PHY6648: Quantum Field Theory I

This course is the first semester of a three semester course on modern quantum field theory and the standard model of elementary particles. Although the course is mandatory for students interested in high energy particle physics, it should also be valuable to students of other specialties including condensed matter physics and atomic and molecular physics. For example, in the first semester we shall develop, in our treatment of the Dirac equation, the technique of second quantization so useful in many body theory. Furthermore, the emphasis of the whole course is on Quantum Electrodynamics, which is essential to an understanding of all areas of physics. Quantum Field Theory I is the natural continuation of the graduate quantum mechanics courses PHY6645-46.

PHZ6358: Standard Model of Elementary Particles I/ Quantum Field Theory II

This course is the second semester of quantum field theory and the standard model. The first part of the course will deal with 1 loop Quantum Electrodynamics (QED) and its renormalization. Then nonabelian gauge theory will be introduced with applications in QCD the gauge theory of strong interactions. The gauge group of the standard model will be presented. Spontaneous breaking of global symmetries will be introduced with first applications to chiral symmetry breaking and pions as Goldstone bosons. Then spontaneous breaking of local (i.e. Gauge) symmetries will be discussed with application to the electroweak sector of the standard model.

PHZ7359: Standard Model of Elementary Particles II and Quantum Field Theory II

Continuation of PHZ6358.

PHZ6358 Course Information:

Below are links to course information, a syllabus, a convention and formula sheet, and my lecture notes.

Course Information
Syllabus for PHY6648.
Syllabus for PHZ6358.
Syllabus for PHZ7359.
- String Theory Outline
- String Lecture Notes
Books on QFT and Standard Model. .
Conventions and Useful Formulae. . Note that our conventions agree with Srednicki, but not with Peskin and Schroeder. Discrepancies with the latter are noted.
Lecture Notes on Quantum Field Theory (Chapters 1-28)

Class and contact Information

email: thorn@phys.ufl.edu

Lectures: MWF period 8 (3:00PM-3:50pm), NPB 1011.

Office hours: MW period 7 (1:55-2:45 pm), F period 9 (4:00-5:00pm), and by appointment, NPB 2069.

Our grader:TBD

email:TBD

Office hours: TBD.

Students will be notified when the evaluation period opens, and can complete evaluations through the email they receive from GatorEvals, in their Canvas course menu under GatorEvals, or via https://ufl.bluera.com/ufl/ . Summaries of course evaluation results are available to students at https://gatorevals.aa.ufl.edu/public-results/

Announcements, Spring2020: PHZ6359

Problem Set 1 posted 3 January 2020.

Problem Set 2 posted 19 January 2020.

Solution Set 1 posted 04 February 2020.

Problem Set 3 posted 05 February 2020.

Solution Set 2 posted 14 February 2020.

Problem Set 4 posted 19 February 2020.

Solution Set 3 posted 9 March 2020.

Problem Set 5 posted 9 March 2020.

For Monday's online class (16 March) I plan to discuss lecture notes sections 29.1.4: Su(3) assignments to low mass baryons and 29.1.5: Gell-Mann-Okubo Mass relations

For Wednesday's online class I plan to discuss sections 29.1.5: Gell-Mann-Okubo Mass relations/ (Finidh) and 29.1.6 Rotational excitations of Mesons

Solution Set 4 posted 20 March 2020.

There is a typo in Problem 13 of Set 5: A factor of $I_2$ should multiply the $sin\theta$ on the right of the identity to be proved.

Problem 15 of Problem Set 5 is moved to Problem Set 6. this is to give us a chance to discuss beta decay more in class before it is due. If you have already solved it, you may either hand it in with Set 5 or Set 6 as you wish.

Tomorrow, 23 March, I plan to finish the string model by discussing normal modes and quantization. Then we will move on to section 29.2. Hopefully we will make a good start on subsection 29.2.1 to be continued on Wednesday.

Problem Set 6 posted 24 March 2020.

Tomorrow, 25 March, I plan to finish with pion beta decay (Section 29.2.1) and start baryon beta decay, Section 29.2..2, Vector currents and 29.2.3 Axial currents.

This afternoon, Friday 27 March, I plan to finish our discussion of the axial current in baryon beta decay (subsection 29.2.3) and get a good start on section 29.3 other semi-leptonic processes.

