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Constant electric field in vacuum

Summary (or abstract) not available for this node.
cbse cbse's picture 22/02/20

Electomagnetic waves, radiation

Summary (or abstract) not available for this node.
cbse cbse's picture 22/02/20

Repository of Problems

  • This collection is primarily meant for internal use of Proofs program.
  • The experts may  find it useful for selecting problems for homework
    and examination papers
kapoor kapoor's picture 22/02/20

Problem/QFT/06008 Dirac particle in uniform magnetic field

Consider an electron in a uniform and constant magentic field \(\vec{B}\) along the \(z-\)axis. Obtain the most general four component positive energy eigennfunctions. Show that the energy eigenvalues are given by
\[ E= \sqrt{m^2c^4 + c^2p_3^2 + 2ne\hbar c|\vec{B}|}\]
with \(n=0,1,2,...\). List all the constants of motion.

kapoor kapoor's picture 22/02/20

Problem/QFT/06007

 

Show that under time reversal \(\bar{u}(p) \to  u(—p)B\) and \(v(p) \to \(\bar{v}(—p) B\). Use this
to show that under \(P T\) together
\[\bar{u}(p') \gamma_{\alpha_1} \gamma_{\alpha_2}\ldots \gamma_{\alpha_n}
u(p) \to  \bar{u}(p)\gamma_{\alpha_n}\gamma_{\alpha_{n-1}}\ldots
\gamma_{\alpha_1} u(p')) \]

kapoor kapoor's picture 22/02/20

Problem/QFT/06006

Let \(p^\mu\) be a time like momentum  vector. Let \(n^\mu\)  be a four vector
such that
\begin{equation}
 n^\mu p_\mu=0,  \text{ and } n^\mu n_\mu=-1.
\end{equation}
How many such independent four vectors \(n^\mu\) exist? How that the operators
\begin{equation}
 \Pi^\pm_n =\frac{1}{2}\big(1\pm \gamma_5 \slashed{n}\big)
\end{equation}
are projection operators satisfying.
\begin{equation}
 \Pi^{(+)2}_n = \Pi^{(-)2}_n = I, \qquad \Pi^{(+)}_n \Pi^{(-)}_n =0.
\end{equation}
The notation here is same as in Bjorken and Drell, Gasiorowicz. 

kapoor kapoor's picture 22/02/20

Prob/QFT/06004

Does there exist an invertible matrix \(S\) such that \[ S \gamma_\mu  S^{-1} = \gamma_\mu'\] where  \[\gamma_1'= \gamma_2\gamma_3, \quad \gamma_2'=\gamma_3\gamma_1, \quad \gamma_3'= \gamma_1\gamma_2, \gamma_4'=\gamma_5 \gamma_4?\] 

kapoor kapoor's picture 22/02/20

A Sample Path

This is a path page with a path diagram.

The path page has an embedded tool - path diagram editor, which has its separate toolbar (maybe hidden - look for a button with '»' sign, above the path diagram on the left).

A path page may have additional text below the path diagram.

ranjan ranjan's picture 21/02/20

Organize Content Using a Path Page

This path page shows how you can organize (study-)items as a diagram showing their inter-dependencies. The path diagram embedded below shows some Khan Academy videos within boxes connected by lines/arrows.

ranjan ranjan's picture 21/02/20

Time-saving summary of the principal formulas for the relevant area of physics

Summary (or abstract) not available for this node.
ranjan ranjan's picture 20/02/20

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