The infinite mass limit of the two-particle Green's function in QED

The behavior of the two-particle Green's function in QED is analyzed in the limit when one of the particles becomes infinitely massive. It is found that the dependences of the Green's function on the relative times of the ingoing and outgoing particles factorize and that the bound state spectrum is the same as that of the Dirac equation with the static potential created by the heavy particle. The Bethe-Salpeter wave function is also determined in terms of the Dirac wave function. The present result excludes the existence, in the above limit, of abnormal solutions due to relative time excitations as predicted by the Bethe-Salpeter equation in the ladder approximation.Comment: 13 pages, Tex, no figure

The relativistic two-body potentials of constraint theory from summation of Feynman diagrams

The relativistic two-body potentials of constraint theory for systems composed of two spin-0 or two spin-1/2 particles are calculated, in perturbation theory, by means of the Lippmann-Schwinger type equation that relates them to the scattering amplitude. The cases of scalar and vector interactions with massless photons are considered. The two-photon exchange contributions, calculated with covariant propagators,are globally free of spurious infra-red singularities and produce at leading order O(\alpha^4) effects that can be represented in three-dimensional x-space by local potentials proportional to (\alpha/r)^2. Leading contributions of n-photon exchange diagrams produce terms proportional to (\alpha/r)^n. The series of leading contributions are summed. The resulting potentials are functions, in the c.m. frame, of r and of the total energy. Their forms are compatible with Todorov's minimal substitution rules proposed in the quasipotential approach.Comment: 60 pages, Latex, with four pages of figures included at the end of the article in a Latex file calling the FEYNMAN macropackag

Incorporation of anomalous magnetic moments in the two-body relativistic wave equations of constraint theory

Using a Dirac-matrix substitution rule, applied to the electric charge, the anomalous magnetic moments of fermions are incorporated in local form in the two-body relativistic wave equations of constraint theory. The structure of the resulting potential is entirely determined, up to magnetic type form factors, from that of the initial potential descibing the mutual interaction in the absence of anomalous magnetic moments. The wave equations are reduced to a single eigenvalue equation in the sectors of pseudoscalar and scalar states ($j=0$). The requirement of a smooth introduction of the anomalous magnetic moments imposes restrictions on the behavior of the form factors near the origin, in $x$-space. The nonrelativistic limit of the eigenvalue equation is also studied.Comment: 25 pages, Latex file, no figur

Pionium lifetime and \pi\pi scattering lengths in generalized chiral perurbation theory

The relationship between the pionium lifetime and the $\pi\pi$ scattering lengths is established, including the sizable electromagnetic corrections. The bound state formalism that is used is that of constraint theory which provides a covariant three-dimensional reduction of the Bethe--Salpeter equation. The framework of generalized chiral perturbation theory allows then an analysis of the lifetime value as a function of the $\pi\pi$ scattering lengths, the latter being dependent on the quark condensate value.Comment: 4 pages, 1 figure (included in the text), Latex. Uses espcrc2.sty. Talk given at the QCD99 Conference, Montpellier, 7-13 July 1999. To appear in the Proceeding

Gauge transformations in relativistic two-particle constraint theory

Using connection with quantum field theory, the infinitesimal covariant abelian gauge transformation laws of relativistic two-particle constraint theory wave functions and potentials are established and weak invariance of the corresponding wave equations shown. Because of the three-dimensional projection operation, these transformation laws are interaction dependent. Simplifications occur for local potentials, which result, in each formal order of perturbation theory, from the infra-red leading effects of multiphoton exchange diagrams. In this case, the finite gauge transformation can explicitly be represented, with a suitable approximation and up to a multiplicative factor, by a momentum dependent unitary operator that acts in $x$-space as a local dilatation operator. The latter is utilized to reconstruct from the Feynman gauge the potentials in other linear covariant gauges. The resulting effective potential of the final Pauli-Schr\"odinger type eigenvalue equation has the gauge invariant attractive singularity $\alpha^2/r^2$, leading to a gauge invariant critical coupling constant $\alpha_c =1/2$.Comment: 32 pages, latex file with 3 figures, uses epsfile.sty for figure

