
The
light-front quantization
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 ...
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
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, qua ...
wave functions. The quantization is based on the choice of light-front coordinates,
where
plays the role of time and the corresponding spatial coordinate is
. Here,
is the ordinary time,
is one
Cartesian coordinate, and
is the speed of light. The other two Cartesian coordinates,
and
, are untouched and often called transverse or perpendicular, denoted by symbols of the type
. The choice of the
frame of reference
In physics and astronomy, a frame of reference (or reference frame) is an abstract coordinate system whose origin, orientation, and scale are specified by a set of reference points― geometric points whose position is identified both mathema ...
where the time
and
-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 solution of the LFQCD Hamiltonian eigenvalue equation will utilize the available mathematical methods of quantum mechanics and contribute to the development of advanced computing techniques for large quantum systems, including
nuclei. For example, in the discretized light-cone quantization method (DLCQ),
periodic conditions are introduced such that momenta are discretized and the size of the Fock space is limited without destroying Lorentz invariance. Solving a quantum field theory is then reduced to diagonalizing a large sparse
Hermitian matrix. The DLCQ method has been successfully used to obtain the complete spectrum and light-front wave functions in numerous model quantum field theories such as QCD with one or two space dimensions for any number of
flavors
Flavor or flavour is either the sensory perception of taste or smell, or a flavoring in food that produces such perception.
Flavor or flavour may also refer to:
Science
*Flavors (programming language), an early object-oriented extension to Lis ...
and quark masses. An extension of this method to
supersymmetric theories, SDLCQ,
takes advantage of the fact that the light-front Hamiltonian can be factorized as a product of raising and lowering
ladder operator
In linear algebra (and its application to quantum mechanics), a raising or lowering operator (collectively known as ladder operators) is an operator that increases or decreases the eigenvalue of another operator. In quantum mechanics, the raisin ...
s. SDLCQ has provided new insights into a number of supersymmetric theories including direct numerical evidence
for a supergravity/super-Yang–Mills duality conjectured by Maldacena.
It is convenient to work in a Fock basis
where the light-front momenta
and
are diagonal. The state
is given by an expansion
:
with
:
is interpreted as the wave function of the contribution from states with
particles. The eigenvalue problem
is a set of coupled integral equations for these wave functions. Although the notation as presented supports only one particle type, the generalization to more than one is trivial.
Discrete light-cone quantization
A systematic approach to discretization of the eigenvalue problem is the DLCQ method originally suggested by Pauli and Brodsky.
In essence it is the replacement of integrals by trapezoidal approximations, with equally-spaced intervals in the longitudinal and transverse momenta
:
corresponding to
periodic boundary conditions
Periodic boundary conditions (PBCs) are a set of boundary conditions which are often chosen for approximating a large (infinite) system by using a small part called a ''unit cell''. PBCs are often used in computer simulations and mathematical mode ...
on the intervals