The Hamiltonian is the energy, which is just one component of a four-vector and therefore not Lorentz invariant.

The Lagrangian is the Legendre transform of the Hamiltonian and I was wondering if there is some good reason why we get through the Legrendre transform something invariant?

The Hamiltonian is the energy, which is just one component of a four-vector and therefore not Lorentz invariant.

The Lagrangian is the Legendre transform of the Hamiltonian and I was wondering if there is some good reason why we get through the Legendre transform something invariant?

The Hamiltonian is the energy, which is just one component of a four-vector and therefore not Lorentz invariant.

The Lagrangian is the Legendre transform of the Hamiltonian and I was wondering if there is some good reason why we get through the Legrendre transform something invariant?

The Hamiltonian is the energy, which is just one component of a four-vector and therefore not Lorentz invariant.

The Lagrangian is the Legendre transform of the Hamiltonian and I was wondering if there is some good reason why we get through the Legrendre transform something invariant?

The Hamiltonian is directly related to the energy, which is just one component of a four-vector and therefore not Lorentz invariant. The Lagrangian is the Legendre transform of the Hamiltonian and I was wondering if there is some good reason why we get through the Legrendre transform something invariant?

The Hamiltonian is the energy, which is just one component of a four-vector and therefore not Lorentz invariant. 

The Lagrangian is the Legendre transform of the Hamiltonian and I was wondering if there is some good reason why we get through the Legrendre transform something invariant?