Measurement of the degree of customer satisfaction cases: HABIB BOURGUIBA Hospital

تقدم كل مستشفى حاليًا استطلاعات رضا لمرضاها لمراقبة كيفية تقييمهم لخدمات الرعاية، في الواقع من المهم لكل مستشفى مهما كان، أن يهتم برأي مرضاه حول الرعاية المقدمة لهم. تسمح هذه الاستطلاعات للمستشفيات بالنظر في رضا المرضى كمؤشر للحكم على جودة الرعاية والخدمات المقدمة. في المستشفيات لا يتوافق إرضاء المريض مع التدخل أو الاستشارة البسيطة فقط، على العكس من ذلك فهو يبدأ عند تحديد الموعد، ثم يستمر عند وصول المريض إلى المستشفى وينتهي عند مغادرته.تهدف هذه الدراسة إلى قياس المستوى العام لرضا المرضى عن جميع جوانب رعايتهم في مستشفى حبيب بورقيبة، لتفسير طول مدة الإقامة في المستشفى، حيث يمكننا أن نتخيل أنه كلما طالت مدة بقاء المرضى في خدمة الرعاية، زادت مصادر عدم الرضا.خلصت الدراسة إلى أن أهم شيء بالنسبة للمريض هو أنه يغادر المستشفى قد "شُفي".Currently each hospital offers satisfaction surveys to its patients to observe how they evaluate the care services. Indeed, it is important for each hospital, whatever it is, to take an interest in the opinion of its patients about the care provided to them. These surveys allow hospitals to consider patient satisfaction as an indicator for judging the quality of care and services offered. In hospitals, patient satisfaction does not only correspond to the intervention or a simple consultation. On the contrary, it begins when the appointment is made, then continues when the patient arrives at the hospital and ends when he leaves. This study aims to measure the general level of patient satisfaction with all aspects of their care at Habib Bourguiba Hospital, to explain the length of stay in the hospital, as we can imagine that the longer patients stay in the care service, the greater the sources of dissatisfaction.We concluded that the most important thing for the patient is that he leaves the hospital “healed”. Currently each hospital offers satisfaction surveys to its patients to observe how they evaluate the care services. Indeed, it is important for each hospital, whatever it is, to take an interest in the opinion of its patients about the care provided to them. These surveys allow hospitals to consider patient satisfaction as an indicator for judging the quality of care and services offered. In hospitals, patient satisfaction does not only correspond to the intervention or a simple consultation. On the contrary, it begins when the appointment is made, then continues when the patient arrives at the hospital and ends when he leaves. This study aims to measure the general level of patient satisfaction with all aspects of their care at Habib Bourguiba Hospital, to explain the length of stay in the hospital, as we can imagine that the longer patients stay in the care service, the greater the sources of dissatisfaction.We concluded that the most important thing for the patient is that he leaves the hospital “healed”

There are no abnormal solutions of the Bethe-Salpeter equation in the static model

The four-point Green's function of static QED, where a fermion and an antifermion are located at fixed space positions, is calculated in covariant gauges. The bound state spectrum does not display any abnormal state corresponding to excitations of the relative time. The equation that was established by Mugibayashi in this model and which has abnormal solutions does not coincide with the Bethe-Salpeter equation. Gauge transformation from the Coulomb gauge also confirms the absence of abnormal solutions in the Bethe-Salpeter equation

Relativistic effects in the pionium lifetime

The pionium decay width is evaluated in the framework of chiral perturbation theory and the relativistic bound state formalism of constraint theory. Corrections of order O(\alpha) are calculated with respect to the conventional lowest-order formula, in which the strong interaction amplitude has been calculated to two-loop order with charged pion masses. Strong interaction corrections from second-order perturbation theory of the bound state wave equation are found to be of the order of 0.4%. Electromagnetic radiative corrections, due to pion-photon interactions, are estimated to be of the order of -0.1%. Electromagnetic mass shift insertions in internal propagators produce a correction of the order of 0.3%. The correction due to the passage from the strong interaction scattering amplitude evaluated with the mass parameter fixed at the charged pion mass to the amplitude evaluated with the mass parameter fixed at the neutral pion mass is found to be of the order of 6.4%.Comment: 47 pages, 4 figures, Latex, calls the FEYNMAN macropackage for drawing figure

