Light-front quantization of the sine-Gordon model

It is shown how to modify the canonical light-front quantization of the (1+1)-dimensional sine-Gordon model such that the zero-mode problem of light-front quantization is avoided. The canonical sine-Gordon Lagrangian is replaced by an effective Lagrangian which does not lead to divergences as $k^{+}=\frac{(k^0+k^1)}{\sqrt{2}}\to 0$. After canonically quantizing the effective Lagrangian, one obtains the effective light-front Hamiltonian which agrees with the naive light-front (LF) Hamiltonian, up to one additional renormalization. The spectrum of the effective LF Hamiltonian is determined using discrete light-cone quantization and agrees with results from equal-time quantization.