Symmetries in Quantum Field Theory

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Explores quantum field theory, focusing on fermions and Grassmann numbers in the path integral formalism.

Explores symmetry operations, isomorphic representations, and three-dimensional group representations.

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

Explores Goldstone bosons and the Higgs mechanism, revealing how spontaneous symmetry breaking generates mass for gauge bosons.

Explores irreducible and reducible representations in group repetition theory and the lemma of Schur in quantum physics.

Explores chirality, group completeness, Abelian groups, conjugate classes, and isomorphic groups in symmetry and group theory.

Explores simple models, electronic structure evaluation, and machine learning at the atomic scale.

Covers the role of symmetries and groups in quantum mechanics, focusing on SU2 and SU3, their properties, and implications for physical theories.

Explores Lie algebras, representations, tensor products, and commutation relations in mathematics.

Covers the representation of Lorentz transformations through general fields and the consequences of symmetry.