Measurement of the degree of customer satisfaction cases: HABIB BOURGUIBA Hospital

تقدم كل مستشفى حاليًا استطلاعات رضا لمرضاها لمراقبة كيفية تقييمهم لخدمات الرعاية، في الواقع من المهم لكل مستشفى مهما كان، أن يهتم برأي مرضاه حول الرعاية المقدمة لهم. تسمح هذه الاستطلاعات للمستشفيات بالنظر في رضا المرضى كمؤشر للحكم على جودة الرعاية والخدمات المقدمة. في المستشفيات لا يتوافق إرضاء المريض مع التدخل أو الاستشارة البسيطة فقط، على العكس من ذلك فهو يبدأ عند تحديد الموعد، ثم يستمر عند وصول المريض إلى المستشفى وينتهي عند مغادرته.تهدف هذه الدراسة إلى قياس المستوى العام لرضا المرضى عن جميع جوانب رعايتهم في مستشفى حبيب بورقيبة، لتفسير طول مدة الإقامة في المستشفى، حيث يمكننا أن نتخيل أنه كلما طالت مدة بقاء المرضى في خدمة الرعاية، زادت مصادر عدم الرضا.خلصت الدراسة إلى أن أهم شيء بالنسبة للمريض هو أنه يغادر المستشفى قد "شُفي".Currently each hospital offers satisfaction surveys to its patients to observe how they evaluate the care services. Indeed, it is important for each hospital, whatever it is, to take an interest in the opinion of its patients about the care provided to them. These surveys allow hospitals to consider patient satisfaction as an indicator for judging the quality of care and services offered. In hospitals, patient satisfaction does not only correspond to the intervention or a simple consultation. On the contrary, it begins when the appointment is made, then continues when the patient arrives at the hospital and ends when he leaves. This study aims to measure the general level of patient satisfaction with all aspects of their care at Habib Bourguiba Hospital, to explain the length of stay in the hospital, as we can imagine that the longer patients stay in the care service, the greater the sources of dissatisfaction.We concluded that the most important thing for the patient is that he leaves the hospital “healed”. Currently each hospital offers satisfaction surveys to its patients to observe how they evaluate the care services. Indeed, it is important for each hospital, whatever it is, to take an interest in the opinion of its patients about the care provided to them. These surveys allow hospitals to consider patient satisfaction as an indicator for judging the quality of care and services offered. In hospitals, patient satisfaction does not only correspond to the intervention or a simple consultation. On the contrary, it begins when the appointment is made, then continues when the patient arrives at the hospital and ends when he leaves. This study aims to measure the general level of patient satisfaction with all aspects of their care at Habib Bourguiba Hospital, to explain the length of stay in the hospital, as we can imagine that the longer patients stay in the care service, the greater the sources of dissatisfaction.We concluded that the most important thing for the patient is that he leaves the hospital “healed”

Bethe-Salpeter equation: 3D reductions, heavy mass limits and abnormal solutions

We show that the 3D reductions of the Bethe-Salpeter equation have the same bound state spectrum as the original equation, with the possible exception of some solutions for which the corresponding 3D wave function vanishes. The abnormal solutions of the Bethe-Salpeter equation (corresponding to excitations in the relative time-energy degree of freedom), when they exist, are recovered in the 3D reductions via a complicated dependence of the final potential on the total energy. We know however that the one-body (or one high mass) limit of some 3D reductions of the exact Bethe-Salpeter equation leads to a compact 3D equation (by a mutual cancellation of the ladder and crossed graph contributions), which does not exhibit this kind of dependence on the total energy anymore. We conclude that the exact Bethe-Salpeter equation has no abnormal solution at this limit, or has only solutions for which our 3D wave function vanishes. This is in contrast with the results of the ladder approximation, where no such cancellation occurs. We draw the same conclusions for the static model, which we obtain by letting the mass of the lighter particle go also to infinity. These results support Wick's conjecture that the abnormal solutions are a spurious consequence of the ladder approximation.Comment: 11 pages Latex, 1 figure Postscript. Submitted to Journal of Physics