The evolution of an elementary particle

1. Gedanken or thought experiment The evolution of an elementary particle and we can film its evolution with a video camera Let us consider that this object is an electron Martin Rivas UPV/EHU

2. Now we take the first frame of the film and depict on it the reference axis associated to some particular inertial observer V Because we know how the state of the electron is described by this observer, we depict in the other frames of the film the reference axis of those observers who measure the state of the electron like in the first picture. Martin Rivas UPV/EHU

3. Evolution of the elementary particle and the associated systems of instantaneous inertial observers who measure the particle in the same state Martin Rivas UPV/EHU

4. Now we take any frame and erase the information concerning the electron because we know how the state of the electron is described we can always depict it again Martin Rivas UPV/EHU

5. Evolution of the associated systems of instantaneous inertial reference frames Martin Rivas UPV/EHU

6. Because we can depict the electron again in any frame, it is equivalent the dynamical description of these inertial observers to the description of the evolution of the elementary particle The variables which describe any inertial reference frame are the variables we need to describe the evolution of an elementary particle. The kinematical group of space-time symmetries supplies the classical variables to describe an elementary particle. Martin Rivas UPV/EHU

7. If we restrict ourselves to the Galilei or Poincaré group, then every inertial frame is described by giving the position of its origin r, the velocity of this point v, and the orientation of the Cartessian frame a. Because each picture has a definite time label, the variables which characterise the initial (and final) states of the evolution of the electron in a Lagrangian description are: time t, position r, velocity v and orientationa. The Lagrangian depends also on the next order time derivatives of these variables Martin Rivas UPV/EHU

8. One thing is the electron and another the geometricaldescription of its evolution as that of a single point and the Cartesian frame associated to this point. Since the Lagrangian depends on the acceleration of the point, the center of mass and center of charge are different points and the particle has spin. martin.rivas@ehu.es http://tp.lc.ehu.es/martin.htm Martin Rivas UPV/EHU