GAUGE TRANSFORMATION IN STRING THEORY

In this paper,the authors find a transformation which connects the covariant formalism with the light-cone formalism in bosonic open string theory,which leads to the connection between covariant statevectors and light-cone statevectors,and yields an orthogonal complete set of states in covariant formalism and a physical projective operator for arbitrary space-time dimension D and intercept of Regge trajectory α(0).The later reduces to the result given by L.Brink and D.Olive in the case of D=26,α(0)=1.Finally,we explicitly show that in covariant formalism,the mass square operator M²≥0 except for the tachyon of ground state.     

Four-photon scattering amplitude in bosonic open string field theory

The covariant string field theory, which is formulated as a natural generalization of the light-cone gauge approach, is used to calculate three- and four-photon scattering amplitudes explicitly at tree level. The results are found to be consistent with the first quantized covariant approach.     

Dirac Oscillator in a Galilean Covariant Non-commutative Space

We study the Galilean Dirac oscillator in a non-commutative situation, with space-space and momentum-momentum non-commutativity. The wave equation is obtained via a ‘Galilean covariant’ approach, which consists in projecting the covariant equations from a (4,1)-dimensional manifold with light-cone coordinates, to a (3,1)-dimensional Galilean space-time. We obtain the exact wave functions and their energy levels for the plane and discuss the effects of non-commutativity.     

Wk structure of A SU(2)-level k from covariant construction of Kac-Moody algebras

The W_k structure underlying the transverse realization of affine SU(2) at level k is analyzed. The extension of the equivalence existing between the covariant and light-cone gauge realization of an affine Kac-Moody algebra to W_k algebras is given. Higher spin generators are extracted by the less singular terms in the operator product expansion of the parafermions constructed by means of the projection of the covariant on the light-cone gauge. These fields can be written in terms of only one free boson compactified on a circle.     

Spinless Duffin-Kemmer-Petiau Oscillator in a Galilean Non-commutative Phase Space

We examine Galilei-invariant linear wave equations in a non-commutative phase space. Specifically, we establish and solve the Galilean covariant Duffin-Kemmer-Petiau equation for spin-0 fields in a harmonic oscillator potential. We obtain these wave equations with a Galilean covariant approach, based on a (4+1)-dimensional manifold with light-cone coordinates followed by a reduction to a (3+1)-dimensional spacetime. We find the exact wave functions and their energy levels, and we examine the effects of non-commutativity.     

Covariant quantum description of the N = 2 Brink-Schwarz superparticle

The covariant quantum effective action for the N = 2 Brink-Schwarz superparticle is constructed starting from the canonical formulation in the light-cone gauge. BRST quantization is discussed.     

Tensor representations of conformal algebra and conformally covariant operator product expansion

A conformally covariant formulation of operator product expansion is discussed as an expansion of the product of two representations into a direct sum of irreducible representations. The basic irreducible representations are analyzed and classified. The isomorphism between the conformal algebra and the O(4, 2) algebra is used to obtain a manifestly covariant formalism. The implications of the isomorphism in the derivation of the representations is discussed. The covariant O(4, 2) formalism directly relates dominant terms to nondominant terms in the light-cone limit. The essential coincidence of the problem of a conformal covariant operator product expansion to the problem of determining the form of the three-point function is stressed, together with the relevance of a selection rule for two-point functions following from exact (not spontaneously broken) conformal covariance. The role of Ward identities in a conformal covariant scheme is pointed out, and the mathematical implications on the n-point functions from causality are described.     

Singular and regular gauges in soft–collinear effective theory: The introduction of the new Wilson line T

Gauge invariance in soft–collinear effective theory (SCET) is discussed in regular (covariant) and singular (light-cone) gauges. It is argued that SCET, as it stands, is not capable to define in a gauge invariant way certain non-perturbative matrix elements that are an integral part of many factorization theorems. Those matrix elements involve two quark or gluon fields separated not only in light-cone direction but also in the transverse one. This observation limits the range of applicability of SCET. To remedy this we argue that one needs to introduce a new Wilson line as part of SCET formalism, that we call T. This Wilson line depends only on the transverse component of the gluon field. As such it is a new feature to the SCET formalism and it guarantees gauge invariance of the non-perturbative matrix elements in both classes of gauges.     

Possible Minkowskian language in two-level systems

One hundred years ago, in 1908, Hermann Minkowski completed his proof that Maxwell’s equations are covariant under Lorentz transformations. During this process, he introduced a four-dimensional space called the Minkowskian space. In 1949, P.A.M. Dirac showed the Minkowskian space can be handled with the light-cone coordinate system with squeeze transformations. While the squeeze is one of the fundamental mathematical operations in optical sciences, it could serve useful purposes in two-level systems. Some possibilities are considered in this report. It is shown possible to cross the light-cone boundary in optical and two-level systems while it is not possible in Einstein’s theory of relativity.     

Contact interactions in superstring theory

Contact interactions are shown to be required in superstring theory in order to ensure either world-sheet supersymmetry in a covariant formalism or spacetime supersymmetry in the light-cone gauge. These interactions only contribute for specific ranges of the momenta of the emitted particles. Their rôle is to ensure analyticity of S-matrix elements in much the same way as with contact terms in ordinary field theories with point particles. For tree diagrams the usual functional calculations, performed at sufficiently spacelike momentum transfer, give correct results. For other values of the momenta the correct answer is obtained either by analytic continuation or by adding the contribution of the contact interactions. In certain loop calculations the effect of the contact interactions must be taken into account. In the light-cone gauge formalism the contact terms ensure positivity of the hamiltonian.     

