International Journal of Modern Physics A

In this article old and new relations between gauge fields and strings are discussed. We add new arguments that the Yang–Mills theories must be described by the noncritical strings in the five-dimensional curved space. The physical meaning of the fifth dimension is that of the renormalization scale represented by the Liouville field. We analyze the meaning of the zigzag symmetry and show that it is likely to be present if there is a minimal supersymmetry on the world sheet. We also present the new string backgrounds which may be relevant for the description of the ordinary bosonic Yang–Mills theories. The article is written on the occasion of the 40th anniversary of the IHES.

The system of coupled nonlinear partial differential equations called the Massive Thirring Model is reviewed. In particular it is analyzed in the chiral fermion version, which is extended by introducing a local gauge symmetry in place of the usual global symmetry. This is done by minimally coupling the fermions with a SU_L(2) ⊗ SU_R(2) gauge potential. Following the formalism of path integrals, we then formulate the study of chiral gauge anomalies in the quantum theory of this gauge extended model. The ultimate goal of it would be to compute the divergence of the chiral fermion current for a nonlinear anomalous theory. Actually, in this work we merely exhibit the Lax pair representation of the system of partial differential equations just derived; it holds to the first order approximation in the infinitesimal gauge parameters and coupling constants present.

Our aim is to hint a motivation in searching for explicit solutions of anomalous nonlinear gauge field theories, at least in simple cases.

The pinched/nonpinched classification of intersections of causal singularities of propagators in Minkowski space is reconsidered in the context of the theory of asymptotic operation as a first step towards extension of the latter to non-Euclidean asymptotic regimes. A highly visual distribution-theoretic technique of singular wave fronts is tailored to the needs of the theory of Feynman diagrams. Besides a simple derivation of the usual Landau equations in the case of the conventional singularities, the technique naturally extends to other types of singularities, for example due to linear denominators in non-covariant gauges, etc. As another application, the results of Euclidean asymptotic operation are extended to a class of quasi-Euclidean asymptotic regimes in Minkowski space.

We investigate how a uniformly rotating frame is defined as the rest frame of an observer rotating with constant angular velocity Ω around the z axis of an inertial frame. Assuming that this frame is a Lorentz one, we second quantize a free massless scalar field in this rotating frame and obtain a new rotating vacuum (of a massless scalar field) different from the Minkowski one. After this we consider a monopole detector interacting with the field. The radiative processes are discussed from a rotating and inertial frame point of view. Finally using this formalism, the polarization effects of electrons in circular accelerators is discussed.

Accurate and approximate methods are compared in the framework of models of the nucleon with valence quarks interacting linearly with a pion cloud. In order to establish the comparison, nucleon properties are computed from model states resulting from diagonalization of the Hamiltonian, and from approximate solutions based on variational and perturbative methods.

By considering N=2 superconformal algebra in d=2 dimensions, we construct an N=2 superconformal algebra in d=1 dimension. An N=1 superconformally invariant action for a particle is constructed. It is not what is obtained by dimensional reduction of the action for a superconformally invariant string.

Using a finite energy cutoff method, we derive one-loop renormalization group equations (RGE's) for Yukawa coupling parameters of quarks and for the vacuum expectation values of the Higgs doublets in the general framework of the Standard Model with two Higgs doublets (2HDM "type III"). In the model, the neutral-Higgs-mediated flavor-changing neutral currents are allowed but are assumed to be reasonably suppressed at low energies. The popular "type II" and "type I" models are just special cases of this framework. We then compare our RGE results with those of other authors who derived them for general (semi)simple gauge groups. We find out that our one-loop results disagree with those of Vaughn and Machacek, and agree with those of Jack and Osborn. We identify the mistakes of the former authors. We subsequently present a numerical example for the RGE flow of Yukawa coupling parameters and masses of quarks. The example shows a remarkable persistence of the suppression of the neutral-Higgs-mediated FCNC's as the energy of probes increases, in contrast to the usual expectations and reservations about this model.

The β-function is calculated for an SU(N) Yang–Mills theory from an ansatz for the vacuum wavefunctional. Direct comparison is made with the results of calculations of the β-function of QCD. In both cases the theories are asymptotically free, the only difference being in the numerical coefficient of the β-function, which is found to be -4 from the ansatz and from other QCD calculations. This is because, due to the constraint of Gauss' law applied to the wavefunctional, some interactions between gluons (which contribute the ) are omitted. The renormalisation procedure is understood in terms of "tadpole" and "horseshoe" Feynman diagrams which must be interpreted with a nonlocal propagator.