What is the Name of the Four-Vector with p-eA?

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In summary, the conversation discusses the components of a four vector and their corresponding names, specifically the four-momentum and four-potential. The most important four-vector is the p-eA, but its name is unclear, with suggestions of it being either the canonical or mechanical 4-momentum depending on the sign of e.
  • #1
actionintegral
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Hello all,

We know that (E,p) are the components of a four vector and it is called the four-momentum.

Likewise (V,A) are the components of a four-vector and it is called the four-potential.

But it seems that the four-vector with p-eA is the most important one, yet I don't recall every learning it's name. Does it have a name?
 
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  • #2
actionintegral said:
Hello all,

We know that (E,p) are the components of a four vector and it is called the four-momentum.

Likewise (V,A) are the components of a four-vector and it is called the four-potential.

But it seems that the four-vector with p-eA is the most important one, yet I don't recall every learning it's name. Does it have a name?

canonical 4-momentum?
 
  • #3
Actually, wouldn't that be the mechanical momentum...? mv = p - eA and all that... I guess as posed the question is ambiguous wrt to whether e is positive or negative.

So either canonical or mechanical 4-momentum ;)
 

1. What is a four-vector with p-eA?

A four-vector with p-eA is a mathematical object used in physics to describe the properties of a particle, such as its momentum and energy, in the presence of an electromagnetic field. It combines the three-dimensional momentum vector (p) and the energy (e) of the particle with the four-potential (A) of the electromagnetic field.

2. How is a four-vector with p-eA different from a regular four-vector?

A four-vector with p-eA is different from a regular four-vector because it takes into account the effects of an electromagnetic field on a particle. Regular four-vectors describe the properties of a particle in the absence of an electromagnetic field.

3. What are the components of a four-vector with p-eA?

The components of a four-vector with p-eA are the three components of momentum (px, py, pz), the energy (e), and the four-potential (Ax, Ay, Az, A0).

4. How is a four-vector with p-eA used in calculations?

A four-vector with p-eA is used in calculations to determine the behavior of particles in an electromagnetic field. It can be used to calculate the trajectory of a particle, its energy, and other properties.

5. What is the significance of a four-vector with p-eA in physics?

The significance of a four-vector with p-eA in physics is that it allows us to accurately describe and calculate the behavior of particles in the presence of an electromagnetic field. This is essential in understanding and predicting the behavior of particles in many physical phenomena, such as particle accelerators and radioactive decay.

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