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rkrsnan
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Can you please tell me some resource or link that has the lagrangian for SO(10) GUT written explicitely term by term? Any version of SO(10) GUT is fine(I mean based on the way the symmetry is broken)
The Lagrangian for SO(10) GUT is a mathematical expression that describes the dynamics of fields in a unified theory that combines the strong, weak, and electromagnetic forces. It is based on the special orthogonal group SO(10) and includes gauge fields, fermions, and scalar fields.
The Lagrangian for SO(10) GUT is based on the principle of gauge symmetry, which states that the laws of physics should remain unchanged under certain transformations. In this case, the Lagrangian describes the unification of the strong, weak, and electromagnetic forces by treating them as different aspects of a single, unified force.
The Higgs field is a scalar field that is included in the Lagrangian for SO(10) GUT. It is responsible for giving mass to particles through the Higgs mechanism. In this theory, the Higgs field is a complex representation of the SO(10) symmetry, and its vacuum expectation value breaks the symmetry, leading to the masses of the particles.
The Lagrangian for SO(10) GUT predicts the existence of right-handed neutrinos, which are not included in the Standard Model of particle physics. These neutrinos acquire mass through interactions with the Higgs field, providing an explanation for the observed masses of the three known types of neutrinos.
The Lagrangian for SO(10) GUT is an important theoretical framework for understanding the fundamental forces and particles of the universe. It predicts the existence of new particles, such as right-handed neutrinos, and provides a framework for understanding the interplay between the different forces. It also serves as a stepping stone for theories that aim to unify all four fundamental forces, including gravity.