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### Constant electric field in vacuum

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

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

kapoor 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 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 22/02/20

### Problem/QFT/06006

Let $$p^\mu$$ be a time like momentum  vector. Let $$n^\mu$$  be a four vector
such that

n^\mu p_\mu=0,  \text{ and } n^\mu n_\mu=-1.

How many such independent four vectors $$n^\mu$$ exist? How that the operators

\Pi^\pm_n =\frac{1}{2}\big(1\pm \gamma_5 \slashed{n}\big)

are projection operators satisfying.

\Pi^{(+)2}_n = \Pi^{(-)2}_n = I, \qquad \Pi^{(+)}_n \Pi^{(-)}_n =0.

The notation here is same as in Bjorken and Drell, Gasiorowicz.

kapoor 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 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 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 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 20/02/20