Solution Set 5 posted 27 March 2020.

Topics for Monday, 30 March. I plan to introduce the neutral kaon system with a preliminary description of K-Kbar mixing, Subsection 29.3.1. Then we will discuss section 29.4, Flavor changing weak processes.

Topics for Wed. 1 April. I will finish subsection 29.3.1 by illustrating the usefilness of effective field theory ideas. Then we will begin a discussion of non-leptonic weak decays, section 29.6.

Topics for Friday, 3 April I will continue with non-leptonic decays Section 29.5. I will say more about evidence for the delta I=1/2 rule and then sketch theoretical ideas for explaining it. I will omit subsection 29.5.1 and move on to a more detailed analysis of K0-K0bar mixing if there is time.

Problem Set 7 posted 5 April 2020.

Tomorrow (6 April) I will discuss section 29.5.2, modelling K0-K0bar mixing with box Feynman diagrams.

Some eq. numbers refrred to in problem 15 of Set 6 have been corrected.

Topics for today, 10 April: We will discuss KKbar oscillations allowing for CP violation (Section(29.5.3. If time permits we will also discuss neutrino oscillations.

Tentative plan for final exam: I will post it at 5pm on Friday, 24 April and the deadline for returning (via email) your solutions to me is 5pm on Saturday, 25 April.

Faculty Course evaluations open 11 April2020 and will continue until 24 April 2020. These evaluations provide very important feedback, so it is essential that we all do our best to maximize the number of responses. You can access the evaluation form at your leisure from the web site: https://ufl.bluera.com/ufl/

Students are expected to provide professional and respectful feedback on the quality of instruction in this course by completing course evaluations online via GatorEvals. Guidance on how to give feedback in a professional and respectful manner is available at https://gatorevals.aa.ufl.edu/students/ . Students will be notified when the evaluation period opens, and can complete evaluations through the email they receive from GatorEvals, in their Canvas course menu under GatorEvals, or via https://ufl.bluera.com/ufl/ . Summaries of course evaluation results are available to students at https://gatorevals.aa.ufl.edu/public-results/

Topics for Monday, 13 April. We will start with a brief discussion of neutrino oscillations Section (29.5.4. Then we will start learning about deep inelastic lepto-production Section (29.6). I expect to finish deep inelastic scattering on Wednesday.

Student course evaluations are now open. Pkease take a few minutes to offer feedback on this course.

Topics for today, 15 April: We will finish discussion of deep inelastic scattering. The two main topics are Feynman's parton model and the QCD analysis based on the operator product expansion and asymptotic freedom. We conclude with a brief discussion of final hadronic states.

Solution Set 6 posted 15 April 2020.

Topics for today, 17 April: We start with a brief discussion of final hadronic states in deep inelastic scattering, introducing the concept of hadron jets. We extend the discussion to jets in hadron hadron scattering at fixed angle. Then we will start an overview of the Regge limit: hadron scattering at fixed momentum transfer.

Topics for Monday, 20 April: I will present the Veneziano amplitude as a simple example of Regge behaved scattering. I will also explain its interpetation as the scattering of two open strings in their ground stats. Then I will try to indicate the relevance of Regge ideas to scattering of hadrons in QCD.

Topics for Wednesday, 22 April: Today in our last class, I will give an overview of Grand Unified Theories, which aim to find a simple group that contains the standard model gauge group. We will focus on the simplest possibility $SU(5)$.

I will post solutions to Set 7 after 5pm this evening. Final exam reminder. I will post the exam on this page at 5pm on 24 April, and solutions are due at 12 noon Monday 27 April. I will also email the exam to you at the same time.

Solution Set 7 posted 23 April 2020.

I have decided to give you the whole weekend to complete the final: The due date and time will now be 12 noon 27 April 2020. the start date and time will remain 5pm 24 April (today).

Homework Assignments

In the homework assignments, I will refer to problems in Srednicki's book by prefixing the problem number with S. Note that there are many problems in his book which ask the reader to fill in gaps in the preceding discussion (e.g. S 2.1 through 2.7). I will generally not assign such problems to be graded, but you should nonetheless make sure you understand how to do them.

