S-matrix or scattering matrix

introduction

• transition amplitude are too hard to calculate from the theory, except in infinite time limits
• those limits are the entries of the S-matrix
• typical way to compute S-matrix entries is using correlation functions and Ward identity

 

 

probability amplitude

• probability amplitude from initial states to final states
• Feynman diagram is a tool to compute the probability amplitudes.
  
  • transition amplitude
  • scattering amplitude 
    
    • computation of S-matrix (S = Scattering)
    • cross section
• these are important because they are physically measurable quantity
  
  • similar to correlation functions in Conformal Field Theory
  • look at correlation functions and Ward identity page

 

 

S-matrix

• functions of complex rapidity difference \theta
• unitarity
• crossing-symmetry
• rapidity in special relativity

 

 

exact S-matrices

• affine Toda field theory (ATFT)
• Factorizable scattering and exact S-matrices in ATFT

 

 

 

 

history

• http://www.google.com/search?hl=en&tbs=tl:1&q=

 

 

related items

• Path integral
• string S-matrix
• affine Toda field theory
• quantum sine-Gordon field theory
• Ising CFT

 

encyclopedia

• http://en.wikipedia.org/wiki/S-matrix

 

expositions

• Torrielli, Alessandro. 2011. “Yangians, S-matrices and AdS/CFT”. 1104.2474 (4월 13). http://arxiv.org/abs/1104.2474.
• White, Alan. R. 2000. The Past and Future of S-Matrix Theory. hep-ph/0002303 (February 29). http://arxiv.org/abs/hep-ph/0002303.
• Dorey, Patrick. ‘Exact S-Matrices’. arXiv:hep-th/9810026, 5 October 1998. http://arxiv.org/abs/hep-th/9810026.
• MacKay, N. J. ‘On the Bootstrap Structure of Yangian-Invariant Factorized S-Matrices’. arXiv:hep-th/9211091, 20 November 1992. http://arxiv.org/abs/hep-th/9211091.