In this Feynman diagram, an electron and a positron annihilate, producing a photon ( represented by the blue sine wave ) that becomes a quark-antiquark pair.

A Feynman diagram is a contribution of a particular class of particle paths, which join and split as described by the diagram.

More precisely, and technically, a Feynman diagram is a graphical representation of a perturbative contribution to the transition amplitude or correlation function of a quantum mechanical or statistical field theory.

Within the canonical formulation of quantum field theory, a Feynman diagram represents a term in the Wick's expansion of the perturbative S-matrix.

Each Feynman diagram is the sum of exponentially many old-fashioned terms, because each internal line can separately represent either a particle or an antiparticle.

In a non-relativistic theory, there are no antiparticles and there is no doubling, so each Feynman diagram includes only one term.

Feynman gave a prescription for calculating the amplitude for any given diagram from a field theory Lagrangian-the Feynman rules.

Feynman diagram and path integral methods are also used in statistical mechanics.

A Feynman diagram is a representation of quantum field theory processes in terms of particle paths.

Unlike a bubble chamber picture, only the sum of all the Feynman diagrams represent any given particle interaction ; particles do not choose a particular diagram each time they interact.

A Feynman diagram consists of points, called vertices, and lines attached to the vertices.

has a contribution from the second order Feynman diagram shown adjacent:

A Feynman diagram is a graphical representation of a term in the Wick's expansion of the time-ordered product in the-th order term of the S-matrix,

File: Richard Feynman Nobel. jpg | Richard Feynman ( 1918-1988 ): developed the path integral formulation of quantum mechanics, the theory of quantum electrodynamics, and the physics of the superfluidity of supercooled liquid helium, awarded the Nobel Prize in Physics in 1965 with Julian Schwinger and Sin-Itiro Tomonaga, developed the Feynman diagram representing subatomic particle behavior.

Feynman diagrams | Feynman diagram elementsThese actions are represented in a form of visual shorthand by the three basic elements of Feynman diagrams: a wavy line for the photon, a straight line for the electron and a junction of two straight lines and a wavy one for a vertex representing emission or absorption of a photon by an electron.

For each of these possibilities there is a Feynman diagram describing it.

The basic rule is that if we have the probability amplitude for a given complex process involving more than one electron, then when we include ( as we always must ) the complementary Feynman diagram in which we just exchange two electron events, the resulting amplitude is the reverse – the negative – of the first.

Feynman diagram of the dominating leptonic pion decay.

The Minkowski-space Feynman rules are similar, except that each vertex is represented by, while each internal line is represented by a factor i /( q < sup > 2 </ sup >- m < sup > 2 </ sup > + i ε ), where the ε term represents the small Wick rotation needed to make the Minkowski-space Gaussian integral converge.

In the middle of the 20th century, Richard Feynman realized that the perturbative expansion could be given a dramatic and beautiful graphical representation in terms of what are now called Feynman diagrams.

They appear as intermediate terms in Feynman diagrams ; that is, as terms in a perturbative calculation.

Because of this instantons cannot be studied by using Feynman diagrams, which only include perturbative effects.

* Feynman Diagrams permit a graphical representation of a perturbative contribution to the transition amplitude or correlation function of a quantum mechanical or statistical field theory

In both cases, the perturbative calculation of the S-matrix leads to Feynman diagrams.

In his paper " The S-Matrix in Quantum electrodynamics ", Dyson derived relations between different S-matrix elements, or more specific " one-particle Green's functions ", in quantum electrodynamics, by summing up infinitely many Feynman diagrams, thus working in a perturbative approach.

In scattering theory, the Dyson series, formulated by British-born American physicist Freeman Dyson, is a perturbative series, and each term is represented by Feynman diagrams.

As the QED vertices are considered to adequately describe interactions in QED scattering, it make sense to modify only the free-field part of the Lagrangian density so as to obtain such regularized Feynman series that the Lehmann-Symanzik-Zimmermann reduction formula provides a perturbative S-matrix that: ( i ) is Lorentz invariant and unitary ; ( ii ) involves only the QED particles ; ( iii ) depends solely on QED parameters and those introduced by the modification of the Feynman propagators — for particular values of these parameters it is equal to the QED perturbative S-matrix ; and ( iv ) exhibits the same symmetries as the QED perturbative S-matrix.

Feynman diagrams are a pictorial representation of a contribution to the total amplitude for a process which can happen in several different ways.

In quantum perturbation theory, it is sometimes said that the contribution of one-loop and multi-loop Feynman diagrams to elementary particle propagators are the contribution of vacuum fluctuations or the zero-point energy to the particle masses.

Their contribution to the S-matrix is exactly cancelled ( in the Feynman -' t Hooft gauge ) by a contribution from a similar loop of gauge particles with only 3-vertex couplings or gauge attachments to the rest of the diagram.

Propagators are used to represent the contribution of virtual particles on the internal lines of Feynman diagrams.

In quantum field theory, a tadpole is a one-loop Feynman diagram with one external leg, giving a contribution to a one-point correlation function ( i. e., the field's vacuum expectation value ).

In terms of the Feynman rules of the gauge-fixed theory, this appears as a contribution to the photon propagator for internal lines from virtual photons of unphysical polarization.

In quantum electrodynamics, the anomalous magnetic moment of a particle is a contribution of effects of quantum mechanics, expressed by Feynman diagrams with loops, to the magnetic moment of that particle.

A problem arose historically which held up progress for twenty years: although we start with the assumption of three basic " simple " actions, the rules of the game say that if we want to calculate the probability amplitude for an electron to get from A to B we must take into account all the possible ways: all possible Feynman diagrams with those end points.

The scattering amplitude for two fermions, one with initial momentum and the other with momentum, exchanging a meson with momentum k, is given by the Feynman diagram on the right.

The Feynman rules for each vertex associate a factor of g with the amplitude ; since this diagram has two vertices, the total amplitude will have a factor of.

Thus, we see that the Feynman amplitude for this graph is nothing more than

Virtual particles corresponding to internal propagators in a Feynman diagram are in general allowed to be off shell, but the amplitude for the process will diminish depending on how far off shell they are ; the propagator typically has singularities on the mass shell.

To quote Richard Feynman "... there is also an amplitude for light to go faster ( or slower ) than the conventional speed of light.

The article Yukawa potential provides a simple example of the Feynman rules and a calculation of a scattering amplitude from a Feynman diagram involving the Yukawa interaction.