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Crossing matrices for particles of arbitrary isospin
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ABSTRACTH
ment of Physics and Astronomy, University of Maryland, College Park, &Iaryland, AND S. DESER, Physics Department, Brandeis University, Waltham, Massachusetts. The properties of very dense sources of the gravitational field are examined. The sources are spherically symmetric initially static distributions of neutral or charged dust, treated as dynamical systems with no phenomenological pressure term. The exterior Schwarzschild solution is analyzed from this point of view as generated by a realistic “bare” matter stresstensor with appropriate initial Cauchy dat,a. A coordinate frame is introduced in which the radial coordinate coincides with the invariant distance (gT7 = l), and the initial value equations are solved in this frame. The systems considered become, in the limit, models for neutral and charged particles, and so provide solutions for the problems of interaction between “point” particles and the gravitational field. It is shown that, at the instant of time symmetry, there is a miniml~m invariant extension for a particle, below which no solution of the field equations exists; this fact emerges especially clearly in the invariant radial frame used here. The clothed (or ext,erior) mass and invariant properties of the interacting systems as a function of the bare mass, charge, and extension are given. The results are in agreement with those obtained previously in another frame, in terms of whose radial coordinate the particle had vanishing extension in the limit. The significance of the necessary departure of a particle from strictly pointlike structure as a result of its gravitational coupling is discussed. Crossing Matrices for Particles of Arbitrary Isospin. PETER A. CARRUTHERS AND JEAN P. KRUSCH, Laboratory for Nuclear Studies, Cornell University, Ithaca New York and Physics Department, University of Michigan, Ann Arbor, Michigan. An elementary and systematic discussion is given of isospin crossing symmetry for “twobody” collisions involving particles of arbitrary isospins. Special attention is given to the question of phase relations among the states in the various crossed channels. Explicit formulas for the various crossing matrices are given in terms of Hacah coefficients. Numerical forms are given for reactions of especial interest. In an appendix the behavior of the relevant fields and operators under charge conjugation and G-conjugation is described. An
Example of the Mandelstam Representation in Perturbation Theory. PAUL FEDERBUSH, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts. A Feynman diagram that has three particle intermediate states in all channels is studied. Picking special values of the masses, in particular, taking infrared divergent terms as certain masses go to zero, we explicitly calculate the spectral functions in this limit. They are nonzero in all three regions.
ABSTRACTH
ment of Physics and Astronomy, University of Maryland, College Park, &Iaryland, AND S. DESER, Physics Department, Brandeis University, Waltham, Massachusetts. The properties of very dense sources of the gravitational field are examined. The sources are spherically symmetric initially static distributions of neutral or charged dust, treated as dynamical systems with no phenomenological pressure term. The exterior Schwarzschild solution is analyzed from this point of view as generated by a realistic “bare” matter stresstensor with appropriate initial Cauchy dat,a. A coordinate frame is introduced in which the radial coordinate coincides with the invariant distance (gT7 = l), and the initial value equations are solved in this frame. The systems considered become, in the limit, models for neutral and charged particles, and so provide solutions for the problems of interaction between “point” particles and the gravitational field. It is shown that, at the instant of time symmetry, there is a miniml~m invariant extension for a particle, below which no solution of the field equations exists; this fact emerges especially clearly in the invariant radial frame used here. The clothed (or ext,erior) mass and invariant properties of the interacting systems as a function of the bare mass, charge, and extension are given. The results are in agreement with those obtained previously in another frame, in terms of whose radial coordinate the particle had vanishing extension in the limit. The significance of the necessary departure of a particle from strictly pointlike structure as a result of its gravitational coupling is discussed. Crossing Matrices for Particles of Arbitrary Isospin. PETER A. CARRUTHERS AND JEAN P. KRUSCH, Laboratory for Nuclear Studies, Cornell University, Ithaca New York and Physics Department, University of Michigan, Ann Arbor, Michigan. An elementary and systematic discussion is given of isospin crossing symmetry for “twobody” collisions involving particles of arbitrary isospins. Special attention is given to the question of phase relations among the states in the various crossed channels. Explicit formulas for the various crossing matrices are given in terms of Hacah coefficients. Numerical forms are given for reactions of especial interest. In an appendix the behavior of the relevant fields and operators under charge conjugation and G-conjugation is described. An
Example of the Mandelstam Representation in Perturbation Theory. PAUL FEDERBUSH, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts. A Feynman diagram that has three particle intermediate states in all channels is studied. Picking special values of the masses, in particular, taking infrared divergent terms as certain masses go to zero, we explicitly calculate the spectral functions in this limit. They are nonzero in all three regions.