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If \(A^\mu\) is a light like four vector show that there exist a light like and two time like vectors \(B^\mu\) such that \(B^\mu A_\mu=0\). Extend the above result to the case when \(A^\mu\) is
(a) space like;   (b) light like.

kapoor kapoor's picture 23/10/18


Let \(\epsilon\) and \(\lambda\) be two light like fur vectors. What is the range of allowed values of \(\epsilon\cdot\lambda\)? Express your answer in terms of \(\epsilon^0\) and \(\lambda^0\).

kapoor kapoor's picture 23/10/18


If \(A_{\lambda\sigma}\) and \(B_{\lambda\sigma}\) are two second rank tensors satisfying \[ A_{\lambda\sigma}x^\lambda x^\sigma =  B_{\lambda\sigma}x^\lambda x^\sigma\] for arbitrary four vector \(x^\mu\), what is the relationship between \(A_{\lambda\sigma}\) and \( B^{\lambda\sigma}\)?

kapoor kapoor's picture 23/10/18


Consider \(S_{\mu\nu}\) to be a second rank tensor having the following properties:

  1. \(S_{\mu\nu}\) is symmetric : \( S_{\mu\nu} = S_{\nu\mu} \);
  2. \(S_{\mu\nu}\) is antisymmetric : \( S_{\mu\nu} = - S_{\nu\mu} \);
  3. \(S\) is traceless:\( g^{\mu\nu} S_{\mu\nu} = 0\).

Show that the above properties are remain invariant under Lorentz transformations.

kapoor kapoor's picture 23/10/18


If \(p^\mu=(p^0,0,0,p)\) with \( p^{02} -\vec{p}^2 = m^2\), find all vectors \(\epsilon^\mu\) such that \(\epsilon^\mu p_\mu=0\). How many linearly independent vectors can you make?

kapoor kapoor's picture 23/10/18


  1. Find the charge \(Q\) which will exert the same force on an electron as Sun's gravitational pull on the earth when the distance between the charge \(Q\) and the electron is equal to the Sun -Earth distance.
  2. For an electron on the surface of Pb nucleus, find the ratio of the electric and gravitational potentials.
kapoor kapoor's picture 23/10/18


Show that if deuterons are scattered by protons the maximum scattering angle in the centre of mass and the lab frames are \(120^o\) and \(30^o\) respectively. but if the protons are scattered by deuterons the maximum scattering angle is \(180^o\) in both the systems.

kapoor kapoor's picture 23/10/18


Starting from the Lagrangian for a complex scalar field obtain the Hamiltonian for a free complex Klein Gordon field.
Write ETCR and for the quantized field prove that \begin{equation}\label{EQ01}
\big[H, \pi(x)\big] = - i \big( \nabla^2- \mu^2\big) \phi^*(x) .
\end{equation} Does relation,\eqref{EQ01}, hold only as equal time commutator or does it hold for  \(H\) and \(\pi(x)\) at arbitrary different times ?  Explain your answer.
Use \eqref{EQ01} to derive the usual Euler Lagrange equation of motion for the Klein Gordon field.

kapoor kapoor's picture 22/10/18

Lectures-EM-12 Maxwell's Equations in Relativistic Notation

Summary (or abstract) not available for this node.
kapoor kapoor's picture 22/10/18

Lectures-EM-12 Potentials as Four Vectors

Summary (or abstract) not available for this node.
kapoor kapoor's picture 22/10/18