Old-fashioned Perturbation Theory Research Articles

The constructive method for massive particles in QED

The constructive method of determining amplitudes from on-shell pole structure has been shown to be promising for calculating amplitudes in a more efficient way. However, challenges have been encountered when a massless internal photon is involved in the gluing of three-point amplitudes with massive external particles. In this paper, we use the original on-shell method, old-fashioned perturbation theory, to shed light on the constructive method, and show that one can derive the Feynman amplitude by correctly identifying the residue even when there is an internal photon involved.

On some aspects of the definition of scattering states in quantum field theory

Abstract The problem of extending quantum-mechanical formal scattering theory to a more general class of models that also includes quantum field theories is discussed, with the aim of clarifying certain aspects of the definition of scattering states. As the strong limit is not suitable for the definition of scattering states in quantum field theory, some other limiting procedure is needed. Two possibilities are considered, the abelian limit and adiabatic switching. Formulas for the scattering states based on both methods are discussed, and it is found that generally there are significant differences between the two approaches. As an illustration of the applications and the features of these formulas, S-matrix elements and energy corrections in two quantum field theoretical models are calculated using (generalized) old-fashioned perturbation theory. The two methods are found to give equivalent results.

MASS RENORMALIZATION IN A HAMILTONIAN APPROACH

We consider the energies of the one-particle states of relativistic quantum field theories in old-fashioned perturbation theory, and treat their regularization and renormalization from a strictly Hamiltonian perspective. We show that the one-loop diagrams lead to the renormalization of the mass for bosons and fermions identically to covariant perturbation theory, provided an appropriate regularization scheme is used. In particular, we show that a naive spatial momentum cutoff breaks covariance (in the limit where the cutoff is removed) in the case of the one-fermion states.

Deep inelastic structure functions in light-front QCD: Radiative corrections

Recently, we have introduced a unified theory to deal with perturbative and non-perturbative QCD contributions to hadronic structure functions in deep inelastic scattering. This formulation is realized by combining the coordinate space approach based on light-front current algebra techniques and the momentum space approach based on Fock space expansion methods in the Hamiltonian formalism of light-front field theory. In this work we show how a perturbative analysis in the light-front Hamiltonian formalism leads to the factorization scheme we have proposed recently. The analysis also shows that the scaling violations due to perturbative QCD corrections can be rather easily addressed in this framework by simply replacing the hadron target by dressed parton target and then carrying out a systematic expansion in the coupling constant $\alpha_s$ based on the perturbative QCD expansion of the dressed parton target. The tools employed for this calculation are those available from light-front old-fashioned perturbation theory. We present the complete set of calculations of unpolarized and polarized deep inelastic structure functions to order $\alpha_s$. We extract the relevant splitting functions in all the cases. We explicitly verify all the sum rules to order $\alpha_s$. We demonstrate the validity of approximations made in the derivation of the new factorization scheme. This is achieved with the help of detailed calculations of the evolution of structure function of a composite system carried out using multi-parton wavefunctions.

KAON Δ = ½ RULE, KL—KS MASS DIFFERENCE AND OLD-FASHIONED PERTURBATION THEORY

We construct a very short-distance weak interaction Δ = ½ Hamiltonian and use it in an old-fashioned perturbation theory to explain both first-order weak [Formula: see text] and [Formula: see text] decays and the second-order weak KL—KS mass difference.

Light-front QCD. II. Two-component theory.

The light-front gauge ${A}_{a}^{+}=0$ is known to be a convenient gauge in practical QCD calculations for short-distance behavior, but there are presistent concerns about its use because of its "singular" nature. The study of nonperturbative field theory quantizing on a light-front plane for hadronic bound states requires one to gain a priori systematic control of such gauge singularities. In the second paper of this series we study the two-component old-fashioned perturbation theory and various severe infrared divergences occurring in old-fashioned light-front Hamiltonian calculations for QCD. We also analyze the ultraviolet divergences associated with a large transverse momentum and examine three currently used regulators: an explicit transverse cutoff, transverse dimensional regularization, and a global cutoff. We discuss possible difficulties caused by the light-front gauge singularity in the applications of light-front QCD to both old-fashioned perturbative calculations for short-distance physics and upcoming nonperturbative investigations for hadronic bound states.

Erratum: Lowest-order mass corrections for a (1+1)-dimensional Yukawa model in light-front perturbation theory

In this work we {ital explicitly} demonstrate the equivalence of covariant (Feynman) perturbation theory with noncovariant light-front perturbation theory (LFPT) for lowest-order self-energy corrections in the (1+1)-dimensional Yukawa model. We also perform calculations in old-fashioned perturbation theory in the infinite-momentum frame (OFPT{sub {infinity}}) to elucidate the differences between LFPT and OFPT{sub {infinity}}.

Lowest-order mass corrections for a (1+1)-dimensional Yukawa model in light-front perturbation theory.

