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Physics and Astronomy (Phys)200 |300 |400 |Graduate Courses | www.physics.iastate.edu/
Eli Rosenberg, Chair of Department
For the undergraduate curriculum in liberal arts and sciences, major in physics, leading to the degree bachelor of science, see Liberal Arts and Sciences, Curriculum.
Physics and astronomy are basic natural sciences which attempt to describe and provide an understanding of both our world and our universe. Physics serves as the underpinning of many different disciplines including the other natural sciences and technological areas. Graduates are proficient in the methods of rigorous scientific analysis, relevant mathematical techniques, and modern computational and laboratory methods. They have a broad knowledge of physics, including mechanics, electricity and magnetism, thermodynamics, and modern physics. They are able to communicate clearly and effectively at general and technical levels. They are prepared to pursue a wide range of careers as a professional physicist, astronomer, or science educator. They are also prepared to pursue advanced studies and careers in areas as diverse as engineering, medicine, law, and business administration.
Many opportunities exist for students who terminate their studies with a bachelor's degree, especially when combined with technology studies in other areas. Students who meet the necessary scholastic standards often continue their studies in a graduate college, exploring and contributing to new developments in the field.
The department normally expects each student majoring in physics to complete at least the following courses: Phys 221, 222, 321, 321L, 322, 322L, 304, 306, 361, 362, 364, 365, and three credits of laboratory work chosen from 310, 311, 311T, 470L, or Astro 344L. All students are required to earn at least 5 credits in laboratory work in physics in addition to the laboratory components of Phys 221 and 222. These 5 credits must be in courses numbered 300 or higher or in approved substitutions. All students must earn at least 20 credits in physics and astronomy courses numbered 304 or higher. The basic list of expected courses is not a rigid requirement and changes in this basic list will be approved by the department curriculum committee on recommendation of the student's adviser when such changes will better serve the student's needs. In particular, students planning a physics major and also seeking certification for high school teaching may, with the approval of their adviser, follow a significantly different program designed to meet their particular needs; these students should consult the department for further information. Further information concerning programs of study, including sample degree programs, is available from the department.
Students majoring in physics who wish an emphasis in astronomy/astrophysics should consider a minor in astronomy (see below). Those planning graduate work in physics or astronomy/astrophysics should add to the basic list the courses Phys 480 and 481. Other useful courses include Phys 496, Math 365, 426, and 471, and Stat 447. One or more of Astro 405, Phys 511 or 526 may also be added according to interest.
The department offers a minor in physics which may be earned by completing 20 credits in physics courses chosen as follows: Phys 221, 222; 321; at least one credit of laboratory chosen from 321L, 322L, 310, 311, and 311T. Other acceptable courses are 304, 306, 322, 361, 362, 364, 365, 480, 481, and 496.
The department offers a minor in astronomy which may be earned by completing 15 credits chosen as follows: a total of 12 or more credits in Astro courses (must include Astro 344L and may include one of the courses Astro 120, Astro 150 or Astro 250), with the remaining 3 credits (if applicable) chosen from among Physics 304, 321, 361, 362, 364, 365, 480, 481, or 496; 12 or more credits must be at the 300 level or higher. Note that the same course may not be used to satisfy both the requirements of a physics major and an astronomy minor.
Communication Proficiency requirement: The department requires a grade of C or better in each of Engl 150 and 250 (or 250H), and a C or better in Engl 302, 305, 309 or 314. Students are also encouraged to study at least one foreign language.
The expected outcomes for students in these programs are: (1) a broad knowledge of physics, including mechanics, electricity and magnetism, thermodynamics, wave motion and modern physics; (2) proficiency in laboratory methods; (3) proficiency in modern scientific computational methods; and (4) a sound foundation in the liberal arts including proficiency in communication skills.
In addition to the performance on exams and course grades, information on evaluating of the success in meeting these goals is obtained by: (1) an annual written survey of all students majoring in the program: (2) an annual written survey of all graduating seniors; (3) a periodic written survey of program alumni; (4) student evaluations of all courses; (5) adviser evaluations; and (6) a bimonthly meeting of program majors with the department chair.
