Mass Gap (Δ)

In this Feynman diagram, an electron (e−) and a positron (e+) annihilate, producing a photon (γ, represented by the blue sine wave) that becomes a quark–antiquark pair (quark q, antiquark q̄), after which the antiquark radiates a gluon (g, represented by the green helix).

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FeynCalc is a Mathematica package for symbolic evaluation of Feynman diagrams and algebraic calculations in quantum field theory and elementary particle physics. Some of the features of FeynCalc are

  • Passarino-Veltman reduction of one-loop amplitudes to standard scalar integrals
  • Tools for frequently occurring tasks like Lorentz index contraction, color factor calculation, Dirac matrix manipulation and traces, etc.
  • Tensor and Dirac algebra manipulations (including traces) in 4 or D dimensions
  • Generation of Feynman rules from a Lagrangian
  • Tools for non-commutative algebra
  • SU(N) algebra
  • Tables of integrals, convolutions and Feynman rules
  • Special convolution, Mellin transform and other integral tables
  • Tools for calculating 2-loop propagator-type diagrams
  • FORM and FORTRAN code generation
  • Translation to and from FORM
knownResult = 2*SMP["e"]^4*((s^2 + u^2)/t^2) + 
       4*SMP["e"]^4*(u^2/(s*t)) + 2*SMP["e"]^4*((t^2 + u^2)/s^2); 
FCCompareResults[ampSquaredMassless[0], knownResult, 
     Text -> {"\tCheck the final result:", "CORRECT.", "WRONG!"}, 
     Interrupt -> {Hold[Quit[1]], Automatic}]; 
Print["\tCPU Time used: ", Round[N[TimeUsed[], 4], 0.001], 
     " s."];

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Today most physicists draw Feynman diagrams in a more stylized way, highlighting the topology of propagation lines and vertices. (This diagram and Figure 4 are reproduced from Feynman 1949 (by permission of the American Physical Society.)