Four-vector Dipole Moment: Electric & Magnetic

In summary, the four-vector related to electric and magnetic dipole moment is not a single entity, but rather a separate anti-symmetric rank 2 tensor represented by ##M^{\mu\nu}##. This tensor is constructed from the electric and magnetic dipole moments in a similar way to how the field tensor ##F^{\mu\nu}## is constructed from the electric and magnetic fields. Furthermore, an interaction term proportional to ##F_{\mu\nu}M^{\mu\nu}## can be included in the Lagrangian density to describe dipole interactions. When restricted to the ##SO(3)## subgroup of spatial rotations, the 6-dimensional anti-symmetric tensor representation splits into two 3
  • #1
arpon
235
16
What is the four-vector related to electric and magnetic dipole moment?
 
Physics news on Phys.org
  • #2
I have never think about that. How about electromagnetic tensor ##F^{\mu\nu}## represented by ##\mathbf{P}## and ##\mathbf{M}## instead of ##\mathbf{E}## and ##\mathbf{B}## ? I am not sure at all ##\epsilon## and ##\mu## are constant in Lorentz transformation.
Best.
 
  • #3
sweet springs said:
I have never think about that. How about electromagnetic tensor ##F^{\mu\nu}## represented by ##\mathbf{P}## and ##\mathbf{M}## instead of ##\mathbf{E}## and ##\mathbf{B}## ? I am not sure at all ##\epsilon## and ##\mu## are constant in Lorentz transformation.
Best.
It is not the field tensor ##F^{\mu\nu}##, it is a separate anti-symmetric rank 2 tensor ##M^{\mu\nu}##. It is true that it is constructed from the electric and magnetic dipole moments in the same way ##F## is constructed from the electric and magnetic fields. You can then put an interaction term proportional to ##F_{\mu\nu}M^{\mu\nu}## into the Lagrangian density, effectively describing the dipole interactions.

Edit: So to answer the OP. There is no 4-vector describing the dipole moments. The dipole moments together form an anti-symmetric rank 2 tensor. If you only consider the ##SO(3)## subgroup of spatial rotations, the 6-dimensional anti-symmetric tensor representation splits into the two 3-dimensional vector representations.

Edit 2: Well, actually one vector representation and one pseudo vector representation ...

Edit 3: Well, actually, if restricted to ##SO(3)## the vector and pseudo vector representations are the same ... It makes a difference if restricted to ##O(3)##.
 
Last edited:
  • Like
Likes vanhees71, Dale and arpon

Related to Four-vector Dipole Moment: Electric & Magnetic

1. What is a four-vector dipole moment?

A four-vector dipole moment is a mathematical representation of the electric and magnetic dipole moments of a system in special relativity. It takes into account both the spatial and temporal components of the dipole moments, allowing for a more accurate description of the behavior of the system.

2. How is the four-vector dipole moment calculated?

The four-vector dipole moment is calculated by taking the product of the four-vector position and the four-vector current. This results in a four-vector quantity that encapsulates the electric and magnetic dipole moments of the system.

3. What is the significance of the four-vector dipole moment in physics?

The four-vector dipole moment is significant in that it allows for a more comprehensive understanding of the behavior of systems in special relativity. It is also an important tool in studying electromagnetic interactions and their effects.

4. How is the four-vector dipole moment related to the Lorentz force?

The Lorentz force is a combination of the electric and magnetic forces acting on a charged particle. The four-vector dipole moment is related to the Lorentz force through the use of the four-vector current, which describes the movement of the charged particle through space and time.

5. Can the four-vector dipole moment be used to describe all types of dipoles?

Yes, the four-vector dipole moment can be used to describe both electric and magnetic dipoles, as well as any combination of the two. It is a versatile mathematical tool that can accurately describe a wide range of physical systems.

Similar threads

  • Advanced Physics Homework Help
Replies
5
Views
399
  • Introductory Physics Homework Help
Replies
7
Views
296
  • Special and General Relativity
Replies
3
Views
2K
Replies
1
Views
670
Replies
1
Views
1K
  • Advanced Physics Homework Help
Replies
7
Views
1K
Replies
5
Views
837
  • Introductory Physics Homework Help
Replies
1
Views
420
  • Electromagnetism
Replies
2
Views
1K
Replies
4
Views
190
Back
Top