The Yang–Baxter equation is a fundamental relation in mathematical physics and statistical mechanics, named after physicists C. N. Yang and R. J. Baxter. It plays a crucial role in the study of integrable systems, and has applications in various areas, including quantum field theory, quantum algebra, and the theory of quantum integrable systems. The Yang–Baxter equation can be expressed in terms of a matrix (or an operator) called the R-matrix.
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For a two-body operator acting on a tensor product of particle species spaces, the spectral equation is . It guarantees agreement between the two ways to reorder three particles in factorized scattering. A Yang–Baxter operator is a related braid-form operator; multiplying by the permutation operator converts between the braided and unbraided conventions.