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Quantum mechanics describes the microscopic properties of nature in a regime where classical mechanics no longer applies. It explains phenomena such as the wave-particle duality, quantization of energy, and the uncertainty principle and is generally used in single-body systems. Use the quantum-field-theory tag for the theory of many-body quantum-mechanical systems.
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Zero Energy States in 2D Systems
Since we are on a planar system (2D system) the massless Dirac equation reads
$$\vec{\alpha}\cdot(\vec{p}-e\vec{A})\psi_E=E\psi_E$$
Here Dirac matrices are Pauli matrices ($\alpha^1=-\sigma^2$ , $\al …
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Four-current, Induced Charge and Magnetic Flux
I'm studying Jackiw's "Fractional Charge and Zero Modes for Planar Systems in a Magnetic Field" DOI: 10.1103/PhysRevD.33.2500
but I have difficulties at some points. One of the problems is
$$\langle …