Show that the fermion operator set ( left a, a dagger , a dagger a frac 1 2 ight ) obeys and that this is equivalent to the ( mathrm SU (2) ) Lie algebra of Eq (3 18) Data from Eq 3 18 a,a 2(a a ) a'a ,a a a'a , a' a,...

The Answer is in the image, click to view ...

Show that the fermion operator set (left{a, a^{dagger}, a^{dagger} a-frac{1}{2} ight}) obeys and that this is equivalent

Question:

Show that the fermion operator set $\left\{a, a^{\dagger}, a^{\dagger} a-\frac{1}{2}\right\}$ obeys

and that this is equivalent to the $\mathrm{SU}(2)$ Lie algebra of Eq. (3.18).

Data from Eq. 3.18

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Symmetry Broken Symmetry And Topology In Modern Physics A First Course

ISBN: 9781316518618

1st Edition

Authors: Mike Guidry, Yang Sun

See More Books

Question Posted: Mar 30, 2024 01:01 AM

See More Questions

For the single-fermion example worked out in Problems 21.3 and 21.4 , take as a reference state the minimal weight $\mathrm{SU}(2)$ state $\left|\frac{1}{2}-\frac{1}{2} ightangle$ corresponding...
Show that the coset representative is \[\Omega(\xi)=e^{\xi J_{+}-\xi^{*} J_{-}}=e^{\xi a^{\dagger}-\xi^{*} a}\] for the generalized coherent state approximation corresponding to the single-fermion...
Construct the Hilbert space corresponding to the Lie algebra for a single fermion in Problem 21.3 . Remember that for a fermion the Pauli principle must be obeyed, which greatly restricts allowed...
11. Which one is not a source for collecting references? Ans : O Proquest Ebscohost O Scopus Safe assign
If we use the data given in Exercise 1 with two-way analysis of variance, we get the accompanying display. What do you conclude? Statdisk DF: SS: MS: Test Stat, F: Critical F: P-Value: Source:...
Access the website for CVS Corporation and locate the companys 2005 annual report. Conduct a comprehensive ratio analysis that compares the companys performance in 2005 and 2004. If you have computed...
Figure P25.9 is an edge-on view of a 10-cm-diameter circular loop rotating in a uniform $0.050 \mathrm{~T}$ magnetic field. What is the magnetic flux through the loop when $\theta$ is...
Jay and Mike are opening a paint store. There are no competing paint stores in the area. Their fundamental decision is how to organize the business. They anticipate profits of $300,000 the first...
(6 points) Let A Cnxn. Show that A is normal iff a unitary U Cnn and diagonal D Cn such that D = U*AU, namely, A = UDU*.
Show that the coherent state corresponding to the single-fermion problem worked out in Problems 21.3 through 21.6 is where $\theta$ and $\phi$ are angular variables parameterizing a sphere...
For the coherent state of atoms in Section 21.4 , prove that starting from Eq. (21.29) and that $J_{ \pm} \equiv J_{1} \pm i J_{2}$. Data from Eq. 21.29 Data from Section 21.4 ...... () = exp : 0
What was the volume of securities lent by the Federal Reserve in the most recent week?
You buy a new Ford F150. The tires that come with the truck are final goods. intermediate goods. transfer goods. financial goods
When stock price movements are governed by a multistep binomial tree we can treat each binomial step separately and work back from the end of the life of the option to the beginning to obtain the...
Accounting standards are the technical process of balancing accounts. rules for preparing financial statements. the levels of tax payments needed. the rules for performing an audit
Please modify the below scripts to get the attached output: #!/usr/bin/env python3 f = open('file1.txt', 'w') f.write('Line 1Line 2 is a little longerLine 3 is too') f.close() f = open('file2.txt',...
Calculate ending equity if opening paid in capital (share capital) was $100,000 and retaining earnings were $10,000, but during the year recorded an after-tax profit of $30,000 and no dividends were...
In the discussion of ULTs versus KLTs, it was pointed out that a disadvantage of ULTs is that when a ULT executes a system call, not only is that thread blocked, but also all of the threads within...
For each equation, (a) Write it in slope-intercept form (b) Give the slope of the line (c) Give the y-intercept (d) Graph the line. 7x - 3y = 3
What role does effective leadership play in orchestrating collaborative efforts towards common goals and objectives?
a. What is the smallest unit of measurement on the ruler above? (e.g., millimeter, centimeter) b. How accurate do you think you can be when measuring an object with this ruler? Explain your answer....
6. [6 marks] Two forces act horizontally on a mass. F is 200 N [S25E]. F is 130 N [E15N]. a) Find the resultant force FR = F + F. b) Find the equilibrant force FE. c) Draw a vector diagram showing F,...

Show that the fermion operator set (left{a, a^{dagger}, a^{dagger} a-frac{1}{2} ight}) obeys and that this is equivalent

Question:

[a,a] = 2(a*a-) [a'a-,a] = ==a [a'a-, a'] = a,

Step by Step Answer:

Symmetry Broken Symmetry And Topology In Modern Physics A First Course

Students also viewed these Sciences questions