Propagator Causal

Along each power line chosen at step I propagate bicausality from the double source to the double detector and propagate causality through the junction structure taking into account the causality constraints ofO- and I-junctions, TF-and GY-elements. If at this step causal conflicts or non-solvable causal loops appear, repeat the previous steps with another set of disjoint I/O power lines. If none of them solves the problem of causal conflicts or non-solvable causal loop appearance then the model is not invertible (Criterion 3) and the procedure stops. 

J. P. Vigier, Superluminal propagation of the quantum potential in the causal interpretation of quantum mechanics, Lett. Nuovo Cimento 24(8) (Ser. 2), 258-264 (1979). 

Obviously, such interpetation led to disregard advanced solutions as nonphysical. For instance, Ritz [30] and Tetrode [31] considered that the mathematical existence of advanced solutions was a major weakness of Maxwell s equations. An attempt to provide a physical basis for advanced potentials is due to Lewis, who proposed focusing on the process of propagation from an emitter to an absorber far away from the emitter [32]. This concept also appears in the work of Wheeler and Feynman [33]. However, such model constitutes another form of causality violation. Lewis [32, p. 25] himself stated I shall not attempt to conceal the conflict between these views and common sense. ... 

It is natural to define the causal representation, e.g., the stationary wave irc(E), given by the causal propagator Gc(f) as follows... 

For X > 0 our integration contour in the upper-half -plane encloses only the pole at J. The scattered wave packet is proportional to e i as in the unscattered case (4.160). At times before the wave-packet centre reaches the scattering centre the wave packet is propagated without change of shape. Another name for this condition is causality. Disturbances due to the target appear after the centre of the wave packet has reached the target. Causality requires the scattering amplitude to be analytic in the upper-half -plane. 

The real parts of r r and the causal propagator defined in Eq. (3) are the same, whereas the imaginary parts are different. The real parts of the poles, i.e. the excitation energies, as well as the transition moments are also the same for the causal and the retarded propagators. Thus, for our purpose they are... 

The central role of PrPc in the pathogenesis of prion diseases was demonstrated in transgenic mice with a targeted disruption of the PrP gene PrP0/0 mice are resistant to prion diseases and do not propagate infectious prions [32]. Moreover, inherited prion diseases in humans are causally linked to mutations in Pmp (reviewed in [22, 33]). 

In a strict sense, the time-evolution generated by the operator (2) is acausal A wavepacket that is initially strictly localized in a finite region of space instantaneously spreads over the whole space. Even for the Dirac equation there are some problems with causality and localization (see, e.g., [5]), but since the propagator of the Dirac equation (the time-evolution kernel) has support in the light-cone, distortions of wave functions and wave fronts can at most propagate with the velocity of light. 

The causal photon propagator in Coulomb gauge can be defined, in a similar manner to (62), by... 

Understanding the electronic movement in physical atomic as being driven by the conneeted and correlated functions especially by the (temporally) causal Green-fimction/quantum propagators Describing the physical atom as a semiclassical description of quantum motion, i.e., merely quantum than classical yet with certain orders of Planck constant contributions in electronic orbits in atom Learning the difference between the second and the fourth order of path integral expansion of the quantum amplitude of electronic orbits as quantifies in the associated partition functions ... 

This postulate allows the consistent formulation of the Schrodinger, Interaction, and the Heisenberg pictures, the treatment of time dependent perturbations, as well as the description of the quantum events by means of the so-called propagators (Green functions) linking them in a causal ... 

Literature has many theories and concepts discussing human reliability and associated human error causal factors that always trigger incidents and accidents within safety-critical systems. The main - by definition - characteristics of such safety occurrences are their randonmess, rare predictability, sophisticated, yet vague sequence of propagation. Such characteristics can basically allow for the retrospective analysis of these occurrences and their causes at various sectors and levels within industry such that re-occurrence margins are reduced if not totally eliminated. The major drawback of such reactive treatment... 

A causality change at a switch port propagates at least locally into the bond graph and affects the causality at the ports of other elements as indicated in Fig. 2.6 for the example of the mechanical stop. 

The causality resistor R / 2 clearly avoids the propagation of causality changes at the port of the ideal switch into the rest of the bond graph and captures the diode s high resistance Roft in reverse mode. The resistor R Ri represents the diode s small ON-resistance Ron-... 

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