

Quantum physics and quantum information
May 24, 2016 11:00, Moscow






Gauge transformation of quantum states in probability representation
Ya. A. Korennoi^{a}, V. I. Man'ko^{ab} ^{a} P. N. Lebedev Physical Institute, Russian Academy of Sciences, Moscow
^{b} Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region

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Abstract:
The gauge invariance of evolution equations of tomographic probability distribution functions of quantum particles in an electromagnetic field will be illustrated [1]. Optical and symplectic tomograms, which are determined by conventional gaugeindependent dequantizers (see [2]), are gaugedependent and are converted by means of an integral transformation simultaneously with a gauge transformation of the 4potential of the electromagnetic field, and the evolution equations of such tomograms, being gaugeinvariant, are dependent on the gauge. Contrary to the quantum case, optical and symplectic tomograms of a classical distribution function in the phase space possess of the property of gaugeindependence, and their evolution equations (Liouville equation in corresponding representations) are also gaugeindependent. To decide this problem we introduced gaugeindependent optical and symplectic tomographic quasidistributions and tomographic probability distributions, and obtained their gaugeindependent evolution equations, which are converted in the classical limit to the Liouville equation in corresponding tomographic representations.
References

Ya.A.Korennoy, V.I.Man'ko, Gauge transformation of quantum states in probability representation // arXiv:1511.00364.

G.G.Amosov, Ya.A.Korennoy, V.I.Man'ko, Description and measurement of observables in the optical tomographic probability representation of quantum mechanics // Phys.Rev.A 85,052119 (2012).

