Syllabus

Syllabus#

Course Information#

  • Instructor(s): Michael McNeil Forbes m.forbes+581@wsu.edu

  • Course Assistants:

  • Office: Webster 947F

  • Office Hours: TBD

  • Course Homepage: https://schedules.wsu.edu/List/Pullman/20233/Phys/581/01

  • Class Number: 581

  • Title: Phys 581: The Standard Model of Particle Physics

  • Credits: 3

  • Recommended Preparation:

  • Meeting Time and Location: MW, 4:10pm - 4:00pm, Webster 941, Washington State University (WSU), Pullman, WA

  • Grading: Grade based on assignments and project presentation.

Prerequisites#

This course is intended for a broad audience. As such, the only formal background assumed is a strong background in fundamental mathematical techniques, including complex analysis, calculus, differential equations, and linear algebra as described in Linear Algebra.

Familiarity with the core physics areas of classical mechanics, quantum mechanics, statistical mechanics, and electromagnetism would be helpful, but we will try to supplement any missing knowledge in the course. (Speak up if you have a gap!)

Textbooks and Resources#

Required#

Donoghue and Sorbo: “A Prelude to Quantum Field Theory” (2022)

[Donoghue and Sorbo, 2022] This is a principle textbook for the course. It contains a fairly accessible introduction to the types of manipulations needed to do quantum field theory calculations. Unfortunately, the eBook and required reader are pretty awful, so I highly recommend purchasing a paper copy. Occasionally these go on sale for half-price.

Langacker: “The Standard Model and Beyond (2017)

[Langacker, 2017] This is a principle textbook for the course. It contains a complete and fairly straightforward introduction to the form of The Standard Model, as well as a nice discussion of possible extensions. The CRC Press has made this open access, making this an economical option. Some of this will be a bit tough going if you don’t have the background, but my hope is that you can follow the discussion and use it as a reference once you complete the course.

Georgi: “Lie Algebras in Particle Physics” (2019)

[Georgi, 2019] This is a fun introduction to group theory and Lie algebras with a focus on building the Standard Model. The CRC Press has made this open access.

‘t Hooft: “The Conceptual Basis of Quantum Field Theory”

[`t Hooft, 2016] This is a set of notes by Gerard ‘t Hooft that briefly discusses some of the conceptual foundations and issues with QFT and the Standard Model. ‘t Hooft has one of the most beautiful and deep understandings of field theory, and does not shy away from some of the difficult aspects of the field. This will probably be hard going, but should give you a flavor for some of the subtle and deep aspects of the field.

Additional Resources#

Here are some additional optional resources. Although they are not official texts for the course, I will often refer to sections of them. Feel free to ask questions about these in class.

  • [Zee, 2010]: “Quantum Field Theory in a Nutshell”. This is a fun book to read by one of the masters of the field. However, Zee presents things in such a way that it is easy for readers to feel they understand more than they do. This book should be read in conjunction with a more careful text, and used for perspective.

  • [Zee, 2023]: “Quantum Field Theory, As Simply As Possible”. Bedtime reading with minimal equations. Another good complement for a more serious text to help you gain perspective (if you enjoy Zee’s style).

  • [Donoghue et al., 2014]: “Dynamics of the Standard} Model”. This is a serious and complete presentation of the Standard Model, similar to [Langacker, 2017], but more complete, and, consequently, more difficult to understand. It is a great reference, but I fear will be very difficult for most students to understand.

  • [Lancaster and Blundell, 2014]: “Quantum Field Theory for the Gifted Amateur”. A fairly easy textbook to start with if you want to learn QFT more thoroughly.

  • [Maggiore, 2005]: “A Modern Introduction to Quantum Field Theory”. Another good starting textbook that develops QFT technology starting from symmetries.

  • [Nǎstase, 2019]: “Classical Field Theory”. A comprehensive presentation of classical field theory – i.e. electromagnetism, gravitation, etc. This is a good place to refresh your knowledge of relativity.

  • [Cornwell, 1997]: “Group Theory for Physics” A very fast and thorough introduction to group theory and its applications to physics. Skips over proofs (with references) to emphasize the physics.

  • [Boyd, 1999] “The Devil’s Invention: Asymptotic, Superasymptotic and Hyperasymptotic Series”, and [Bender and Orszag, 1999] “Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and Perturbation Theory”: These provide technical details about asymptotic series of the type common in QFT.

  • [Huang, 2013] A fun high-level discussion of renormalization. Fig. 13 provides the basis for my general picture of physics.

