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Wednesday, July 28, 2010
Tao level 0: Tao Diagrams
The Feynman Diagrams are a brilliant graphical tool designed in the 40s by the Nobel Prize in Physics 1965 Richard Feynman, to display in the form of graph or chart the interaction (scattering) made between elementary particles in Quantum Field Theory and in the Quantum Electrodynamics (QED), providing an immediate visual representation of complex quantum field solutions based on the interaction probability.
The particles are represented by lines that may be of various kinds depending on the type of particle they are associated. A point where the lines intersect is called the interaction point, or just the top. The lines are divided into three categories: internal lines (which connect two vertices), incoming lines (which come from the past and come into a vertex and representing the originally non-interacting) and outgoing lines (which start at a vertex and extend "the future" and the final states are not interacting). Sometimes the tables are turned and the past is down, and the future high.
For example in the floor of the University of British Columbia is reproduced a Feynman diagram involving an electron and a positron (the antiparticle of the electron).. The wave line represents the exchange of a photon interaction. The horizontal axis represents the vertical space and time. Note that a particle, the positron, is represented as an electron traveling backward in time.
The Feynman diagrams are pictorial representations of a time series of the perturbative scattering amplitude for a process defined by the initial and final states. In some quantum field theories (like QED), one can obtain excellent approximations of the scattering amplitude from few terms of the perturbation series corresponding to a few simple Feynman diagrams with the same incoming and outgoing lines connected to different vertices and internal lines . A more complex diagram is less likely to happen, but it is never zero if the diagram is feasible.
The Feynman diagrams are just a graph, there is not the concept of location or space, nor time apart from the distinction of incoming and outgoing lines. Moreover, only one set of Feynman diagrams can be said to represent a given interaction, the particles do not "choose" a particular diagram every time they interact.
In these diagrams, for example an electron in an electromagnetic field (continuous double line) may have the following behaviors: (a) emits and absorbs a virtual photon (wavy line) ;(b) emits and absorbs a virtual electron-positron pair (double circle ); (c) emits a photon and immediately after another, with an overlap in time; (d) where the virtual electron-positron pair is emitted electron emits a virtual photon is absorbed.
A single particle may divides into its components and then recompose, as in the case of a proton p:
The particles are represented by lines that may be of various kinds depending on the type of particle they are associated. A point where the lines intersect is called the interaction point, or just the top. The lines are divided into three categories: internal lines (which connect two vertices), incoming lines (which come from the past and come into a vertex and representing the originally non-interacting) and outgoing lines (which start at a vertex and extend "the future" and the final states are not interacting). Sometimes the tables are turned and the past is down, and the future high.For example in the floor of the University of British Columbia is reproduced a Feynman diagram involving an electron and a positron (the antiparticle of the electron).. The wave line represents the exchange of a photon interaction. The horizontal axis represents the vertical space and time. Note that a particle, the positron, is represented as an electron traveling backward in time.
The Feynman diagrams are pictorial representations of a time series of the perturbative scattering amplitude for a process defined by the initial and final states. In some quantum field theories (like QED), one can obtain excellent approximations of the scattering amplitude from few terms of the perturbation series corresponding to a few simple Feynman diagrams with the same incoming and outgoing lines connected to different vertices and internal lines . A more complex diagram is less likely to happen, but it is never zero if the diagram is feasible.
The Feynman diagrams are just a graph, there is not the concept of location or space, nor time apart from the distinction of incoming and outgoing lines. Moreover, only one set of Feynman diagrams can be said to represent a given interaction, the particles do not "choose" a particular diagram every time they interact.
Even without interaction with other the same particle can emit and absorb other particles, called virtual:
In these diagrams, for example an electron in an electromagnetic field (continuous double line) may have the following behaviors: (a) emits and absorbs a virtual photon (wavy line) ;(b) emits and absorbs a virtual electron-positron pair (double circle ); (c) emits a photon and immediately after another, with an overlap in time; (d) where the virtual electron-positron pair is emitted electron emits a virtual photon is absorbed.A single particle may divides into its components and then recompose, as in the case of a proton p:
There is even no need for the presence of a "real" particle since in vacuum a continuous creations of pairs of virtual particles (vacuum polarization) happens:
The Feynman diagrams are well representative of the enormous probabilistic dynamic existing at level 0.
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Wednesday, July 21, 2010
Tao Analysis/Tao Synthesis
A system is completely characterized when you know the relation, or function, or operator OUT/IN for each value of a variable of interest, such as the value of IN, the time or its inverse, frequency.
In some areas (Networks Theory) OUT / IN is called the Transfer Function of the system.
In some areas (Networks Theory) OUT / IN is called the Transfer Function of the system.
The procedure of Analysis of the system can be carried out when system is completely know, that is all its elements, their characteristics and functionalities, and all the relationships between the elements, the circuit, and one wants to establish the OUT/IN relationship. This, with previous assumptions, is always possible, even if only with numerical methods for very complicated
The inverse procedure of Analysis is the Synthesis of the system, i.e. given a OUT/IN determine the system that creates it. This is not always possible, if not with methods and numerical approximations, even for OUT/IN relationship is relatively simple.
The two inverse procedures of Analysis/Synthesis therefore have a very different behavior. The situation is similar to that which occurs, for example, in Differential Calculus, where is relatively simple differentiable and integrable functions easily allow the calculation of the derivative function, but not, formally, the integral, except by numerical methods.
The inverse procedure of Analysis is the Synthesis of the system, i.e. given a OUT/IN determine the system that creates it. This is not always possible, if not with methods and numerical approximations, even for OUT/IN relationship is relatively simple.
The two inverse procedures of Analysis/Synthesis therefore have a very different behavior. The situation is similar to that which occurs, for example, in Differential Calculus, where is relatively simple differentiable and integrable functions easily allow the calculation of the derivative function, but not, formally, the integral, except by numerical methods.
Thursday, July 15, 2010
level 0 Tao: elements and interactions
The model which describes all the elementary particles of the matter is known as Standard Model
Including into the Standard Model also the non-elementary particles as molecules, atoms, hadrons and mesons, a complete list of all the elements concerning the physical level of the Universe so far discovered or hypothesized is available.
The interactions between elements are formed by the four fundamental interactions: gravitation, electromagnetism, strong and weak interaction.
Including into the Standard Model also the non-elementary particles as molecules, atoms, hadrons and mesons, a complete list of all the elements concerning the physical level of the Universe so far discovered or hypothesized is available.The interactions between elements are formed by the four fundamental interactions: gravitation, electromagnetism, strong and weak interaction.
Wednesday, July 14, 2010
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