Evolution of uniformly accelerated system

[paweld]

Consider system with Hamiltonian H. If this system is attached to inertial observer its
evolution is described by unitary operator: U_t = \exp(t H) where t is time
measured by inertial observer. What if the observer accelerates (with constant
acceleration in its comoving frame). Is it stil true that U_\tau = \exp(\tau H)
wher \tau is time measured by accelerating observer (the length of its
world line). Is hamiltonian idependent of type of observer whom we attache the system to?

 

[azntoon]

No, the unitary operator is not necessarily U_\tau = \exp(\tau H). The Hamiltonian of the system will depend on the type of observer it is attached to. In general, the Hamiltonian of a system in a curved spacetime is given by the Hamilton-Jacobi equation, which depends on the metric of the spacetime. For an accelerating observer, the spacetime metric is different than for an inertial observer, so the Hamiltonian will be different.