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The Philosophy of Vacuum Part 13

The Philosophy of Vacuum Part 13. Physicists will find it extremely interesting, covering, as it does, technical subjects in an accessible way. For those with the necessary expertise, this book will provide an illuminating and authoritative exposition of a many-sided subject." -John D. Barrow, Times Literary Supplement. | The Vacuum on Null Planes 113 planes or null planes for short Fig. 2 . These null planes are flat three-dimensional sections of Minkowski space-time which are tangent to light cones and thus in any inertial frame have the appearance of an advancing wave- ront of a plane electromagnetic wave in vacuum.The dynamical evolution of a physical system in this scheme is monitored from null plane to null plane either by translation with the null plane remaining parallel to itself or by reorientation sliding around the light cone but always preserving the null-plane character. It turns out as Dirac discovered that null planes have a seven-parameter stability group so that the dynamical evolution is determined by the structure of only three independent generators of the Poincare group. To put it another way when interactions are turned on in the Front Form only three Poincare generators change their structure. In Dirac s view this recommended the further study of the Front Form to the physics community. The three Poincare generators that carry the dynamical structure in the Front Form are not any of the ten generators with which we are familiar from our experience with the Instant Form. Instead one analyses the Poincare group with respect to those subgroups and quotients associated with the transformation and propagation of null-plane data. In the context of that analysis the three dynamical generators appear the remaining having purely kinematical roles to play. From this analysis one learns that the stability group of a null plane is isomorphic to E2 x D x T3 where D is the dilation group. In the Point Form the initial data and fundamental commutation relations were given on Lorentz-invariant hyper-hyperboloids of revolution lying inside future light cones. As indicated by their definition the stability group for these hyper-hyperboloids is isomorphic to the homogeneous Lorentz group leaving the four translation generators to carry all the dynamical structure. The advantage