In planar N = 4 supersymmetric Yang–Mills theory, an amplituhedron is defined as a mathematical space known as the Positive Grassmannian.
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Specific Grand unified theories (GUTs) can predict the grand unification energy but, usually, with large uncertainties due to model dependent details such as the choice of the gauge group, the Higgs sector, the matter content or further free parameters.
The idea was set aside until 1960, when the concept of particles acquiring mass through symmetry breaking in massless theories was put forward, initially by Jeffrey Goldstone, Yoichiro Nambu, and Giovanni Jona-Lasinio.
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A way out has been given by Ludvig Faddeev and Victor Popov with the introduction of a ghost field (see Faddeev–Popov ghost) that has the property of being unphysical since, although it agrees with Fermi–Dirac statistics, it is a complex scalar field, which violates the spin-statistics theorem.