Charges as integrals over densities: An alternative formulation of Coleman's theorem

The charge operator is hermitean if and only if the vacuum is invariant. In that case the charge must be invariant under time translations.     

Symmetry conservation and integrals over local charge densities in quantum field theory

For conserved local currents ^µ j ^µ (x)=0 in quantum field theory it is shown that anR-dependence of _R (x ₀) inj ₀(f _R(x)· _R (x ₀)) leads to nicer properties than a fixed (x ₀). The behaviour of j ₀(f _R(x)·_R(x ₀) is discussed under this aspect.     

Calculating contracted tensor Feynman integrals

A recently derived approach to the tensor reduction of 5-point one-loop Feynman integrals expresses the tensor coefficients by scalar 1-point to 4-point Feynman integrals completely algebraically. In this Letter we derive extremely compact algebraic expressions for the contractions of the tensor integrals with external momenta. This is based on sums over signed minors weighted with scalar products of the external momenta. With these contractions one can construct the invariant amplitudes of the matrix elements under consideration, and the evaluation of one-loop contributions to massless and massive multi-particle production at high energy colliders like LHC and ILC is expected to be performed very efficiently.     

Quantum kinks on the null plane

We consider the quantization of a 1+1 dimensional field theory with kink solutions on a null plane. We present a field expansion which diagonalizes the operatorM ²=2P ⁺ P ^? including first order quantum corrections, reobtaining thereby the well known result for the kink mass. The quantization scheme treats classical solutions of different rapidity on an equal footing and the translation mode cancels completely, at least in the order considered here.     

Evaluating massive planar two-loop tensor vertex integrals

Using the parallel/orthogonal space method, we calculate the planar two-loop three-point diagram and two rotated reduced planar two-loop three-point diagrams. Together with the crossed topology, these diagrams are the most complicated ones in the two-loop corrections necessary, for instance, for the decay of the Z⁰ boson. Instead of calculating particular decay processes, we present a new algorithm which allows us to perform arbitrary next-to-next-to-leading order (NNLO) calculations for massive planar two-loop vertex functions in the general mass case. All integration steps up to the last two are performed analytically and will be implemented under xloops as part of the Mainz xloops-GiNaC project. The last two integrations are done numerically using methods like VEGAS and Divonne. Thresholds originating from Landau singularities are found and discussed in detail. In order to demonstrate the numerical stability of our methods we consider particular Feynman integrals which contribute to different physical processes. Our results can be generalized to the case of the crossed topology.     

Relativistic dynamics on a null plane

In view of possible applications to the quark model and to hadron spectroscopy, we investigate relativistic Hamiltonian quantum theories of finitely many degrees of freedom. We make use of the fact that if null planes are used as initial surfaces, the structure of the theory closely resembles nonrelativistic quantum mechanics: the inner variables that describe the structure of the system uncouple from the motion of the system as a whole. The dynamical content of such a theory resides in the operators M, $\text{j}$ of mass and spin that act in the space carrying the inner degrees of freedom. Relativistic invariance is equivalent to the requirement that M and $\text{j}$ generate a unitary representation of U(2). In contrast to this requirement, the condition that the wavefunctions of the system transform covariantly strongly restricts the dynamics. It is proven that for systems containing two constituents, covariance is equivalent to an algebraic relation that involves M and $\text{j}$ — the angular condition. A class of solutions of the angular condition is provided by a particular type of local manifestly covariant wave equations. One nontrivial solution of this class, a relativistic oscillator is given in detail. Confinement models of this type represent an interesting alternative to the solutions of the angular condition that result from the perturbation expansion of a local field theory through the three-dimensional quasipotential versions of the Bethe-Salpeter equation.     

A recursive reduction of tensor Feynman integrals

We perform a new, recursive reduction of one-loop n-point rank R   tensor Feynman integrals [in short: (n,R)$(n,R)$-integrals] for n?6$n?6$ with R?n$R?n$ by representing (n,R)$(n,R)$-integrals in terms of (n,R−1)$(n,R-1)$- and (n−1,R−1)$(n-1,R-1)$-integrals. We use the known representation of tensor integrals in terms of scalar integrals in higher dimension, which are then reduced by recurrence relations to integrals in generic dimension. With a systematic application of metric tensor representations in terms of chords, and by decomposing and recombining these representations, a recursive reduction for the tensors is found. The procedure represents a compact, sequential algorithm for numerical evaluations of tensor Feynman integrals appearing in next-to-leading order contributions to massless and massive three- and four-particle production at LHC and ILC, as well as at meson factories.     

