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Non-compact Groups, Coherent States, Relativistic Wave Equations and the Harmonic Oscillator

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Relativistic geometrical action for a quantum particle in the superspace is analyzed from theoretical group point of view. To this end an alternative technique of quantization outlined by the authors in a previous work and that is based in the correct interpretation of the square root Hamiltonian, is used. The obtained spectrum of physical states and the Fock construction consist of Squeezed States which correspond to the representations with the lowest weights \(\lambda=\frac{1}{4}\) and \(\lambda=\frac{3}{4}\) with four possible (non-trivial) fractional representations for the group decomposition of the spin structure. From the theory of semigroups the analytical representation of the radical operator in the superspace is constructed, the conserved currents are computed and a new relativistic wave equation is proposed and explicitly solved for the time-dependent case. The relation with the Relativistic Schrödinger equation and the Time-dependent Harmonic Oscillator is analyzed and discussed.

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  1. Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980, Dubna, Russian Federation

    Diego Julio Cirilo-Lombardo

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  1. Diego Julio Cirilo-Lombardo
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Correspondence to Diego Julio Cirilo-Lombardo.

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Cirilo-Lombardo, D.J. Non-compact Groups, Coherent States, Relativistic Wave Equations and the Harmonic Oscillator. Found Phys 37, 919–950 (2007). https://doi.org/10.1007/s10701-007-9133-9

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