Light-cone Commutators Research Articles

High energy behaviour of pion production by neutrinos

Arguments based on light-cone commutators and PCAC are used to show that the cross section σ( νN→ ωN π) should increase logarithmically with energy.

Analysis of weak neutral currents using light-cone algebra

Using the algebra of light-cone commutators and making some simplifying assumptions, we have attempted to determine the isospin structure of a two-parameter weak hadronic neutral current. We have also computed in the light-cone model, they distributions for inclusive neutrino and antineutrino neutral current deep-inelastic interactions. Contrary to the quark-parton model, we find that both distributions have the same value.

Dynamically parametrized quantization of local operators in the bag model

We argue that the quantization of Chodos, Jaffe, Johnson, Thorn, and Weisskopf (CJJTW) of the bag model in two dimensions is inappropriate for considerations of locality and we present a new quantization in which the parametrization is fixed by positivity. The CJJTW operator algebra is obtained as a subalgebra of an extended system. A boundary regularization procedure is introduced and a local phi (x) operator having cutoff-independent matrix elements is defined. Boundary fluctuation effects are finite. We calculate an example of bag scattering in an external field and show that the crossed-channel bag-pair production and annihilation amplitudes contain only those singularities associated with bag fission. Nontrivial light-cone commutators are calculated. (AIP)

Model-independent study of light-cone current commutators

An attempt is made to extract information on the nature of light-cone current commutators (LCC) in a model-independent manner. Using simple assumptions on the validity of the Deser-Gilbert-Sudarshan (DGS) representation for the structure functions of deep-inelastic scattering and using the Bjorken-Johnson-Low theorem we show that in principle the LCC may be constructed knowing the experimental electron-proton scattering data. On the other hand, the scaling behavior of the structure functions is utilized to study the consistency of a vanishing value for various LCC under mild assumptions on the behavior of the DGS spectral moments.

Causality, equal-time algebra, and light-cone commutators

Extending previous work we discuss the sum rules that follow from causality, scaling, and equal-time algebra for the nonforward (spinless) single-particle matrix element of the commutator of two conserved vector currents, using the recently introduced refined infinite-momentum technique. The complete set of sum rules is found to include those obtained from light-cone commutators. It also contains some additional ones.

Erratum to: Could pion electroproduction be a test of current-current light-cone commutators?

Erratum to: Could pion electroproduction be a test of current-current light-cone commutators?

Could pion electroproduction be a test of current-current light-cone commutators?

Could pion electroproduction be a test of current-current light-cone commutators?

Sum rules for the real part of a current-hadron scattering amplitude and light-cone commutators

Sum rules are derived relating the real part of a current-proton scattering amplitude to the light-cone commutator of two currents. The contribution of the different, connected and disconnected, intermediate states is examined in detail and the relative importance in the infinite (or quasi-infinite) momentum limit is exhibited. The sum rules whose dominant contribution in such a limit comes from direct and/or two-particle disconnected (Z-diagram) intermediate states are related to the parameters appearing in the quark model light-cone current commutation relations and consistent results are then obtained.

Induced Pseudoscalar Coupling Constant and Light-Cone Sum Rules

We derive formulas giving the bilocal form factors, which appear in the matrix element of light-cone commutators, as Fourier transforms of scaling limits of electron scattering structure functions. We deal with the case of nonforward, spin-dependent, virtual Compton scattering. By taking the local limit of an appropriate bilocal form factor we find a new sum rule for the induced pseudoscalar coupling constant of nuclear beta decay.

Equal-time algebra and light-cone commutators

We discuss the sum rules of equal-time algebra in a refined form of the infinite-momentum limit and show that they reduce to those obtained from light-cone commutators.

Diagonalizing Tensor Covariants, Light-Cone Commutators, and Sum Rules

We derive fixed-mass sum rules for virtual Compton scattering including the nucleon spin and not specializing to the forward direction. We use the methods of both Dicus, Jackiw, and Teplitz (for the absorptive parts) and Heimann, Hey, and Mandula (for the real parts). We find a set of tensor covariants such that the corresponding scalar amplitudes are proportional to simple $t$-channel parity-conserving helicity amplitudes. We give a relatively complete discussion of the convergence of the sum rules in a Regge model.

