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There are several important, useful , interesting and lesser known facts that are scattered over text books and jorunals devoted to teaching and learning. These facts are closely connected to topics covered by most text books and to topics that are covered in every standard course.
This series of short BLOGS "Did You Know That .." draws attention to important and interesting facts related to text book topics. These are taken mostly from Journnals and text books. References are provided
QuestionConsider a system of two real scalar fields \(\phi_1, \phi_2\) described by the Lagrangian density\begin{equation} \Lsc = \frac{1}{2} \partial_\mu \phi_i \partial^\mu \phi_i - \frac{1}{2} m^2 \phi_i\phi_i -\frac{1}{4} \lambda (\phi_i\phi_i)^2.\end{equation}Compute the scattering cross section to the lowest order in \(\lambda\). Find the cross sections for the three processes
Write your answers as a constant times \(\sigma_0\equiv \frac{\lambda^2}{64\pi s}\) where \(s\) is the total energy in the center of mass frame.
Answer : a. \(4\sigma_0\) b. \(36 \sigma_0\) c. \(4 \sigma_0\)
Hint : Find symmetry appropriate factor.Remark : Good question
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Obtain solution of the free particle problem in two dimensions using Hamilton Jacobi equation and obtain expression for the Hamilton's principal function.
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