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Trapped Ion Quantum Computing

Quantum mechanics with space-time noncommutativity

arXiv
Authors: Partha Nandi, Sayan Kumar Pal, Aritra N Bose, Biswajit Chakraborty

Year

2017

Paper ID

44019

Status

Preprint

Abstract Read

~2 min

Abstract Words

97

Citations

N/A

Abstract

We construct an effective commutative Schrödinger equation in Moyal space-time in (1+1)-dimension where both t and x are operator-valued and satisfy left\[hat{t}, hat{x} right\] = i θ. Beginning with a time-reparametrised form of an action we identify the actions of various space-time coordinates and their conjugate momenta on quantum states, represented by Hilbert-Schmidt operators. Since time is also regarded as a configuration space variable, we show how an `induced' inner product can be extracted, so that an appropriate quantum mechanical interpretation is obtained. We then discuss several other applications of the formalism developed so far.

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  • We construct an effective commutative Schrödinger equation in Moyal space-time in (1+1)-dimension where both t and x are operator-valued and satisfy left[hatt, hatx right] = i θ.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1708.04769 [2] arXiv https://arxiv.org/abs/1708.04769 [3] Publisher https://arxiv.org/abs/1708.04769

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