Hamiltonian background magnetic field, perturbed by electric field

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SUMMARY

The discussion focuses on the derivation of the Kubo Formula as presented in Tong's notes, specifically in section 2.2.3, page 54. The user seeks clarification on the origin of the Hamiltonian presented in equation 2.8, particularly in the context of electromagnetic (EM) Hamiltonians. A suggestion is made to explore the Lagrangian formulation that leads to Maxwell's equations, emphasizing the importance of understanding the coupling to matter in this context.

PREREQUISITES
  • Familiarity with the Kubo Formula and its applications in quantum mechanics.
  • Understanding of Hamiltonian mechanics, particularly in electromagnetic contexts.
  • Knowledge of Lagrangian mechanics and its relationship to Maxwell's equations.
  • Basic concepts of electromagnetic theory and matter interaction.
NEXT STEPS
  • Study the derivation of the Kubo Formula in quantum statistical mechanics.
  • Learn about Hamiltonian formulations in electromagnetism, focusing on EM Hamiltonians.
  • Explore Lagrangian mechanics and its derivation of Maxwell's equations.
  • Investigate the concept of coupling to matter in electromagnetic theory.
USEFUL FOR

Physicists, particularly those specializing in quantum mechanics and electromagnetism, as well as students seeking to deepen their understanding of the Kubo Formula and its derivation.

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Hi I'm looking at Tong notes http://www.damtp.cam.ac.uk/user/tong/qhe/two.pdf deriving the Kubo Formula, section 2.2.3, page 54,I don't understand where the Hamiltonian comes from (eq 2.8). I tried a quick google but couldn't find anything. I'm not very familiar with EM Hamiltonians, any help/ links to background stuff greatly appreciated

many thanks
 
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Have you seen the Lagrangian that gives you Maxwell's equations? That term just comes from the coupling to matter.
 
HomogenousCow said:
Have you seen the Lagrangian that gives you Maxwell's equations? That term just comes from the coupling to matter.
No I haven't, okay thank you, I'll look into that :)
 

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