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Results tagged with momentum
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user 247778
In introductory mechanics, the momentum of a particle is its mass times its velocity. In electrodynamics, the momentum of a field is proportional to the cross-product of the electric field with the magnetic field. In special relativity, momentum is generalized to four-momentum.
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Deriving the $0$-component of 4-momentum using the relativistic Lagrangian
The $i^{th}$ component of momentum is given by ($i=1, 2, 3$),
$$
P_{i} = \frac{\partial L}{\partial \dot{X^{i}}}. … \tag{3}$$
However, for the time component of 4-momentum, Susskind uses the relativistic Hamiltonian to derive $$P_{0} = m\dot{X^{0}}. …
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