Additional readings and references will be provided as needed. Please see Resources, Readings, and References for details. Details and further resources will also be included on the lecture pages on the Canvas server.

Student Learning Outcomes#

  • Dimensional Analysis: All physical quantities are formed of four fundamental dimensions: mass, time, distance, and charge. This affords a tremendously powerful technique called dimensional analysis that allows physicists to quickly estimate the form of an answer before doing any calculation. Dimensional analysis also allows one to check a calculation or to simplify a calculation by setting up to three independent quantities equal to unity.

    In discussions of the Standard Model, we often set \(\hbar = c = 1\), thereby making equivalent energy, inverse time, and inverse length.

  • Symmetries and Conservation Laws: Symmetry plays a deep role in the formulation of physical theories. Through Noether’s theorem, continuous symmetries lead to conservation laws. For example:

    • Translation invariance ⟹ conservation of linear momentum;

    • Rotational invariance ⟹ conservation of angular momentum;

    • Time-translation invariance ⟹ conservation of energy.

    In the Standard Model, various other symmetries associated with Lie groups, give rise to various conserved charges that play a fundamental role. (E.g. electric charge, baryon number, lepton number). Symmetries also greatly restrict the allowed terms, leading to a complete specification of the model on a few simple properties.

  • Understand the ingredients and basic structure of the Standard Model, and how these come together to explain matter and its interactions. This includes the following:

    • Quantum Field Theory (QFT) as the framework.

    • Fundamental space-time symmetries:

      • Relativistic Poincare invariance (Lorentz invariance + translations).

      • Non-relativistic limit of Galilean invariance (Rotations + boosts + translations).

      • CPT: Charge conjugation times parity times time-reversal invariance. (Relates particles to anti-particles).

    • Representation of symmetries with groups.

    • Organization of matter in terms of spinors – representations of the Poincare group.

      • Spin 0 fields (scalar bosons): the Higgs field.

      • Spin 1/2 fields (spinor fermions): Electron, muon, and tauon; Corresponding Neutrinos; Quarks.

      • Spin 1 fields (vector bosons): Mediators of force (interactions). These vector bosons must be massless to avoid negative energies, and this ensured by imposing gauge symmetries The following gauge bosons exist in the standard model:

        • \(U(1)\): Photon (electromagnetic interactions)

        • \(SU(2)\): \(W\) and \(Z\) bosons (weak interactions)

        • \(SU(3)\): Gluons (strong interaction)

        Note: The Higgs mechanism complicates the relationship betweem the bare gauge bosons that form the \(SU(3)\times SU(2) \times U(1)\) gauge group of the standard model.

      • Spin 2 fields: Graviton. Know that gravity fits within the framework of the Standard Model, but fails to be renormalizable (see below), rendering such a theory of gravity incomplete and lacks predictive power.

    • Principle of mass dimension and renormalizability.

  • Understand how to combine these ingredients to form the Standard Model as the most general quantum field theory with these matter and gauge fields that satisfies all known symmetry constraints and includes only renormalizable terms.

  • QED: Quantum electrodynamics consists of the QFT containing the electron and the photon. Including atomic nuclei (made of protons and neutrons), this theory describes virtually all of the world we interact with daily, including most physical systems, chemistry, and biology. This is the lowest energy scale of the Standard Model, dealing with atomic energies (eV to keV) and lengths scales on the order of angstroms (1Å=\(10^{-10}\)m) (think of the ground state of a Hydrogen atom etc.).

  • EW: Adding to QED the \(W\) and \(Z\) bosons, as well as massive mesons (pions, kaons, and tauons) one obtains electroweak theory which includes phenomena such as radioactive decay: something we experience, but not on a daily basis (I hope!). These occur at energies in the MeV range and lengths scales of picometers (1pm\(=10^{-12}\)m).

  • QCD: Quantum chromodynamics includes the quarks and gluons as degrees of freedom. From these, we obtain the proton, neutron, and mesons included in the previous low-energy theories. These interactions have energies of GeVs on the scale of a fermtometer (sometimes called a “fermi”) 1fm\(=10^{-15}\)m.

  • Asymptotic Freedom: QCD alone has another special feature – the interactions become weaker and weaker as one goes to higher energy. This means that as one probes with higher energies (equivalently, shorter length scales), the theory becomes non-interacting. This introduces the tantalizing possibility that QCD is a correct theory “all the way down”. This is in contrast with QED, where the interactions get stronger at short distance, ultimately leading to a fundamental divergence (sometimes called the “Landau Pole”) that tells us the theory cannot be complete mathematically.

