Download e-book for iPad: Dynamical Collision Theory and its Applications by Sadhan K. Adhikari

By Sadhan K. Adhikari

Dynamical Collision idea and Its Applications

summary: Dynamical Collision idea and Its purposes

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The two-particle disconnected graphs in Fig. 2 correspond to the collision, at some arbitrary time, of two particles with the third passing through freely. Evidently, no point in space-time is distinguished as the collision point. Thus, this disconnectedness structure is a K 3' \^ ^N V, VV 3 3' 1 U 3 3' + 1 ^ ( V V S ( 3 y 3' \ ^ v« 1 V, 3 FIG. 2. The connectivity structure of the three-to-three particle transition amplitude. The bubbles containing c represent either two-particle or three-particle connected amplitudes.

A. 12b) and (A. 12c), we have < A - U4e ) P* = 4 - - - ) and qa = ^iK_h [ma + K\ (A114b) nip + myJ respectively. m. , (A. 15a) for any a, where «■-is*1- "•-i p ·· £ --2spl a} f° r e a c h choice of a. 16) {3) where we have factored out δ (P' — P), we have assumed that we are in the three-body cm.

10) for arbitrary states |χ> and \φ}. 11) and we will suppose that this is always the case. 12) where S is the Heisenberg picture S-operator. 13) where ατ denotes the time-reversed asymptotic configuration. 15) which is quite different from what one obtains from Eq. 12). The symmetries that we have discussed so far are easy to implement in collision theory and their consequences invariably simplify matters. This simplification also occurs when we exploit the consequences of the permutation symmetries among identical particles in collision theory, but the practical implementation of these symmetries is often difficult.

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