Light-cone Quantization Research Articles

Discretized light-cone quantization of (1+1)-dimensional QED reexamined.

We reconsider the discretized light-cone quantization of QED in 1+1 dimensions, paying particular attention to the assumptions used by Eller, Pauli, and Brodsky. One result is an alternative interpretation of confinement to that given by Eller {ital et} {ital al}.

Discretized light-cone quantization: Formalism for quantum electrodynamics

A general nonperturbative method for solving quantum field theories in three space and one time dimensions, discretized light-cone quantization, is outlined and applied to quantum electrodynamics. This numerical method is frame independent and can be formulated such that ultraviolet regularization is independent of the momentum-space discretization. In this paper we discuss the construction of the light-cone Fock basis, ultraviolet regularization, infrared regularization, and the renormalization techniques required for solving QED as a light-cone Hamiltonian theory.

Non-trivial vacuum structure in light-cone quantum field theory

By modifying the Dirac-Bergmann algorithm for the quantisation of constrained systems we solve the massless Schwinger model quantised on a lightlike hyperplane. We obtain a nontrivial θ-type vacuum which is, however, cyclic in Fock space.

Hamiltonian formulation of (2+1)-dimensional QED on the light cone.

It is shown that an improper regularization in the light-cone quantization of field theories can introduce a violation of rotational invariance as well as spurious divergences. Several methods are developed to avoid or cure these problems, as required for a consistent renormalization procedure of gauge theories. Based on these methods, the light-cone Hamiltonian for (2+1)-dimensional QED is constructed. Extension to gauge theories in 3+1 physical dimensions is also discussed.

Nonperturbative vacua in the light-cone quantum field theory

Nonperturbative vacua in the light-cone quantum field theory

European Muon Collaboration effect: Nuclear-binding effect or vivid quark signature?

A relativistic two-level convolution model for deep-inelastic lepton nucleus scattering is presented in which the target nucleus is considered as a composite system of baryon-mesons which are also composite systems of quark-gluons, with each level based on the light-cone quantum field theory, respectively. In this prescription the impulse approximation is justified, the baryon number conservation is naturally guaranteed, and the off-shell ambiguity in the nucleonic approach is fixed. The scaling variable for bound nucleons is derived in a realistic way from the constraint of overall ``energy'' conservation, and a two-level convolution formula for nuclear-structure functions is given. It is shown that the European Muon Collaboration effect seems unable to be explained by the off-shell effect in terms of nucleonic degrees of freedom alone in this prescription.

The vacuum and lightcone quantization of interaction Hamiltonians

Let ϕ denote the conformally invariant neutral free scalar field on ℝ×Sn. The ‘naive’ lightcone Hamiltonian for a ϕp interaction is given by ∭c∶ϕp⋅, where C denotes a lightcone in ℝ×Sn, and the Wick power is relative to the free vacuum. We show that this sesquilinear form annihilates the free vacuum if n≥3 is odd, p>2, and p(n−1)≡0 mod 4.

Non-trivial vacuum structure in light-cone quantum field theory

By modifying the Dirac-Bergmann algorithm for the quantisation of constrained systems we solve the massless Schwinger model quantised on a lightlike hyperplane. We obtain a nontrivial θ-type vacuum which is, cyclic in Fock space.

THE EMC EFFECT IN A NUCLEONIC DESCRIPTION

Deep inelastic lepton-nucleus scattering is treated by considering the nucleus as a bound system of nucleons based on the light-cone quantum field theory. This method has the advantages that the impulse approximation is justified and that baryon number conservation is guaranteed. However, the ambiguities in identifying the structure function for bound nucleons in the conventional nucleonic approach seem not to have been avoided. It is also shown that a consistent calculation gives an unreasonably large Q2 dependence in the calculated nuclear structure function if one makes the most natural assumption to identify the off-"energy"-shell structure function for bound nucleons.

Relativistic Bound States

The standard resul ts of the quark model rely on nonrelativistic descriptions of the wavefunctions of the quarks in the hadron. However, simple uncertainty principle considerations show that the momenta of the quarks are comparable to their (constituent) masses, so that relativistic dynamics must be used in the description of the hadronic structure. In this paper I describe a number of new and old results which illustrate relativistic effects on the quark structure of hardons, and which employ the method of light cone quantisation to handle relativity.

Discretized Light-Cone Quantization Applied to QCD_4

Discretized Light-Cone Quantization Applied to QCD_4

Light-cone quantization of the super-Liouville theory

We quantise the super-Liouville equation using light-cone techniques. The theory is superconformally invariant at the quantum level, and c ̂ is a function of the coupling. When this coupling is tuned to certain rational numbers, c ̂ coincides with its values for the minimal series. We also obtain operator solutions for primary super-fields in the Neveu-Schwarz sector that provide explicit decompositions into monodromy invariant combinations of conformal blocks, and their conformal weights coincide with the known weights for primary fields in the minimal series. Certain terms present in the classical lagrangian are suppressed quantum mechanically as required by the correspondence with the super-Coulomb gas. This suppression also implies that the theory may be deformed into the exactly integrable supersymmetric sine-Gordon model by the addition to the lagrangian of a single primary field. This provides a lagrangian understanding of recent work by Zamolodchikov on the perturbation of the tricritical Ising model away from criticality.