  • Renormalization and Regularization: From this description you see that the theory looks different at different energy scales. This is the idea of renormalization

These ingredients and principles require many interesting and subtle mathematical tools. A good portion of this course will be devoted to explaining these tools, which might have applications elsewhere.

  • Perturbation Theory and Feynman Diagrams:

  • Path Integrals and Generating Functions:

  • Green’s functions:

  • Asymptotic Series:

  • Complex Analysis:

Expectations for Student Effort#

For each hour of lecture equivalent, all students should expect to have a minimum of one hour of work outside class. All students are expected to keep up with the readings assigned in class, asking questions through the Perusall/Hypothes.is forums, complete homework on time, and prepare their projects/presentations.

Assessment and Grading Policy#

There are two options for obtaining a grade in this course.

  • Complete all the assignments, obtaining a grade according to the following scale.

  • Keep and submit a class notebook wherein you document your attempts to learn the material. This notebook should contain at a minimum, dates and times when you work, state your learning goals, and then summarize what worked and what did not. I expect that when you run into difficulties (as documented in your notebook), that you bring these issues to my attention in class, on the forums, or at office hours. If you document a good attempt to learn the material covered in the assignments, then you will get an A for that assignment, even if you cannot successfully complete it.

    Your class notebook can be kept electronically on CoCalc, or you can submit scans of your physical notebook.

    You should treat this as a lab notebook, meaning that you should not edit it. It should contain a chronological record of your progress through course, as an experimentalist would maintain chronological records of the experimental process. Such a notebook is extremely valuable. For example, should you discover something, a notebook can be used to establish academic precedence.

The final grade will be converted to a letter grade using the following scale:

Percentage P

Grade

90.0% ≤ P

A

85.0% ≤ P < 90.0%

A-

80.0% ≤ P < 85.0%

B+

75.0% ≤ P < 80.0%

B

70.0% ≤ P < 75.0%

B-

65.0% ≤ P < 70.0%

C+

60.0% ≤ P < 65.0%

C

55.0% ≤ P < 60.0%

C-

50.0% ≤ P < 55.0%

D+

40.0% ≤ P < 50.0%

D

P < 40.0%

F

Attendance and Make-up Policy#

While there is no strict attendance policy, students are expected attend an participate in classroom activities and discussion. Students who miss class are expected to cover the missed material on their own, e.g. by borrowing their classmates notes, reviewing recorded lectures (if available), etc.

Course Timeline#

As this is the first time we are offering this course as an iSciMath course, the schedule well be extremely fluid in response to the experience of the class.

The Basis of Physics

  • Classical Mechanics

  • Quantum Mechanics

  • What is a Quantum Field Theory

  • Zee’s Baby Problem

Thanksgiving Break – No Classes

Course Review and Future Directions

Other Information#

Policy for the Use of Large Language Models (LLMs) or Generative AI in Physics Courses#

The use of LLMs or Generative AI such as Chat-GPT is becoming prevalent, both in education and in industry. As such, we believe that it is important for students to recognize the capabilities and inherent limitations of these tools, and use them appropriately.

To this end, please submit 4 examples of your own devising:

  • Two of which demonstrate the phenomena of “hallucination” – Attempt to use the tool to learn something you know to be true, and catch it making plausible sounding falsehoods.

  • Two of which demonstrate something useful (often the end of a process of debugging and correcting the AI).

Note: one can find plenty of examples online of both cases. Use these to better understand the capabilities and limitations of the AIs, but for your submission, please find your own example using things you know to be true. If you are in multiple courses, you may submit the same four examples for each class, but are encouraged to tailor your examples to the course.

Being able to independently establish the veracity of information returned by a search, an AI, or indeed any publication, is a critical skill for a scientist. If you are the type of employee who can use tools like ChatGPT to write prose, code etc., but not accurately validate the results, then you are exactly the type of employee that AI will be able to replace.

Any use of Generative AI or similar tools for submitted work must include:

  1. A complete description of the tool. (E.g. “ChatGPT Version 3.5 via CoCalc’s interface” or Chat-GPT 4 through Bing AI using the Edge browser”, etc.)

  2. A complete record of the queries issued and response provided. (This should be provided as an attachment, appendices, or supplement.)

