A numerical experiment in DLCQ: microcausality, continuum limit and all that

The light-front ͑LF͒ quantization of QCD in the light-cone gauge has a number of remarkable advantages, including explicit unitarity, a physical Fock expansion, the absence of ghost degrees of freedom, and the decoupling properties needed to prove factorization theorems in high-momentum transfer inclusive and exclusive reactions. We present a systematic study of LF-quantized gauge theory following the Dirac method, and construct a Dyson-Wick S-matrix expansion based on LF time-ordered products. The free theory gauge field is shown to satisfy the Lorentz condition as an operator equation as well as the light-cone gauge condition. Its propagator is found to be transverse with respect to both its 4 momentum and the gauge direction. The interaction Hamiltonian of QCD can be expressed in a form resembling that of covariant theory, except for additional instantaneous interactions which can be treated systematically. The renormalization constants in YM theory are shown to satisfy the identity Z 1 ϭZ 3 at one-loop order. The QCD ␤ function, computed in the noncovariant light-cone gauge, agrees with that known in the conventional framework. Some comments are also made about the relationship of our LF framework, with a doubly transverse gauge propagator, to the analytic effective charge and renormalization scheme defined by the pinch technique, the unitarity relations, and the spectral representation. LF quantization thus provides a consistent formulation of gauge theory, despite the fact that the hyperplanes x Ϯ ϭ0 used to impose boundary conditions constitute characteristic surfaces of a hyperbolic partial differential equation.

Section: Discussionmentioning

confidence: 98%

Light-front-quantized QCD in the light-cone gauge: The doubly transverse gauge propagator

Srivastava

Brodsky

2001

“…is: yes, it does. Light-like compactification is feasible and DLCQ is consistent (there is no problem neither with causality [17]). The discretized (compactified) formulation of the theory on the light-like surface does exist as a straightforward light front field theory, but not as a limit of a space-like compactification.…”

Section: Discussionmentioning

confidence: 99%

Compactification near and on the light front

Harindranath¹,

Martinovic

Vary

2000

Self Cite

We address problems associated with compactification near and on the light front. In perturbative scalar field theory we illustrate and clarify the relationships among three approaches: (1) quantization on a space-like surface close to a light front; (2) infinite momentum frame calculations; and (3) quantization on the light front. Our examples emphasize the difference between zero modes in space-like quantization and those in light front quantization. In particular, in perturbative calculations of scalar field theory using discretized light cone quantization there are well-known new "zero mode induced" interaction terms. However, we show that they decouple in the continuum limit and covariant answers are reproduced. Thus compactification of a light-like surface is feasible and defines a consistent field theory.

“…The standard result for the commutator function of a scalar field with mass m in two dimensions can be found, e.g., in [70,71]. For κ 0123 → 0 Eq.…”

Section: Microcausalitymentioning

confidence: 97%

Quantum field theory based on birefringent modified Maxwell theory

Schreck

2014

In the current paper the properties of a birefringent Lorentz-violating extension of quantum electrodynamics is considered. The theory results from coupling modified Maxwell theory, which is a CPT-even Lorentz-violating extension of the photon sector, to a Dirac theory of standard spin-1/2 particles. It is then restricted to a special birefringent case with one nonzero Lorentz-violating coefficient. The modified dispersion laws of electromagnetic waves are obtained plus their phase and group velocities are considered. After deriving the photon propagator and the polarization vectors for a special momentum configuration we prove both unitarity at tree-level and microcausality for the quantum field theory based on this Lorentz-violating modification. These analytical proofs are done for a spatial momentum with two vanishing components and the proof of unitarity is supported by numerical investigations in case all components are nonvanishing. The upshot is that the theory is well-behaved within the framework of our assumptions where there is a possible issue for negative Lorentz-violating coefficients. The paper shall provide a basis for the future analysis of alternative birefringent quantum field theories.Comment: 32 pages, 4 figures; in version 3.0: added generalized results on optical theore