Problem Set 1, due 22 January 2020, Solution Set 1

Problem Set 2, due 5 Febriary 2020, Solution Set 2

Problem Set 3, due 19 February 2020, Solution Set 3

Problem Set 4, due 11 March 2020, Solution Set 4

Problem Set 5, due 25 March 2020, Solution Set 5

Problem Set 6, due 8 April 2020, Solution Set 6

Problem Set 7 , due 22 April 2020. Solution Set 7

Final Examination , due 12 noon 27 April 2020.

Information on Final Exam

There will be a take home final examination, posted at 5pm on Friday 24 April with solutions due by email to me by 12 noon Monday 27 April. 2020 the exam will consist of a series of 10 short answer questions,

University Policies:

Students are expected to know and comply with the University's policies regarding academic honesty and use of copyrighted materials. Cheating, plagiarism, or other violations of the Academic Honesty Guidelines will not be tolerated and will be pursued through the University's adjudication procedures.

Students are expected to provide professional and respectful feedback on the quality of instruction in this course by completing course evaluations online via GatorEvals. Guidance on how to give feedback in a professional and respectful manner is available at https://gatorevals.aa.ufl.edu/students/. Students will be notified when the evaluation period opens, and can complete evaluations through the email they receive from GatorEvals, in their Canvas course menu under GatorEvals, or via https://ufl.bluera.com/ufl/. Summaries of course evaluation results are available to students at https://gatorevals.aa.ufl.edu/public-results/

“Students requesting classroom accommodations must first register with the Disabilities Resources Program, located in the Dean of Students Office, P202 Peabody Hall. The Disabilities Resources Program will provide documentation to the student, who must then deliver this documentation to the instructor when requesting accommodations.”

We shall not cease from exploration
And the end of all our exploring
Will be to arrive where we started
And know the place for the first time.

- T. S. Eliot

Announcements, Fall2019: PHZ6358

Problem Set 1 has been posted, 21 August 2019.

Because the University has canceled classes today (4 September), the due date for Problem Set 1 has been pushed back to Monday, 9 September 2019.

Solution Set 1 has been posted, 10 September 2019.

Problem Set 2 posted 8 September 2019. Note that it is due on Monday, 23 Septembe 2019, so that you will have a full two weeks to finish it. I will try to post Set 3 a full two weeks before its normal due date, so by then we will be back on track.

Note the time change for my WF office hours. They will now be the period just before class on those days.

Problem Set 3 has been posted, 25 September 2019. I apologize for rhe lateness if this notice: the link to this file on the course webpage was incorrect. I just caught it today!

Solution Set 2 has been posted, 2 October 2019.

Problem Set 4 posted, 4 October 2019.

Problem Set 5 posted, 17 October 2019.

Solution Set 4 posted, 27 October 2019.

Problem Set 7 posted, 14 November 2019. This last set is due on the last day of class 4 December 2019. To get credit for this and any other late homework, it must be handed in by 5pm 4 December 2018.

My plan for the take home final exam is to hand it to you in my office Friday 6 December with a due date and time of the following Monday 9 December, by 12 noon in my office.

Solution Set 5 posted, 16 November 2019.

Solution Set 6 posted, 25 Bovember 2019.

The course evaluation system is now open.

Faculty Course evaluations open Tuesday, 26 November 2019 and will continue until Friday, 6 December 2019. These evaluations provide very important feedback, so it is essential that we all do our best to maximize the number of responses. You can access the evaluation form at your leisure from the web site: https://ufl.bluera.com/ufl/

Solution Set 7 posted, 4 December 2019.

Revised schedule for take home final: Exam may be picked up in my office after 2:30pm tomorrow (Friday, 6 December). The due date and time will be Monday, 9 December at 12 noon in my office.

Final exam query 1: In question 7(c) do you want us to write the cross section to all orders? Answer: All of problem 7 is done in tree approximation, i.e. no loop diagrams. But no further approximations, except when you do the low energy approximation. Remember you are treating the Lagrangian as an effective Lagrangian. Final query 2: Are the scalar fields in the last problem real ( Hermitian)? Answer: Yes, they are Hermitian (real, classically). Final query 3: is the superscript 4 on \phi in 7d the 4 component of \phi^a? Answer: Yes.

