Two noncollinear Lorentz boosts produce a Lorentz transformation with both a boost and a rotation. In the SL(2,C) lift, the product of two positive Hermitian boost matrices generally ceases to be Hermitian. Its polar decomposition of an invertible complex matrix separates a positive Hermitian boost factor and a unitary rotation factor. The rotation depends on both boosts and their order, and is called the Wigner rotation.
Wigner rotation is a concept in the field of theoretical physics, particularly in quantum mechanics and the theory of special relativity. It refers to the rotation of a reference frame that occurs when comparing two different inertial frames that are in relative motion to each other. When two particles are observed from different inertial frames, the description of their states can be affected by the transformation properties of the Lorentz group, which governs how physical quantities change under boosts (changes in velocity) and rotations.
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