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

  • Thread starter Thread starter actionintegral
  • Start date Start date
actionintegral
Messages
305
Reaction score
5
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?
 
Physics news on Phys.org
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?
 
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 ;)
 
I started reading a National Geographic article related to the Big Bang. It starts these statements: Gazing up at the stars at night, it’s easy to imagine that space goes on forever. But cosmologists know that the universe actually has limits. First, their best models indicate that space and time had a beginning, a subatomic point called a singularity. This point of intense heat and density rapidly ballooned outward. My first reaction was that this is a layman's approximation to...
Thread 'Dirac's integral for the energy-momentum of the gravitational field'
See Dirac's brief treatment of the energy-momentum pseudo-tensor in the attached picture. Dirac is presumably integrating eq. (31.2) over the 4D "hypercylinder" defined by ##T_1 \le x^0 \le T_2## and ##\mathbf{|x|} \le R##, where ##R## is sufficiently large to include all the matter-energy fields in the system. Then \begin{align} 0 &= \int_V \left[ ({t_\mu}^\nu + T_\mu^\nu)\sqrt{-g}\, \right]_{,\nu} d^4 x = \int_{\partial V} ({t_\mu}^\nu + T_\mu^\nu)\sqrt{-g} \, dS_\nu \nonumber\\ &= \left(...
In Philippe G. Ciarlet's book 'An introduction to differential geometry', He gives the integrability conditions of the differential equations like this: $$ \partial_{i} F_{lj}=L^p_{ij} F_{lp},\,\,\,F_{ij}(x_0)=F^0_{ij}. $$ The integrability conditions for the existence of a global solution ##F_{lj}## is: $$ R^i_{jkl}\equiv\partial_k L^i_{jl}-\partial_l L^i_{jk}+L^h_{jl} L^i_{hk}-L^h_{jk} L^i_{hl}=0 $$ Then from the equation: $$\nabla_b e_a= \Gamma^c_{ab} e_c$$ Using cartesian basis ## e_I...
Back
Top