The light-front quantization 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, where x + ≡ c t + z {\displaystyle x^{+}\equiv ct+z} plays the role of time and the corresponding spatial coordinate is x − ≡ c t − z {\displaystyle x^{-}\equiv ct-z} . Here, t {\displaystyle t} is the ordinary time, z {\displaystyle z} is a Cartesian coordinate, and c {\displaystyle c} is the speed of light. The other two Cartesian coordinates, x {\displaystyle x} and y {\displaystyle y} , are untouched and often called transverse or perpendicular, denoted by symbols of the type x → ⊥ = ( x , y ) {\displaystyle {\vec {x}}_{\perp }=(x,y)} . The choice of the frame of reference where the time t {\displaystyle t} and z {\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. The basic formalism is discussed elsewhere. There are many applications of this technique, some of which are discussed below. Essentially, the analysis of any relativistic quantum system can benefit from the use of light-front coordinates and the associated quantization of the theory that governs the system.
Nuclear reactions The light-front technique was brought into nuclear physics by the pioneering papers of Frankfurt and Strikman. The emphasis was on using the correct kinematic variables (and the corresponding simplifications achieved) in making correct treatments of high-energy nuclear reactions. This sub-section focuses on only a few examples. Calculations of deep inelastic scattering from nuclei require knowledge of nucleon distribution functions within the nucleus. These functions give the probability that a nucleon of momentum p {\displaystyle p} carries a given fraction y {\displaystyle y} of the plus component of the nuclear momentum, P {\displaystyle P} , y = p + / P + {\displaystyle y=p^{+}/P^{+}} . Nuclear wave functions have been best determined using the equal-time framework. It therefore seems reasonable to see if one could re-calculate nuclear wave functions using the light front formalism. There are several basic nuclear structure problems which must be handled to establish that any given method works. It is necessary to compute the deuteron wave function, solve mean-field theory (basic nuclear shell model) for infinite nuclear matter and for finite-sized nuclei, and improve the mean-field theory by including the effects of nucleon-nucleon correlations. Much of nuclear physics is based on rotational invariance, but manifest rotational invariance is lost in the light front treatment. Thus recovering rotational invariance is very important for nuclear applications. The simplest version of each problem has been handled. A light-front treatment of the deuteron was accomplished by Cooke and Miller, which stressed recovering rotational invariance. Mean-field theory for finite nuclei was handled Blunden et al. Infinite nuclear matter was handled within mean-field theory and also including correlations. Applications to deep inelastic scattering were made by Miller and Smith. The principal physics conclusion is that the EMC effect (nuclear modification of quark distribution functions) cannot be explained within the framework of conventional nuclear physics. Quark effects are needed. Most of these developments are discussed in a review by Miller. There is a new appreciation that initial and final-state interaction physics, which is not intrinsic to the hadron or nuclear light-front wave functions, must be addressed in order to understand phenomena such as single-spin asymmetries, diffractive processes, and nuclear shadowing. This motivates extending LFQCD to the theory of reactions and to investigate high-energy collisions of hadrons. Standard scattering theory in Hamiltonian frameworks can provide valuable guidance for developing a LFQCD-based analysis of high-energy reactions.
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