Tests of Light-Cone Commutators. II

Tests of Light-Cone Commutators. II

Eikonal Approximation for the Bilocal Vertex Function andνW2in a Fermion—Neutral-Vector-Gluon Model

The eikonal approximation is used to investigate the forward one-fermion matrix element of the bilocal operator that appears in the most singular term of the canonical light-cone current commutators for the fermion---neutral-vector-gluon model. A relationship is exhibited between this matrix element of the bilocal operator and the leading behavior of $\ensuremath{\nu}{W}_{2}$. This relation allows calculations of contributions to the matrix element of the bilocal operator to be applied to the corresponding contribution to $\ensuremath{\nu}{W}_{2}$. A simple set of graphs contributing to the matrix element of the bilocal operator is calculated in the eikonal approximation. This gives a contribution to $\ensuremath{\nu}{W}_{2}$ in agreement with explicit calculations in perturbation theory for the corresponding set of graphs of $\ensuremath{\nu}{W}_{2}$.

Connection Between Equal-Time and Light-Cone Commutators

Integral representations are given for matrix elements of equal-$t$ (equal-time) and equal-$\ensuremath{\tau}$ (light-cone) commutators ($t={x}_{0},\ensuremath{\tau}={x}_{0}+{x}_{3}$) of two vector currents. A plausible assumption is made connecting these commutators. Its consequences are corresponding pairs of general variable-mass sum rules. Each pair reduces to a single sum rule in the fixed-mass limit. Electroproduction is discussed as a special case.

Generalized fixed-mass sum rules

Light-cone commutation relations have been shown to be the natural commutators to use to derive fixed mass (fixed spacelike q 2) sum rules for the structure functions which describe lepton hadron scattering. In this paper we review, in detail, the structure of the light-cone commutators and the methods used to derive sum rules. We then derive new sum rules by using two generalizations of the previous method; 1. (1) we use the light-cone commutator of moments of currents by considering derivatives of the Fourier transform of the current and 2. (2) we expand the integrals in a power series in q 2 before fixing q 2. The new sum rules involve derivatives of the structure functions with respect to q 2 and/or ν. Except for one short separate calculation we consider only conserved vector currents. For the most part we do not sum over the nucleon spin nor restrict ourselves to the forward direction. Our emphasis is on the type of information contained in the different techniques of derivation and we particularly emphasize which sum rules can be derived from the least model dependent commutator.

Spin-dependent finite-energy sum rules and light-cone commutators

Spin-dependent finite-energy sum rules are obtained relating the imaginary part of a current proton scattering amplitude to the light-cone commutator of currents. In the derivation of these sum rules the contribution of disconnected states is examined in detail and it is found that it is generally these states that give the dominant contribution on taking the infinite (or quasi-infinite)-momentum limit for the external states. The consequences of this on the validity of the derivation of the usual sum rules are discussed.

Light-Cone Commutators and Chiral-Symmetry Effects in Deep-Inelastic Processes

From the canonical light-cone commutators in the quark-vector-gluon model, the two most singular terms in the light-cone expansion for commutators of arbitrary Dirac bilinear covariants (local and bilocal) are derived and various interesting commutators are given explicitly. This operator expansion is then applied to deep-inelastic lepton-nucleon scattering, and the parity-violating as well as chiral-symmetry-breaking deep-inelastic structure functions are determined as the Fourier transforms of the diagonal matrix elements of the appropriate bilocal operators. A sum rule is derived which distinguishes between the parton model and the quark-vector-gluon model. In the vector-gluon model with a light-cone quantization, we consider a light-cone $\ensuremath{\sigma}$ term for pion-nucleon scattering which differs from the usual $\ensuremath{\sigma}$ term.

Light cone constraints and two asymptotic domains in lepton-nucleon and meson-nucleon scattering

Effective bare masses of the “current-quarks” are estimated from some testable inequalities, linking deep inelastic lepton-nucleon structure functions and high energy meson-nucleon total cross-sections, derived on the basis of the light-cone commutators of the pseudoscalar densities of quark-field theory.

Light-cone commutators of stress-tensor components

The commutator [ θ μν ( x), θ ϱσ (0)] among components of the in the limit x 2 → 0. The related Bjorken limit of virtual graviton scattering is studied with special attention to its positivity restrictions and the ensuing conditions on the commutator. A complete discussion of scaling for virtual graviton scattering, of the sum rules from equal-time commutators, and of the conditions implied by positivity on the scale dimensions of the symmetry-breaking terms is given.

Light-cone ordering and current commutators

Abstract The light-cone ordered Green functions are constructed with the following properties-causality, unitary, Lorentz covariance, gauge invariance, the light-cone ordering leading to the dividing of the usual Green functions into the terms with the different asymptotics in the scaling limit. The relations between the covariantizing sea-gulls — the main asymptotical terms — and the light-cone current commutators are obtained. The functional method is suggested for the direct calculation of the light-cone sea-gull terms in canonical field theories, in particular in the quark-vector-gluon theory in different gauges. The generalized Bjorken-Johnson-Low theorem for covariant light-cone ordered products is considered. The sum rules expressing the sea-gulls in the virtual Compton amplitude through the measurable scaling functions are derived.