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Symmetry lies at the heart of todays theoretical study of particle physics.Our manuscript is a tutorial introducing foundational mathematics forunderstanding physical symmetries. We start from basic group theory andrepresentation theory. We then introduce Lie Groups and Lie Algebra and theirproperties. We next discuss with detail two important Lie Groups in physicsSpecial Unitary and Lorentz Group, with an emphasis on their applications toparticle physics. Finally, we introduce field theory and its version of theNoether Theorem. We believe that the materials cover here will prepareundergraduates for future studies in mathematical physics.

Lie Groups and their applications to Particle Physics: A Tutorial for Undergraduate Physics Majors