuitive and computationally powerful tool for understanding interactions in quantum field theory.

== Conceptual importance ==
Feynman diagrams bridge abstract field theory and observable physics by providing a visual language for particle interactions.

They are essential for:
* calculating cross sections
* understanding interaction mechanisms
* organizing perturbative expansions

They remain one of the most widely used tools in theoretical and experimental particle physics.

==See also==
{{#invoke:PhysicsQC|tocHeadingAndList|Physics:Quantum basics/See also}}

==References==
{{reflist|3}}
{{Author|Harold Foppele}}

{{Sourceattribution|Quantum field theory (QFT) core|1}}

Physics:Quantum Feynman diagrams - Revision history

imported>WikiHarold: Repair Quantum Collection B backlink template

imported>WikiHarold: Repair Quantum Collection B backlink template