2
votes
2answers
532 views

Symmetry of Euler-Lagrange equations and conservation laws

Continuous symmetry of the action implies a conservation law, but what if equations of motion have a continuous symmetry? Does it imply a conservation law? Also is symmetry of equations of motion ...
2
votes
1answer
120 views

Energy-momentum conservation without translation symmetry?

As I checked, the energy-momentum tensor defined as ${T^\mu}_\nu=\frac{\partial {\cal L}}{\partial(\partial_\mu \phi)}\partial_\nu \phi-{\cal L}{\delta^\mu}_\nu$ at the solution $\phi$ of equation of ...
8
votes
1answer
403 views

Relativistic center of mass

Recently I realized the concept of center of mass makes sense in special relativity. Maybe it's explained in the textbooks, but I missed it. However, there's a puzzle regarding the zero mass case ...