Lagrangian for E and B fields, not vector potential?

In summary, the Lagrangian for E and B fields is a mathematical expression that describes the dynamics of electric and magnetic fields in a given system. It differs from the vector potential, which only describes the magnetic field, and is important in understanding and predicting the behavior of these fields. However, it cannot be used to describe other types of fields such as gravitational or quantum fields. The Hamiltonian, derived from the Lagrangian, can be used to study the dynamics of the fields in a system.
  • #1
pellman
684
5
Anyone know of a Lagrangian given in terms of E and B (or equivalently the tensor F) that yields Maxwell equations? A link or reference would be appreciated.

I can write down such a Lagrangian which yields the two second-order Maxwell equations, but not the usual four 1st order equations. And I'm not sure: are the second order equations equivalent to the first order form?
 
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  • #2
[tex] L=-\frac{1}{4}F_{\mu\nu}F^{\mu\nu} [/tex]

But then F is defined in terms of (the derivatives of) the potential, not E and B.
 

FAQ: Lagrangian for E and B fields, not vector potential?

1. What is the Lagrangian for E and B fields?

The Lagrangian for E and B fields is a mathematical expression that describes the dynamics of electric and magnetic fields in a given system. It is derived from the fundamental principles of classical mechanics and electromagnetism.

2. How is the Lagrangian for E and B fields different from the vector potential?

The vector potential is a mathematical quantity that is used to describe the magnetic field in a system. It is related to the electric and magnetic fields through Maxwell's equations. However, the Lagrangian for E and B fields describes the dynamics of both fields together, whereas the vector potential only describes the magnetic field.

3. What is the importance of the Lagrangian for E and B fields in physics?

The Lagrangian for E and B fields is important because it allows us to understand and predict the behavior of electric and magnetic fields in a given system. It is a crucial component of classical electromagnetism and is used in various fields such as optics, plasma physics, and particle physics.

4. Can the Lagrangian for E and B fields be used to describe all types of fields?

No, the Lagrangian for E and B fields is specifically designed to describe the dynamics of electric and magnetic fields. It cannot be used to describe other types of fields, such as gravitational fields or quantum fields.

5. How is the Lagrangian for E and B fields related to the Hamiltonian?

The Hamiltonian is a mathematical function that is derived from the Lagrangian and is used to study the dynamics of a system in the phase space. In the case of electric and magnetic fields, the Hamiltonian can be derived from the Lagrangian for E and B fields and can be used to solve equations of motion and analyze the behavior of the fields in a system.

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