Abstract
The light-front (LF) quantization is applied for the model of massive scalar field with self-interaction. We check some of the LF postulates by considering the Wightman function for this model. The scale symmetry imposed only on the LF quantization hypersurface and the Lorentz symmetry assumed for all points in Minkowski’s space-time lead to a strong constraint for the Wightman functions, which is satisfied only by a free and massless scalar field. This result agrees with the recent Weinberg’s result for a scale-symmetric theory. This means that one cannot expect the unitary equivalence of the Fock space for scalar fields with different masses at the LF hypersurface.
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Przeszowski, J.A., Żochowski, J. Scale and Lorentz Transformations at the Light-Front. Few-Body Syst 55, 485–491 (2014). https://doi.org/10.1007/s00601-013-0751-9
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DOI: https://doi.org/10.1007/s00601-013-0751-9