On the electron-muon mass ratio

The quantum electrodynamics (QED) of electrons is considered as a theory with a passive dilatation invariance which is perturbed by the electromagnetic coupling to hadrons and muons. A stability criterium is introduced and evaluated in lowest order of the perturbation. The resulting expression for the electron-muon mass ratio in terms of the vacuum polarization can be tested in e+ − e− colliding beam experiments

Renormalization and gauge invariance in quantum electrodynamics

The connection between the field theory and the perturbation expansion of quantum electrodynamics is studied. As a starting point the usual Lagrangian is taken but with bare electron mass and the renormalization constant Z3 set equal to zero. This theory is essentially equivalent to the usual one; however, it does not contain any constant of nature and is dilatational and gauge invariant, both invariances being spontaneously broken. The various limiting procedures implied by the differentiation, the multiplication and the renormalization of the field operators in the Lagrangian are combined in a gauge invariant way to a single limit. Propagator equations are derived which are the usual renormalized ones, except for: (i) a natural cancellation of the quadratic divergence of the vacuum polarization; (ii) the presence of an effective cutoff at p ≈ ϵ−1; (iii) the replacement of the renormalization constants Z1 and Z2 by one gauge dependent function Z(ϵ2); (iv) the limit ϵ → 0 which has to be taken. The value Z(0) corresponds to the usual constants Z1 and Z2. It is expected that in general Z(0) = 0, but this poses no problem in the present formulation. It is argued that the function Z(ϵ2), which is determined by the equations, may render the vacuum polarization finite. One may eliminate the renormalization function from the propagator equations and then perform the limit ϵ → 0; this results in the usual perturbation series. However, the renormalization function is essential for an understanding of the high momentum behaviour and of the relation between the field theory and the perturbation expansion

Degrees of symmetry in quantum field theories

A hierarchy of possible symmetries in quantum field theory is defined, which reaches from a purely mathematical invariance to the conventional physical invariance, including the commonly discussed type of spontaneously broken symmetry (SBS). It is shown that one type of SBS, which is usually not considered, naturally leads to theories with an algebra of non-conserved currents and a non-linearly transforming phenomenological Lagrangian. An exactly solvable model is given and some general remarks are made

Charge commutator for any momentum

The nucleon matrix elements of the charge commutation relations are considered for arbitrary momentum. The resulting expression is exact. The high-momentum limit reduces to the Alder-Weisberger sum rule. For zero momentum one obtains the known low-energy result together with a closed expression for the correction

Bifurcations leading to stochasticity in a cyclotron-maser system

This paper is concerned with the orbital dynamics of electrons in a cyclotron maser [CO Chen, Phys. Rev. A 46,6654 (1992)] with modulated maser fields. Amplitude modulation is a natural result of wave-particle energy exchanges, and for typical system parameters, the nonlinear bifurcations of periodic orbits are investigated as the modulation level increases. Attention is focused on primary stable orbits exhibiting the same periodicity as the modulation for low modulational levels. This interest is related to the fact that the destruction of these orbits is generally associated with considerable spread of chaos over the phase space. It is found that two groups of such orbits do exist, each group located in a particular region of the phase space. As the modulation level grows, the overall behavior can be classified as a function of the modulation frequency. If this frequency is large there are two orbits in the group; one undergoes an infinite cascade of period doubling bifurcations and the other simply collapses with neighboring unstable orbits. If the frequency is small the number of orbits is larger; the collapsing orbit is still present and some of the others may fail to undergo the period doubling cascade

Difusão de neutrons provenientes de fonte pulsada em meio multiplicador

Resumo não disponíve

Difusão de neutrons provenientes de fonte pulsada em meio multiplicador

Resumo não disponíve

On the electron-muon mass ratio

The quantum electrodynamics (QED) of electrons is considered as a theory with a passive dilatation invariance which is perturbed by the electromagnetic coupling to hadrons and muons. A stability criterium is introduced and evaluated in lowest order of the perturbation. The resulting expression for the electron-muon mass ratio in terms of the vacuum polarization can be tested in e+ − e− colliding beam experiments

Renormalization and gauge invariance in quantum electrodynamics

The connection between the field theory and the perturbation expansion of quantum electrodynamics is studied. As a starting point the usual Lagrangian is taken but with bare electron mass and the renormalization constant Z3 set equal to zero. This theory is essentially equivalent to the usual one; however, it does not contain any constant of nature and is dilatational and gauge invariant, both invariances being spontaneously broken. The various limiting procedures implied by the differentiation, the multiplication and the renormalization of the field operators in the Lagrangian are combined in a gauge invariant way to a single limit. Propagator equations are derived which are the usual renormalized ones, except for: (i) a natural cancellation of the quadratic divergence of the vacuum polarization; (ii) the presence of an effective cutoff at p ≈ ϵ−1; (iii) the replacement of the renormalization constants Z1 and Z2 by one gauge dependent function Z(ϵ2); (iv) the limit ϵ → 0 which has to be taken. The value Z(0) corresponds to the usual constants Z1 and Z2. It is expected that in general Z(0) = 0, but this poses no problem in the present formulation. It is argued that the function Z(ϵ2), which is determined by the equations, may render the vacuum polarization finite. One may eliminate the renormalization function from the propagator equations and then perform the limit ϵ → 0; this results in the usual perturbation series. However, the renormalization function is essential for an understanding of the high momentum behaviour and of the relation between the field theory and the perturbation expansion