THE QUANTUM MECHANICS OF AN N=1 SUPERPARTICLE IN AN EXTENDED SUPERSPACE

A new ten-dimensional superparticle action with local symmetries implemented via gauge fields is formulated in a superspace with an extra anticommuting space-time spinor coordinate. Light-cone quantization gives the spectrum of N=1 super-Yang-Mills. Covariant gauge choices in which the gauge fields are set to constants lead to free BRST-invariant quantum actions. Possible ghost systems include one with only a finite number of ghosts and several with an infinite number. In each case, the BRST cohomology class of zero ghost number gives the spectrum of N=1 super-Yang-Mills.

Deep inelastic lepton-nucleus scattering from the light-cone quantum field theory

The authors show that for deep inelastic lepton-nucleus scattering, the conditions which validate the impulse approximation are hardly satisfied when using ordinary instant form dynamics in the rest frame of the nucleus, whereas they are well satisfied when using instant form dynamics in the infinite-momentum frame, or using light-front form dynamics in an ordinary frame. Therefore a reliable theoretical treatment of deep inelastic lepton-nucleus scattering should be performed in the time-ordered perturbation theory in the infinite-momentum frame, or its equivalent, the light-cone perturbation theory in an ordinary frame. To this end, the authors extend the light-cone quantum field theory to the baryon-meson field to establish a relativistic composite model of nuclei. They then apply the impulse approximation to deep inelastic lepton-nucleus scattering in this model. As a first approximation, they consider only the nucleon degrees of freedom and neglect the Z-graph contributions. It is found that the results seem able to explain the EMC effect in trend but overestimate the ratio of the differential cross section for a bound nucleon to that for a free nucleon by about 8%. Some comparisons of the model with several relevant models are also presented.

Discretized light cone quantization in a 3+1 dimensional valence model for quarkonium

Led by successes of the nonperturbative method of discretized light cone quantization (DLCQ) in 1+1-dimensional toy models, we study the feasibility of extending it to 3+1 dimensional theories. Within aSU(Nc) nonabelian gauge theory, DLCQ is applied to a quarkonium system, where the Fock space has been truncated to the valence quark and antiquark only. In the light cone gauge the valenceq\(\bar q\)-model Hamiltonian matrix has an interesting structure which enables us to reduce the problem of diagonalization of some extremely large matrices to an amount of numerical labor already coped with in 1+1 dimensions. The model spectrum and the eigenfunctions are calculated independent of the order of the nonabelian gauge group, in special cases even analytically. The type of spectrum which appears after the calculation has been regularized covariantly may be interpreted as a sign that the quarks are confined in this model.

Hard nuclear reactions with light nuclei — Short range correlations and QCD effects

We review recent developments in investigation of the short range correlations in nuclei: light-cone quantum mechanics of the deuteron, structure of the single nucleon spectral function at large momenta,role of the color screening effect in nuclear structure, and the new options for studying the microscopic nuclear structure at high-energy facilities of the nineties.

Angular-momentum constraints in the light-cone quantum mechanics of the nucleon-nucleon system

We show that in the framework of the light-cone quantum mechanics of the two-nucleon system the constraints due to angular-momentum conservation can be reconstructed from the requirement of Lorentz invariance of the on-mass-shell scattering amplitudes. We have reduced the problem to the analysis of the rotational invariance of a Lippmann-Schwinger type equation and we show that, under plausible assumptions, maintaining rotational invariance of the scattering amplitude requires the two-body potential to be rotationally invariant.

Light-cone quantisation and manifestation of non-perturbative vacuum properties for scalar field theory

For a quantum field theory with interacting scalar fields treated in light-cone quantisation (LCQ) it is shown that the vacuum of the theory is always the perturbative vacuum. The fields can be split up into classical constant fields, determined by minima of the effective action, and quantum fields. The former ones replace the nontrivial vacuum expectation values of the conventionally quantised theory. When spontaneous symmetry breaking occurs, the classical fields are only determined up to symmetry transformations. This degeneracy corresponds to the degeneracy of the vacuum in the conventional approach. The effective actions of the conventional theory and LCQ are identical. Lightcone charges obey the canonical commutation relations with the fields and the canonical charge algebra relations. Ward identities and the appearance of Goldstone Bosons accompanying spontaneous symmetry breaking can be derived in analogy to the conventional case.

The light-cone approach for the calculation of hadronic states

We present an application of the recently proposed method of discretized light-cone quantization to quantum chromodynamics (QCD). We present the general method of light-cone quantization and point out its usefulness for the derivation of covariant integral equations for bound states. We then apply it to QCD and obtain the integral equation for the bound states in the valence sector of the mesons. The numerical solution of the integral equation shows a nice transition to the continuum. The conclusion summarizes the main results and discusses briefly what should be the next improvements of this method.

The fermion condensate of the Nambu-Jona-Lasinio model in Light Cone quantisation

We investigate the incorporation of condensates in Light Cone quantisation in the frame-work of the Nambu-Jona-Lasinio model. Although it is shown that the physical and perturbative vacua are identical, a gap equation for the dynamical quark mass is obtained and chiral symmetry is dynamically broken. The complete fermion condensate is found in the perturbative vacuum. The corresponding Goldstone mode is a zero mass bound state of the Weinberg equation.