International Journal of Modern Physics A

Methods of summation of power series relevant to applications in quantum theory are reviewed, with particular attention to expansions in powers of the coupling constant and in inverse powers of an energy variable. Alternatives to the Borel summation method are considered and their relevance to different physical situations is discussed. Emphasis is placed on quantum chromodynamics. Recent applications of the renormalon language to perturbation expansions (resummation of bubble chains) in various QCD processes are reported and the importance of observing the full renormalization-group invariance in predicting observables is emphasized. News in applications of the Borel-plane formalism to phenomenology are conveyed. The properties of the operator-product expansion along different rays in the complex plane are examined and the problem is studied as to how the remainder after subtraction of the first n terms depends on the distance from the Euclidean region. Estimates of the remainder are explicitly calculated and their strong dependence on the nature of the discontinuity along the cut is shown. Relevance of this subject to calculations of various QCD effects is discussed.

The Gauss–Bonnet type identity is derived in a Weyl–Cartan space on the basis of the variational method.

We analyze a scheme in which three active neutrinos and one sterile neutrino account for the solar, the atmospheric and the LSND neutrino anomalies in a model-independent way. It is shown that if the equivalent number, N_ν, of the light neutrino species is less than 4, then the constraints from these anomalies, accelerator and reactor experiments and big bang nucleosynthesis force a general 4 × 4 mixing matrix to be effectively split into two 2 × 2 matrices. If these neutrinos are of the Majorana type, then negative results of neutrinoless double beta decay experiments imply that the total mass of neutrinos is not sufficient to account for all the hot dark matter components.

We study chiral induced gravity in the light-cone gauge and show that the theory is consistent for a particular choice of chiralities. The corresponding Kac–Moody central charge has no forbidden region of complex values. Generalized analysis of the critical exponents is given and their relation to the SL(2,R) vacuum states is elucidated. All the parameters containing information about the theory can be traced back to the characteristics of the residual symmetry group in the light-cone gauge.

It is shown explicitly that the correlation functions of conformal field theories (CFT) with the logarithmic operators are invariant under the differential realization of Borel subalgebra of -algebra. This algebra is constructed by tensor-operator algebra of differential representation of ordinary . This method allows us to write differential equations which can be used to find general expression for three- and four-point correlation functions possessing logarithmic operators. The operator product expansion (OPE) coefficients of general logarithmic CFT are given up to third level.

We generalize the technique of linked cluster expansions on hypercubic lattices to actions that couple fields at lattice sites which are not nearest neighbors. We show that in this case the graphical expansion can be arranged in such a way that the classes of graphs to be considered are identical to those of the pure nearest neighbor interaction. The only change then concerns the computation of lattice imbedding numbers. All the complications that arise can be reduced to a generalization of the notion of free random walks, including hopping beyond nearest neighbor. Explicit expressions for combinatorical numbers of the latter are given. We show that under some general conditions the linked cluster expansion series have a nonvanishing radius of convergence.

We generalize central-charge relations and differential identities of N = 2 special geometry to N extended supergravity in any dimension 4 ≤ D < 10, and p-extended objects. We study the extremization of the ADM mass per unit of p-volume of BPS extended objects. Runaway solutions for a "dilaton" degree of freedom leading to a vanishing result are interpreted as BPS extremal states having vanishing Bekenstein–Hawking entropy.

We investigate the vacuum state of the lattice gauge theory with fermions in 2 + 1 dimensions. The vacuum in the Hermite form for the fermion part is obtained; the vacuum in the unitary form has been proposed by Luo and Chen. It is shown that the Hermite vacuum has a lower energy than the unitary one through the variational method.

The thermal Euclidean Green functions for Photons propagating in the Rindler wedge are computed by employing an Euclidean approach within any covariant Feynman-like gauge. This is done by generalizing a formula which holds in the Minkowskian case. The coincidence of the found (β = 2π)-Green functions and the corresponding Minkowskian vacuum Green functions is discussed in relation to the remaining static gauge ambiguity already found in previous works. Further generalizations to more complicated manifolds are discussed. Ward identities are verified in the general case.

We re-examine Quantum Electrodynamics (QED) with massless electron as a finite quantum field theory as advocated by Gell-Mann–Low, Baker–Johnson, Adler, Jackiw and others. We analyze the Dyson–Schwinger equation satisfied by the massless electron in finite QED and conclude that the theory admits no nontrivial eigenvalue for the fine structure constant.