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Physicist97

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In summary, the conversation discusses the use of the momentum operator in different contexts, including special relativity and curved spacetime. It is noted that the commutators of the covariant derivatives are not equal to the Riemann Tensor, indicating that a different approach is needed. It is suggested that path-integral quantization may be a more fruitful approach for developing quantum mechanics in curved spacetime. The book "Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets" by Kleiner is recommended as a source for understanding this method.

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Physicist97

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fzero

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Physicist97

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A more fruitful place to start would probably be with the action for a test particle on a curved spacetime. Then one could use path-integral quantization to develop the quantum mechanics. It should be possible to derive the curved-space version of the Klein-Gordon equation, for example.

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Physicist97 said:

Kleinert has a book that he seems to have mostly online at http://users.physik.fu-berlin.de/~kleinert/b5/ I've only just looked at Ch 10 which is on curved space, so I don't know how accessible the early chapters are.

The momentum operator in curved spacetime is a mathematical quantity that describes the motion and momentum of a particle in a curved space. It takes into account the curvature of spacetime, which can be caused by massive objects such as planets or stars.

The momentum operator in curved spacetime takes into account the effects of gravity, which can cause a curved path for a particle. In flat spacetime, the momentum operator follows the laws of classical mechanics, where momentum is conserved and particles move in straight lines unless acted upon by a force.

The momentum operator in curved spacetime is a key component of Einstein's theory of general relativity. It helps to describe how particles move and interact in the presence of massive objects, which cause spacetime to curve.

Yes, the momentum operator in curved spacetime is essential in understanding the motion of planets, moons, and other celestial bodies in our universe. It helps to predict and explain the orbits and trajectories of these objects in the presence of massive bodies like the Sun.

The momentum operator in curved spacetime has many practical applications in fields such as astrophysics, cosmology, and space travel. It is used to calculate the trajectories of spacecraft in orbit around planets, and it helps to explain the behavior of matter and energy in the universe.

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