Homework Assignments

Problem Set 1, due 9 September 2019, Solution Set 1

Problem Set 2, due 23 September 2019, Solution Set 2

Problem Set 3, due 7 October 2019, Solution Set 3

Problem Set 4, due 18 October 2019, Solution Set 4

Problem Set 5, due 1 November 2019, Solution Set 5

Problem Set 6, due 15 November 2019, Solution Set 6

Problem Set 7, due 4 December 2019, Solution Set 7

Information on Final Exam

In grading the final, points will be deducted for errors in calculation and logic. This is in sharp contrast to the grading of the homework which was based more on the amount of work done than its accuracy. Absolutely no collaboration will be allowed. Each student's exam must be entirely his own work.

Announcements, Spring2019: PHY6648

The first problem set 1 has now been posted. The due date is Friday 18 January 2019.

Problem Set 2 posted 17 January 2019. The due date is 25 January 2019.

Solution Set 1 posted 22 January 2019. I posted solutions early because everyone handed in their complete solutions on the due date. Normally solutions will be posted one week after the due date.

Problem Set 3 posted 24 January 2019. The due date is 1 February 2019.

Solution Set 2 posted 29 January 2019. Again all sets were handed in on time!

Problem Set 4 posted 31 January 2019. The due date is 8 February 2019.

Updated lecture notes posted 4 February 2019.

Problem Set 5 posted 8 February 2019. The due date is 15 February 2019.

Solution Sets 3 and 4 posted 9 February 2019.

Problem Set 6 posted 15 February 2019. The due date is 22 February 2019.

Problem Set 7 posted 21 February 2019. The due date is 1 March 2019.

Solution Set 5 posted 23 February 2019.

Problem Set 8 posted 1 March 2019. The due date is 15 March 2019.

Solution Sets 6 and 7 posted 2 March 2019.

Problem Sets 6 and 7 are graded and may be picked up in my office during spring break. During the break I will try to be in my office most afternoons after 2:30 pm. Please stop by or email me if you would like to set up an appointment.

I have to cancel my morning office hour (11:45-12:35) next Wednesday, 20 March 2019. I will meet the afternoon office hour (4-5pm) as usual. Monday and Friday office hours next week will meet as usual.

Problem Set 9 posted 14 March 2019. The due date is 22 March 2019.

Solution Set 8 posted 22 March 2019.

Problem Set 10 posted 23 March 2019. The due date is 29 March 2019.<

Problem Set 11 posted 29 March 2019. The due date is 5 April 2019.

Solution Set 9 posted 31 March 2019.

I have to cancel our 11:45 office hour today (Wednesday). The office hour after class and on Friday morning will be held as usual. Remember you can stop by my office at any time for assistance.

An error in Problem 41 of problem set 11 has been corrected. In some of the formulas $\Omega$ should be replaced by its inverse, as shown in the revised problem set.

Problem Set 12 posted 4 April 2019. The due date is 12 April 2019.

The equation number referred to in problem 46a) of Set 12 should be (10.28) NOT (10.38). The posted HW has now been corrected.

Solution Set 10 posted 10 April 2019.

Problem Set 13 posted 10 April 2019. The due date is 24 April 2019 (the last day of class!).

Typo in problem 45b of Set 12: The denominator inside the integral on the right should be raised to the power $n$ NOT the power 2!

Faculty Course evaluations will be conducted entirely on line. They open 13 April 2019 and will continue until 26 April 2019. These evaluations provide very important feedback, so it is essential that we all do our best to maximize the number of responses. You can access the evaluation form at your leisure from the web site: https://evaluations.ufl.edu/evals/ where you can find instructions and links to a gatorlink login page. It is probably a good idea if you bookmark the page so you can easily find it in the future.

Solution Set 11 posted 16 April 2019.

Solution Set 13 posted 25 April 2019.

Information for the final examination, scheduled for 1 May 2019, 12:30-2:30pm in our classroom. It will be a closed book examination, no electronic devices permitted. The formula sheet Conventions and Useful Formulae will be included with the examination booklet. The exam will consist of 4 questions: one on symmetries of the Dirac equation, one on vacuum polarization, one on gauge invariance of Feynman diagrams, and one simple cross section calculation.

The final exam has been graded, and you may pick them up in my office. Statistics: Average=76, Median=85.

Statistics for total course scores: Average=85, Median=86. Grade assignments: 90-100 A; 80-89 A-; 60-79 B+.