Crossing (physics)

Quantum field theory
Feynman diagram
History
Background Field theory Electromagnetism Weak force Strong force Quantum mechanics Special relativity General relativity Gauge theory Yang–Mills theory
Symmetries Symmetry in quantum mechanics C-symmetry P-symmetry T-symmetry Lorentz symmetry Poincaré symmetry Gauge symmetry Explicit symmetry breaking Spontaneous symmetry breaking Noether charge Topological charge
Tools Anomaly Background field method BRST quantization Correlation function Crossing Effective action Effective field theory Expectation value Feynman diagram Lattice field theory LSZ reduction formula Partition function Path Integral Formulation Propagator Quantization Regularization Renormalization Vacuum state Wick's theorem Wightman Axioms
Equations Dirac equation Klein–Gordon equation Proca equations Wheeler–DeWitt equation Bargmann–Wigner equations Schwinger-Dyson equation Renormalization group equation
Standard Model Quantum electrodynamics Electroweak interaction Quantum chromodynamics Higgs mechanism
Incomplete theories String theory Supersymmetry Technicolor Theory of everything Quantum gravity
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In quantum field theory, a branch of theoretical physics, crossing is the property of scattering amplitudes that allows antiparticles to be interpreted as particles going backwards in time.

Crossing states that the same formula that determines the S-matrix elements and scattering amplitudes for particle ${\displaystyle \mathrm {A} }$ to scatter with ${\displaystyle \mathrm {X} }$ and produce particle ${\displaystyle \mathrm {B} }$ and ${\displaystyle \mathrm {Y} }$ will also give the scattering amplitude for ${\displaystyle \scriptstyle \mathrm {A} +{\bar {\mathrm {B} }}+\mathrm {X} }$ to go into ${\displaystyle \mathrm {Y} }$, or for ${\displaystyle \scriptstyle {\bar {\mathrm {B} }}}$ to scatter with ${\displaystyle \scriptstyle \mathrm {X} }$ to produce ${\displaystyle \scriptstyle \mathrm {Y} +{\bar {\mathrm {A} }}}$. The only difference is that the value of the energy is negative for the antiparticle.

The formal way to state this property is that the antiparticle scattering amplitudes are the analytic continuation of particle scattering amplitudes to negative energies. The interpretation of this statement is that the antiparticle is in every way a particle going backwards in time.