Joint densities for random walks in the plane

We point out the existence of computationally convenient techniques for calculating the joint probability density for the position of a Pearson random walk after n steps. A new Fourier-Bessel function expansion for p_n(r, θ) is developed for this purpose which does not require radial symmetry, but does require that p_n(r, θ) = 0 when r exceeds some maximum radius, R.     

Aspects of QCD current algebra on a null plane

Consequences of QCD current algebra formulated on a light-like hyperplane are derived for the forward scattering of vector and axial–vector currents on an arbitrary hadronic target. It is shown that current algebra gives rise to a special class of sum rules that are direct consequences of the independent chiral symmetry that exists at every point on the two-dimensional transverse plane orthogonal to the lightlike direction. These sum rules are obtained by exploiting the closed, infinite-dimensional algebra satisfied by the transverse moments of null-plane axial–vector and vector charge distributions. In the special case of a nucleon target, this procedure leads to the Adler–Weisberger, Gerasimov–Drell–Hearn, Cabibbo–Radicati and Fubini–Furlan–Rossetti sum rules. Matching to the dispersion-theoretic language which is usually invoked in deriving these sum rules, the moment sum rules are shown to be equivalent to algebraic constraints on forward S$S$-matrix elements in the Regge limit.     

Path integrals over the group manifolds

Particle motion in the SU(2) manifold is quantized by path integrals. It is shown that the Poschl-Teller, Wood-Saxon, and Rosen-Morse potentials are solved by relating their propagators to the path integrations over the SU(2) manifold. Examples with some other groups are mentioned.     

Lovelock tensor as generalized Einstein tensor

We show that the splitting feature of the Einstein tensor, as the first term of the Lovelock tensor, into two parts, namely the Ricci tensor and the term proportional to the curvature scalar, with the trace relation between them is a common feature of any other homogeneous terms in the Lovelock tensor. Motivated by the principle of general invariance, we find that this property can be generalized, with the aid of a generalized trace operator which we define, for any inhomogeneous Euler–Lagrange expression that can be spanned linearly in terms of homogeneous tensors. Then, through an application of this generalized trace operator, we demonstrate that the Lovelock tensor analogizes the mathematical form of the Einstein tensor, hence, it represents a generalized Einstein tensor. Finally, we apply this technique to the scalar Gauss–Bonnet gravity as an another version of string–inspired gravity. This work was partially supported by a grant from the MSRT/Iran.     

Image of electron densities from line and plane projections

We compare Fourier transforms with orthogonal polynomials techniques applied in reconstructing three-dimensional electron–positron momentum densities from two-dimensional angular correlation of annihilation radiation (2D-ACAR) spectra and electron momentum densities from one-dimensional Compton profiles (1D-CP). In the case of Fourier transforms, we show results for two different algorithms: filtered back projection and Fourier–Bessel method. These techniques are presented for 2D-ACAR spectra in Y, ErGa₃ and model profiles. PACS 78.70.Bj; 87.59.Fm; 71.18.+y     

Introduction of a second-rank antisymmetric tensor into null aesthetic field theory

We are able to incorporate an antisymmetric second-rank tensor into null aesthetic field theory. There are some changes in the solutions due to the introduction of this antisymmetric second-rank tensor, which we discuss. We are not able to find an acceptable bounded particle system in four space-time dimensions.     

A general formula for analytic reduction of multi-loop tensor Feynman integrals

We prove a general formula for analytic reduction of tensor integrals which appear in calculations of multi-loop Feynman diagrams in quantum field theory models.     

Impulsive shells of null dust colliding with gravitational plane waves

A two-parameter family of solutions of Einstein's equations, corresponding to distribution valued stress-energy tensors with support on a (pair of intersecting) null hypersurface(s), is presented. They describe the collision of infinitely thin shells of null dust colliding with shells of the same kind and/or gravitational plane waves. For a subclass of this new family of solutions, the typical spacelike singularity that develops after the collision and forms the future boundary of the interaction region gives its place to a nonsingular Killing-Cauchy horizon.     

On the one-link integrals over compact groups

For O(N), U(N) and SU(N) groups, we study the weak coupling behaviour of the one-link integrals using their Schwinger-Dyson equations. Special attention is paid to the perturbative corrections to the large N limit. In the case of unitary groups, the 1/N ² correction is obtained explicitly.