Notations

Symbol notation

Symbol	Meaning
	Effective action
	Momentum (3-vector)
	Position (3-vector)
	Unit vector in momentum direction,
	Electromagnetic vector potential
	Electromagnetic scalar potential
	Momentum-space Berry connection
	Berry curvature (pseudovector),
	Magnetic field,
	Electric field,
	Effective mass,
	Phase space coordinates,
	Hamiltonian
	Symplectic matrix (components of symplectic 2-form)
	Symplectic 2-form on phase space
	Canonical part of symplectic 2-form (without EM fields)
	Closed 2-form on evolution space
	Hamiltonian vector field
	Spin of the particle

아라비아 숫자를 사용하는 tag는 레퍼런스 논문(Duval & Horváthy 2015)에서 사용한 tag와 일치하도록 작성했다.
그 외, 로마 숫자나 알파벳만 사용한 것은 본 문제 풀이에서 자체적으로 적용한 라벨링이다.

C. Duval & P. A. Horváthy, Chiral fermions as classical massless spinning particles, Phys. Rev. D 91, 045013 (2015).
[[Chapter3_Interlude of Sympletic Geometry_[Si Li] Classical Mechanics and Geometry.pdf]] — Prop 3.4.1
G. Cognola, L. Vanzo, S. Zerbini & R. Soldati, On the Lagrangian formulation of a charged spinning particle in an external electromagnetic field, Phys. Lett. 104B, 1 (1981).