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arXiv · 1110.1314

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

Hamsa Padmanabhan·T. Padmanabhan
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Abstract

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. The extra phase acquired by the non-relativistic wave function in an accelerated frame actually arises from the gravitational time dilation and survives in the non-relativistic limit. (c) We provide a detailed description of the non-relativistic limit of the Feynman propagator in a weak gravitational field, and discuss related issues. [Abridged Abstract]

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Hamsa Padmanabhan, T. Padmanabhan. 2011-10-06. Non-relativistic limit of quantum field theory in inertial and non-inertial frames and the Principle of Equivalence. https://doi.org/10.1103/physrevd.84.085018

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