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Gauge transformation of quantum states in probability representation Ya. A. Korennoia, V. I. Man'koab 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 electro-magnetic field will be illustrated [1]. Optical and symplectic tomograms, which are determined by conventional gauge-independent dequantizers (see [2]), are gauge-dependent and are converted by means of an integral transformation simultaneously with a gauge transformation of the 4-potential of the electro-magnetic field, and the evolution equations of such tomograms, being gauge-invariant, 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 gauge-independence, and their evolution equations (Liouville equation in corresponding representations) are also gauge-independent. To decide this problem we introduced gauge-independent optical and symplectic tomographic quasi-distributions and tomographic probability distributions, and obtained their gauge-independent evolution equations, which are converted in the classical limit to the Liouville equation in corresponding tomographic representations. References
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