Noncommutative Spacetime and Quantum Mechanics
Abstract
In this paper we will analyze the the status of gauge freedom in quantum mechanics (QM) and quantum field theory (QFT). Along with this analysis comparison with ordinary QFT will be given. We will show how the gauge freedom problem is connected with the spacetime coordinates status  the very point at which the difficulties of QM begin. A natural solution of the above mentioned problem will be proposed in which we give a slightly more general form of QM and QFT (in comparison to the ordinary QFT) with noncommutative structure of spacetime playing fundamental role in it. We achieve it by reinterpretation of the Bohr's complementarity principle on the one hand and by incorporation of our gauge freedom analysis on the other. We will present a generalization of the Bargmann's theory of exponents of ray representations. It will be given an example involving time dependent gauge freedom describing nonrelativistic quantum particle in nonrelativistic gravitational field. In this example we infer the most general Schroedinger equation and prove equality of the (passive) inertial and the gravitational masses of quantum particle.
 Publication:

arXiv eprints
 Pub Date:
 April 2004
 arXiv:
 arXiv:quantph/0404028
 Bibcode:
 2004quant.ph..4028W
 Keywords:

 Quantum Physics
 EPrint:
 to be published as part of the book "Progress in General Relativity and Quantum Cosmology