Thermal self-energies using light-front quantization

A recent paper by Alves, Das, and Perez contains a calculation of the one-loop self-energy in ${\ensuremath{\varphi}}^{3}$ field theory at $T\ensuremath{\ne}0$ using light-front quantization and concludes that the self-energy is different than the conventional answer and is not rotationally invariant. The changes of variable displayed below show that despite the complicated appearance of the thermal self-energy in light-front variables, it is exactly the same as the conventional result.