In this work we explicitly demonstrate the equivalence of covariant (Feynman) perturbation theory with noncovariant light-front perturbation theory (LEPT) for lowest-order self-energy corrections in the (1+1)-dimensional Yukawa model. We also perform calculations in oldfashioned perturbation theory in the infinite-momentum frame ($\mathrm{OFP}{\mathrm{T}}_{\ensuremath{\infty}}$) to elucidate the differences between LFPT and $\mathrm{OFP}{\mathrm{T}}_{\ensuremath{\infty}}$.

Feynman and Partons

For me, as for so many others, Richard Feynman is a special hero. He became so while I was learning quantum electrodynamics in graduate school at Stanford. The course happened to be organized historically, and for several months it was taught in the 1930s style out of Heitler's classic text, using old-fashioned perturbation theory and Dirac matrices α and β (but not γ). After this trial by fire came a seemingly endless, gloomy, turgid mass of field-quantization formalism. When Feynman diagrams arrived, it was the sun breaking through the clouds, complete with rainbow and pot of gold. Brilliant! Physical and profound! It was instant conversion to discipleship.

Soft-gluon factorization and multi-gluon amplitude

The infrared analysis of perturbative QCD starts from the formula of factorization of the soft-gluon radiation, which has the form of a semi-classical non-abelian current. This formula has been proved within the framework of the old-fashioned perturbation theory but no general proof is available in the more familiar framework of the Feynman-diagram technique. In this paper we present a proof of the factorization formula in Feynman-diagram perturbative amplitudes. This derivation provides further insight into the infrared structure of the theory and in particular into the role of coherence of colour charges. We also discuss the spin- and colour-averaged squared amplitude for the multi-gluon soft emission. We present a new derivation of the planar contribution and show that the first non-planar correction does not contain a leading singularity.

Loop calculations in confined QCD.I

We present a method for calculating one loop corrections in QCD confined to a spherical cavity with bag boundary conditions. We use euclidean Greens functions separated into free space and boundary parts and use oldfashioned perturbation theory. As a first application we calculate that part of the quark self energy that gives rese to the confining mirror charge potential in the nonrelativistic approximation. We obtain a weaker potential for relativistic massive quarks. Some consequences are discussed.

Do form factors at largeQ2and structure functions at largexnecessarily involve far-off-mass-shell quarks?

We study the question of small or large virtuality of the partons involved in elastic form factors at large ${q}^{2}$ and in deep-inelastic lepton scattering at $x\ensuremath{\rightarrow}1$. We consider two classes of models, both allowed by kinematics: the soft ones, small-virtuality models (SVM), where all partons are near the mass shell, and the hard ones, high-virtuality models (HVM), where at least one active parton is far off the mass shell. Taking the Bethe-Salpeter wave function as input, we compare the kinematical and analytical properties of SVM and HVM in the above processes, using successively covariant formalism and old-fashioned perturbation theory at infinite momentum. Both models lead to the Drell-Yan-West relation, but Bloom-Gilman duality looks more natural in SVM. We apply our analysis to the recent quantum-chromodynamic approaches of asymptotic form factors.

Consistent treatment of isobar degrees of freedom in nuclear matter

It is argued that the present situation in nuclear matter requires an explicit description of the 2π exchange contribution to the NN interaction providing the intermediate-range attraction. Especially, a realistic treatment of isobar degrees of freedom is strongly suggested. A suitable scheme is described, which starts from a field-theoretic Hamiltonian and uses old-fashioned perturbation theory consistently in the two- and the many-body problem. Numerical results (for NN scattering data and nuclear matter binding) emerging from such an approach are briefly outlined.

The structure of double scattering in old-fashioned perturbation theory

We study in old-fashioned perturbation theory the time orderings that are relevant for the exchange of two Regge poles (ladders). We determine how the phase of double scattering is established in the Mandelstam diagram. Our analysis clarifies the intermediate state structure of the multiple-scattering expansion and the rǒle of the unitarity constraints.

Optical Model for Diffraction Dissociation

The Deck effect is generalized to include multiple scattering, which should be important in diffractive dissociation on nuclear targets. A simple and intuitively appealing optical (eikonal) representation is given. On the basis of this representation, it is conjectured that form-factor effects should be included as a function of the distance off the energy shell in old-fashioned perturbation theory, at infinite momentum, rather than as a function of the distance off the mass shell, as in the usual double-Regge models. Ways to test this conjecture are discussed, and a procedure is given for including absorptive effects in 2 \ensuremath{\rightarrow} 3 processes.

Dynamics at Infinite Momentum

Old-fashioned perturbation theory is applied to a relativistic theory in a reference frame with infinite total momentum. It is found that many undesirable diagrams disappear. The contribution of the remaining diagrams is described by a new set of rules with properties intermediate between those of Feynman diagrams and old-fashioned diagrams, e.g., energy denominators become covariant, and Feynman parameters appear naturally. The new rules are used to derive some integral equations.