Light front quantization

The light-front quantization^[1][2][3] of quantum field theories provides a useful alternative to ordinary equal-time quantization. In particular, it can lead to a relativistic description of bound systems in terms of quantum-mechanical wave functions. The quantization is based on the choice of light-front coordinates,^[4] where ${\displaystyle x^{+}\equiv ct+z}$ plays the role of time and the corresponding spatial coordinate is ${\displaystyle x^{-}\equiv ct-z}$. Here, ${\displaystyle t}$ is the ordinary time, ${\displaystyle z}$ is one Cartesian coordinate, and ${\displaystyle c}$ is the speed of light. The other two Cartesian coordinates, ${\displaystyle x}$ and ${\displaystyle y}$, are untouched and often called transverse or perpendicular, denoted by symbols of the type ${\displaystyle {\vec {x}}_{\perp }=(x,y)}$. The choice of the frame of reference where the time ${\displaystyle t}$ and ${\displaystyle z}$-axis are defined can be left unspecified in an exactly soluble relativistic theory, but in practical calculations some choices may be more suitable than others.