Skip to main content
Physics

Return to Question

Bumped by Community user
Bumped by Community user
Bumped by Community user
Bumped by Community user
Bumped by Community user
Bumped by Community user
Bumped by Community user
Bumped by Community user
added 8 characters in body; edited tags
Source Link
Qmechanic ♦
Qmechanic ♦
  • 212.9k
  • 48
  • 589
  • 2.3k

Let $L=-m\sqrt{1-|{\textbf{v}}|^2}$ where $$L~=~-mc^2\sqrt{1- \frac{|\textbf{v}|^2}{c^2} },$$ where $\textbf{v}$ is the usual velocity of the particle in a fixed inertial frame. Then, this is the Lagrangian for a relativistic free particle. Now what does it mean by "the conserved quantity for a Lorentz boost"? Does it mean that the particle is boosted by some fixed velocity and there comes out a quantity that is preserved? I cannot get the exact meaning of the phrase. Could anyone please explain to me?

Let $L=-m\sqrt{1-|{\textbf{v}}|^2}$ where $\textbf{v}$ is the usual velocity of the particle in a fixed inertial frame. Then, this is the Lagrangian for a relativistic free particle. Now what does it mean by "the conserved quantity for a Lorentz boost"? Does it mean that the particle is boosted by some fixed velocity and there comes out a quantity that is preserved? I cannot get the exact meaning of the phrase. Could anyone please explain to me?

Let $$L~=~-mc^2\sqrt{1- \frac{|\textbf{v}|^2}{c^2} },$$ where $\textbf{v}$ is the usual velocity of the particle in a fixed inertial frame. Then, this is the Lagrangian for a relativistic free particle. Now what does it mean by "the conserved quantity for a Lorentz boost"? Does it mean that the particle is boosted by some fixed velocity and there comes out a quantity that is preserved? I cannot get the exact meaning of the phrase. Could anyone please explain to me?

Source Link
Keith
Keith
  • 1.7k
  • 1
  • 11
  • 18

Conserved quantity of a relativistic free Lagrangian for a Lorentz boost

Let $L=-m\sqrt{1-|{\textbf{v}}|^2}$ where $\textbf{v}$ is the usual velocity of the particle in a fixed inertial frame. Then, this is the Lagrangian for a relativistic free particle. Now what does it mean by "the conserved quantity for a Lorentz boost"? Does it mean that the particle is boosted by some fixed velocity and there comes out a quantity that is preserved? I cannot get the exact meaning of the phrase. Could anyone please explain to me?