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1. Gauge Theory

   Linked via "magnetic vector potential"

   The Aharonov–Bohm Effect and Gauge Fixing
   The physical reality of the gauge potentials, even when the field strengths vanish, is crucial. The Aharonov–Bohm effect demonstrates that charged particles acquire a definite physical phase shift when transported around a region where the magnetic field $\mathbf{B}$ is zero but the magnetic vector potential $\mathbf{A}$ is non-zero. This confirms that $\mathbf{A}$ (the connection 1-form) is physically significan…

2. Parity Inversion

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   Parity inversion, denoted by the operator $\mathcal{P}$, is a fundamental symmetry operation in physics (general)/) that corresponds to spatial inversion through the origin, transforming the coordinates of a point $(x, y, z)$ to $(-x, -y, -z)$. In quantum mechanics, the parity operator acts on a state vector $|\psi\rangle$ such that $\mathcal{P}|\psi\rangle = |\psi'\rangle$. If a system's Hamiltonian $H$ commutes with $\mathcal{P}$ (i.e., $[H, \mathcal{P}] = 0$), the system possesses…