Light front quantization
For example, when an electron scatters on a proton as in the famous SLAC experiments that discovered the quark structure of hadrons, the interaction with the constituents occurs at a single light-front time.
In contrast, it is a difficult dynamical problem to calculate the effects of boosts of states defined at a fixed instant time
[5][6][7] Quantization on the light-front provides the rigorous field-theoretical realization of the intuitive ideas of the parton model which is formulated at fixed
[15][16][17] The gauge-invariant meson and baryon distribution amplitudes which control hard exclusive and direct reactions are the valence light-front wave functions integrated over transverse momentum at fixed
The "ERBL" evolution[13][14] of distribution amplitudes and the factorization theorems for hard exclusive processes can be derived most easily using light-front methods.
For example, the "handbag" contribution to the generalized parton distributions for deeply virtual Compton scattering, which can be computed from the overlap of light-front wave functions, automatically satisfies the known sum rules.
One can also prove fundamental theorems for relativistic quantum field theories using the front form, including: (a) the cluster decomposition theorem[18] and (b) the vanishing of the anomalous gravitomagnetic moment for any Fock state of a hadron;[19] one also can show that a nonzero anomalous magnetic moment of a bound state requires nonzero angular momentum of the constituents.
[25] Light-front quantization is thus the natural framework for the description of the nonperturbative relativistic bound-state structure of hadrons in quantum chromodynamics.
The light-front Hamiltonian formulation thus opens access to QCD at the amplitude level and is poised to become the foundation for a common treatment of spectroscopy and the parton structure of hadrons in a single covariant formalism, providing a unifying connection between low-energy and high-energy experimental data that so far remain largely disconnected.
Front-form relativistic quantum mechanics was introduced by Paul Dirac in a 1949 paper published in Reviews of Modern Physics.
Wigner[38] and Bargmann[39] showed that this symmetry must be realized by a unitary representation of the connected component of the Poincaré group on the Hilbert space of the quantum theory.
The dynamical nature of this symmetry is most easily seen by noting that the Hamiltonian appears on the right-hand side of three of the commutators of the Poincaré generators,
, can be expressed in terms of their light-front components as In a front-form relativistic quantum theory the three interacting generators of the Poincaré group are
Because of these properties, front-form quantum theory is the only form of relativistic dynamics that has true "frame-independent" impulse approximations, in the sense that one-body current operators remain one-body operators in all frames related by light-front boosts and the momentum transferred to the system is identical to the momentum transferred to the constituent particles.
In the absence of interactions, Stone's theorem applied to tensor products of known unitary irreducible representations of the Poincaré group gives a set of self-adjoint light-front generators with all of the required properties.
, can be constructed using the generalized wave operators for different orientations of the light front[49][50][51][52][53] and the kinematic representation of rotations Because the dynamical input to the
Karmanov[54][55][56] introduced a covariant formulation of light-front quantum theory, where the orientation of the light front is treated as a degree of freedom.
The result is that by choosing the light front components of the spin to be kinematic it is possible to realize full rotational invariance at the expense of cluster properties.
Light-front relativistic quantum mechanics is formulated on the direct sum of tensor products of single-particle Hilbert spaces.
One of the advantages of light-front quantum mechanics is that it is possible to realize exact rotational covariance for system of a finite number of degrees of freedom.
Thus, one can again match the instant form to the front-form formulation where such vacuum loop diagrams do not appear in the QED ground state.
This non-covariant definition destroys the spatial symmetry that, in its turn, results in a few difficulties related to the fact that some transformation of the reference frame may change the orientation of the light-front plane.
complicates also the construction of the states with definite angular momentum since the latter is just a property of the wave function relative to the rotations which affects all the coordinates
There were formulated the rules of graph techniques which, for a given Lagrangian, allow to calculate the perturbative decomposition of the state vector evolving in the light-front time
means that the operator of the total angular momentum in explicitly covariant light-front dynamics obtains an additional term:
The fact that the transformations changing the orientation of the light-front plane are dynamical (the corresponding generators of the Poincare group contain interaction) manifests itself in the dependence of the coefficients
[73] The central issue for light-front quantization is the rigorous description of hadrons, nuclei, and systems thereof from first principles in QCD.
The approximate duality in the limit of massless quarks motivates few-body analyses of meson and baryon spectra based on a one-dimensional light-front Schrödinger equation in terms of the modified transverse coordinate
The nonzero quark masses introduce a non-trivial dependence on the longitudinal momentum, and thereby highlight the need to understand the representation of rotational symmetry within the formalism.
Exploring AdS/QCD wave functions as part of a physically motivated Fock-space basis set to diagonalize the LFQCD Hamiltonian should shed light on both issues.
