Non-relativistic limit of quantum field theory in inertial and non-inertial frames and the Principle of Equivalence

Understand

We discuss the non-relativistic limit of quantum field theory in an inertial frame, in the Rindler frame and in the presence of a weak gravitational field, highlighting and clarifying several subtleties.

• We study the following topics: (a) While the action for a relativistic free particle is invariant under the Lorentz transformation, the corresponding action for a non-relativistic free particle is not invariant under the Galilean transformation, but picks up extra contributions at the end points.
• This leads to an extra phase in the non-relativistic wave function under a Galilean transformation, which can be related to the rest energy of the particle even in the non-relativistic limit.
• (b) We show how the solution to the generally covariant Klein-Gordon equation in a non-inertial frame, which has a time-dependent acceleration, reduces to the quantum mechanical wave function in the presence of an appropriate (time-dependent) gravitational field, in the non-relativistic limit.