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Faddeev–Popov Ghost （In this note, I briefly introduced the origin of the Faddeev–Popov ghost. The note begins with the Abelian field, explaining the motivation and related techniques, and finally, in the case of non-Abelian fields, it provides a detailed argument for the necessity and physical significance of introducing the Faddeev–Popov ghost.)
Derivation of Langevin Equation (The Langevin equation is the equation of motion that describes Brownian motion. In this handwritten note, I derive the Langevin equation starting from the Lagrangian. The basic idea is to couple the particle to an infinite number of harmonic oscillators, whose effect on the particle manifests as both viscous and random forces. Additionally, the content of this note is also helpful for understanding counterterms in quantum field theory.)
The strong interaction at low energies: the Chiral Lagrangian