  3. An attribution statement consistent with the following: “The author generated this <text/code/etc.> in part with <GPT-3, OpenAI’s large-scale language-generation model/etc.> as documented in appendix <1>. Upon generating the draft response, the author reviewed, edited, and revised the response to their own liking and takes ultimate responsibility for the content.”

Policy for the Use of Large Language Models (LLMs) or Generative AI in Physics Courses#

The use of LLMs or Generative AI such as Chat-GPT is becoming prevalent, both in education and in industry. As such, we believe that it is important for students to recognize the capabilities and inherent limitations of these tools, and use them appropriately.

To this end, please submit 4 examples of your own devising:

  • Two of which demonstrate the phenomena of “hallucination” – Attempt to use the tool to learn something you know to be true, and catch it making plausible sounding falsehoods.

  • Two of which demonstrate something useful (often the end of a process of debugging and correcting the AI).

Note: one can find plenty of examples online of both cases. Use these to better understand the capabilities and limitations of the AIs, but for your submission, please find your own example using things you know to be true. If you are in multiple courses, you may submit the same four examples for each class, but are encouraged to tailor your examples to the course.

Being able to independently establish the veracity of information returned by a search, an AI, or indeed any publication, is a critical skill for a scientist. If you are the type of employee who can use tools like ChatGPT to write prose, code etc., but not accurately validate the results, then you are exactly the type of employee that AI will be able to replace.

Any use of Generative AI or similar tools for submitted work must include:

  1. A complete description of the tool. (E.g. “ChatGPT Version 3.5 via CoCalc’s interface” or Chat-GPT 4 through Bing AI using the Edge browser”, etc.)

  2. A complete record of the queries issued and response provided. (This should be provided as an attachment, appendices, or supplement.)

  3. An attribution statement consistent with the following: “The author generated this <text/code/etc.> in part with <GPT-3, OpenAI’s large-scale language-generation model/etc.> as documented in appendix <1>. Upon generating the draft response, the author reviewed, edited, and revised the response to their own liking and takes ultimate responsibility for the content.”

Academic Integrity#

You are responsible for reading WSU’s Academic Integrity Policy, which is based on Washington State law. If you cheat in your work in this class you will:

  • Fail the course.

  • Be reported to the Center for Community Standards.

  • Have the right to appeal the instructor’s decision.

  • Not be able to drop the course or withdraw from the course until the appeals process is finished.

If you have any questions about what you can and cannot do in this course, ask your instructor.

If you want to ask for a change in the instructor’s decision about academic integrity, use the form at the Center for Community Standards website. You must submit this request within 21 calendar days of the decision.

University Syllabus#

Students are responsible for reading and understanding all university-wide policies and resources pertaining to all courses (for instance: accommodations, care resources, policies on discrimination or harassment), which can be found in the university syllabus.

Students with Disabilities#

Reasonable accommodations are available for students with a documented disability. If you have a disability and need accommodations to fully participate in this class, please either visit or call the Access Center at (Washington Building 217, Phone: 509-335-3417, E-mail: mailto:Access.Center@wsu.edu, URL: https://accesscenter.wsu.edu) to schedule an appointment with an Access Advisor. All accommodations MUST be approved through the Access Center. For more information contact a Disability Specialist on your home campus.

Campus Safety#

Classroom and campus safety are of paramount importance at Washington State University, and are the shared responsibility of the entire campus population. WSU urges students to follow the “Alert, Assess, Act,” protocol for all types of emergencies and the “Run, Hide, Fight” response for an active shooter incident. Remain ALERT (through direct observation or emergency notification), ASSESS your specific situation, and ACT in the most appropriate way to assure your own safety (and the safety of others if you are able).

Please sign up for emergency alerts on your account at MyWSU. For more information on this subject, campus safety, and related topics, please view the FBI’s Run, Hide, Fight video and visit the WSU safety portal.

Students in Crisis - Pullman Resources#

If you or someone you know is in immediate danger, DIAL 911 FIRST!

  • Student Care Network: https://studentcare.wsu.edu/

  • Cougar Transit: 978 267-7233

  • WSU Counseling and Psychological Services (CAPS): 509 335-2159

  • Suicide Prevention Hotline: 800 273-8255

  • Crisis Text Line: Text HOME to 741741

  • WSU Police: 509 335-8548

  • Pullman Police (Non-Emergency): 509 332-2521

  • WSU Office of Civil Rights Compliance & Investigation: 509 335-8288

  • Alternatives to Violence on the Palouse: 877 334-2887

  • Pullman 24-Hour Crisis Line: 509 334-1133