Faddeev-Jackiw Quantization and Its Application to the Linear σ Model for Disoriented Chiral Condensates

The equivalence between the Faddeev-Jackiw formalism and Dirac-Bergmann algorithm is proved. A two-dimensional constrained system and a charged vector field are quantized in the Faddeev-Jackiw formalism. This symplectic method is technically developed, without recourse to Hamiltonian or Lagrangian, to quantize systems whose equations of motion are known. Examples are given to show this role. For constructing quantum approaches to the disoriented chiral condensates, the linear σ model is quantized in the instant form, light-cone form and covariant form.     

Supersymmetrical dual string theory

It is proved that the physical states of the open-string sector of the ten-dimensional string theory form supersymmetry multiplets. The proof is achieved by first constructing a new formulation of the spectrum generating algebra, and then forming the supersymmetry operator (as well as associated operators) and demonstrating that it transforms as a spinor under Lorentz transformations and has the correct anticommutation relations. The results can be interpreted either in terms of a covariant formulation or in terms of a light-cone gauge formulation. In the former case certain formulas are not completely proved, although they are in the latter. When interpreted in four dimensions (by dimensional reduction) the string theory provides an interacting theory of an infinite number of massive representations of N = 4 supersymmetry involving particles of arbitrarily high spin.     

Deuteron and neutron structure functions and the effect of relativistic Fermi motion

The deep-inelastic deuteron structure function (SF) F₂^D in the covariant approach in the light-cone variables is considered. The neutron SF F₂ⁿ is extracted from the deuteron and proton experimental data taking into account the relativistic deuteron model and the parametrization of F₂ⁿ is obtained. The effect of the relativistic Fermi motion is estimated to be 6% at x0.7. The extracted neutron SF is used to verify the Gottfried sum rule. It is shown that the violation of the flavour symmetry of the sea can be large with increasing Q².     

I=0 toI=1 transition form factors

A method is proposed to extend the hard scattering picture of Brodsky and Lepage to transitions between hadrons with orbital angular momentuml=0 andl=1. The use of covariant spin wave functions turns out to be very helpful in formulating that method. As a first application we construct a light-cone wave function of the nucleon resonance N^*(1535) in the quark-diquark picture. Using this wave function and the extended hard scattering picture, theN-N ^* transition form factors are calculated at large momentum transfer and the results compared to experimental data. As a further application of our method we briefly discuss the- a₁ form factors in an appendix.Supported by the Deutsche Forschungsgemeinschaft.     

Properties of the covariant formulation of superstring theories

The covariant two-dimensional action principle that describes the dynamics of free superstrings in a Minkowski background is reviewed. Covariant gauge conditions are formulated, which simplify the equations of motion of the superspace coordinates to free equations. In this gauge there are bosonic and fermionic constraints whose generators give a supersymmetric generalization of the Virasoro algebra. As in certain supersymmetric field theories, closure of the algebra requires using the equations of motion. Covariant constrained bracket relations are obtained for the classical theory, but it is very difficult to extend them to quantum mechanical commutation relations. Interaction vertices satisfying supersymmetry and the necessary gauge conditions are constructed. They reduce in a special frame to ones found in earlier work in the light-cone gauge, and then can be interpreted quantum mechanically.     

Light-like noncommutativity,light-front quantization and new light on UV/IR mixing

We revisit the problem of quantizing field theories on noncommutative Moyal space–time with light-like   noncommutativity. To tackle the issues arising from noncommuting and hence nonlocal time, we argue that for this case light-front quantization procedure should be employed. In this appropriate quantization scheme we perform the non-planar loop analysis for the light-like noncommutative field theories. One of the important and peculiar features of light-front quantization is that the UV cutoff of the light-cone Hamiltonian manifests itself as an IR cutoff for the light-cone momentum, p⁺$p^{+}$. Due to this feature, the naive results of covariant quantization for the light-like case allude to the absence of the UV/IR mixing in the light-front quantization. However, by a careful analysis of non-planar loop integrals we show that this is not the case and the UV/IR mixing persists. In addition, we argue in favour of the perturbative unitarity of light-like noncommutative field theories in the light-front quantization scheme.     

Light cone and mass shells

We propose a hypothesis which generalizes the notion of duality to off-mass-shell current matrix elements. The hypothesis, referred to as strong light-cone dominance, is formulated in terms of the light-cone sum rules, which reflect causality and the light-cone structure of current commutators: We postulate that these sum rules are saturated quasilocally by individual resonance peaks, in a similar manner as duality requires resonances to saturate the FESR for the hadronic on-shell amplitudes. This reconstitutes scaling in an average sense in regions where the leading light-cone singularity does not dominate. In coordinate space this hypothesis implies that the leading light-cone singularity regulates (tames) the entire light-cone expansion in a neighbourhood of the surface of the light-cone, whose extension is of the order of an inverse mass difference between consecutive resonances. We investigate the hypothesis of strong light-cone dominance in the framework of narrow resonance models for the vertex and show that the leading light-cone singularity indeed normalizes the single particle contributions by means of a relation of the Drell-Yan-West type. A simple Veneziano-like vertex model is exhibited, which is strongly light-cone dominated. Furthermore, we show how to exploitthe hypothesis in a rather model-independent way. We present some applications to the non-forward four-point function and show in particular that strong light-cone dominancerequires scaling for exclusive electroproduction processes like $\text{γ}{}^1\text{+}\text{N}\text{→ π +}\text{N}$.