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A set of gauge transformations of a relativistic field of quantum harmonicoscillators is studied in a mathematically rigorous manner. Each wave functionin the domain of the number operator of a single oscillator generates aFrechet-differentiable field of wave functions. Starting from a coherent wavefunction one obtains a two-dimensional differentiable manifold of coherentvector states. As an illustration it is shown that the gauge transformation canbe chosen in such a way that the resulting fields describe a freely-propagatingwave.

Gauge transformations of a relativistic field of quantum harmonic oscillators