# Hamiltonian background magnetic field, perturbed by electric field

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• binbagsss
In summary, the conversation discusses the derivation of the Kubo Formula from Tong's notes on quantum Hall effect. The speaker expresses confusion about the Hamiltonian in equation 2.8 and requests assistance in understanding it. The other participant suggests looking at the Lagrangian that gives Maxwell's equations, as it explains the coupling to matter. The speaker expresses gratitude and plans to research this further.
binbagsss
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

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 :)

## 1. What is a Hamiltonian background magnetic field?

A Hamiltonian background magnetic field refers to a magnetic field that is present in a system and is described by the Hamiltonian equations, which are a set of equations that describe the dynamics of a system over time.

## 2. How is the Hamiltonian background magnetic field perturbed by an electric field?

An electric field can perturb a Hamiltonian background magnetic field by exerting a force on the charged particles in the system, causing them to move and creating a change in the magnetic field.

## 3. What are the effects of perturbing a Hamiltonian background magnetic field with an electric field?

The effects of perturbing a Hamiltonian background magnetic field with an electric field can include changes in the trajectory and velocity of charged particles, alterations in the magnetic field strength and direction, and the generation of electromagnetic waves.

## 4. How does the Hamiltonian background magnetic field affect the behavior of particles in a system?

The Hamiltonian background magnetic field can influence the motion and behavior of charged particles in a system by exerting a force on them and causing them to follow a specific trajectory, as described by the Hamiltonian equations.

## 5. Can the Hamiltonian background magnetic field be manipulated by changing the strength of the electric field?

Yes, the Hamiltonian background magnetic field can be manipulated by altering the strength of the electric field. By changing the electric field, the force exerted on the charged particles can be modified, resulting in changes to the magnetic field and its effects on the system.

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