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### Problem-EPP-01027

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 23/10/18

### Problem-EPP-01026

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 23/10/18

### Problem-EPP-01025

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 23/10/18

### Problem-EPP-01024

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 23/10/18

### Problem-EPP-01023

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 23/10/18

### Problem-EPP-01022

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 23/10/18

### Problem-EPP-01021

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 23/10/18

### Problem-QFT-05001

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 \label{EQ01}
\big[H, \pi(x)\big] = - i \big( \nabla^2- \mu^2\big) \phi^*(x) .
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 22/10/18

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

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

### Lectures-EM-12 Potentials as Four Vectors

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