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We examine (3ϩ1)-dimensional QED quantized in the ''front form'' with finite ''volume'' regularization, namely, in discretized light-cone quantization. Instead of the light-cone or Coulomb gauges, we impose the light-front Weyl gauge A Ϫ ϭ0. The Dirac method is used to arrive at the quantum commutation relations for the independent variables. We apply ''quantum-mechanical gauge fixing'' to implement Gauss' law, and derive the physical Hamiltonian in terms of unconstrained variables. As in the instant form, this Hamiltonian is invariant under global residual gauge transformations, namely, displacements. On the light cone the symmetry manifests itself quite differently.

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The Fourier transform for slowly increasing functions is defined by the Parseval equation for tempered distributions. This definition was supplemented by a novel method of performing practical calculations by computing the Fourier transform for a suitably tempered function and then by integration by parts. The application of this method is illustrated both for the toy case, in which the function is integrable, so its Fourier transform can also be computed using the standard formula, and for the case of Coulomb-like potentials, which are only locally integrable functions. All of them have spherical symmetry, and two of them additionally have dilation symmetry. The proposed novel method does not violate these symmetries at any stage of the calculation.