The department offers studies for the degrees master of science and doctor of philosophy with majors at both levels in applied physics, astrophysics, condensed matter physics, high energy physics, nuclear physics, and physics; and minor credit courses for students majoring in other departments.
Facilities of various research groups of the department, the Ames Laboratory, and the Applied Science Center, including the Microelectronics Research Center, are available for research.
Students with bachelor's degrees in physics or astronomy from other institutions ordinarily will qualify for graduate study at Iowa State provided they have satisfactorily completed course work similar to that suggested for undergraduate majors here intending to go on to graduate school. In some cases additional instruction at the intermediate level may be required.
Graduates have a broad understanding of physical science, as well as mastery of state-of-the-art methods in their area of specialization. They are able to communicate effectively to a wide range of audiences, from the general public to research colleagues. Their skills in rigorous scientific
thinking prepare them for leadership in the broader community. They are skilled in carrying out research, communicating research results, and soliciting research support. They have considerable teaching experience. They have developed problem solving skills that prepare them for careers in either industry or academia.
All candidates for an advanced degree in physics are expected to complete Phys 531, 564, 571, 572, 591 and 592. Candidates for an advanced degree in applied physics are expected to complete Phys 571, 591, 470L (6 cr.), 699 ( 3 cr.), and either 572 or 531. Candidates for a Ph.D. in Astrophysics should complete Phys 571, 591, either 564 or 531, Astro 505, 510 and three of the 580 level Astro courses. A minimum of 72 graduate credits must be earned for a Ph.D. At least 36 credits, including all dissertation research credits, must be earned under the supervision of the student's Program of Study committee. At least 24 of these credits must be earned during two consecutive semesters or during a continuous period including two semesters and a summer session while in residence at the university.
Except for the applied physics major where a thesis is always required, the degree Master of Science is offered both with and without thesis.For all areas of study except applied physics the basic requirements for the M.S. are the same: at least 30 credits of acceptable graduate work must be completed, not less than 21 of which must be in physics or astronomy. Students must complete not less than 6 credits from outside their major area, with 3 credits being required from outside the department, and 3 credits from a 500 or 600 level course in another area of specialization. Students choosing a M.S. degree with thesis may apply up to 8 credits of 699 but no credits of 599 toward the minimum 30 credits. Students choosing a degree without thesis should apply 2 credits of 599, but may not apply any credits of 699 toward the minimum 30 credits.
Students whose major area is applied physics must complete at least 30 credits of acceptable graduate work for the M.S. degree and not less than 19 credits of these must be in the required courses listed above; the remaining 11 credits of the 30 credit minimum may be chosen freely either from within the student's major area or from without and either from the department or outside, but it should be noted that not more than 3 credits of Phys 699 may be applied toward the 30 credit minimum.
In addition to course work in the major area of study, all candidates for the Ph.D. degree must complete 12 credits from outside this area. Of these 6 must be taken from other departments and 6 must be taken from the department with the additional constraint that this latter 6 must include at least one 500 or 600 level introductory course in another area of specialization. Each candidate for the Ph.D. degree is required to teach one year of elementary physics or astronomy.
Graduate students interested in a physics minor should contact the department for requirements.
Courses open for nonmajor graduate credit: Phys 304, 310, 311, 361, 362, 364, 365, 480, 481, 496, and Astro 342, 344L, 346.
Courses primarily for undergraduate students
Phys 101. Physics for the Nonscientist. (3-0) Cr. 3. F.S. Survey of the principal areas of both classical and modern physics. Emphasis on the nature of the physical universe and the application of physical principles to life in the modern world.
Phys 106. The Physics of Common Experience. (4-2) Cr. 4. F.S. Elementary topics from mechanics, heat, electricity, sound, and light, emphasizing the use of basic principles to understand everyday experience. Includes practical problem exercises and a coordinated laboratory.
Phys 111. General Physics. (4-2) Cr. 4. F.S.SS. Prereq: 1 1/2 years of high school algebra, 1 year of geometry, 1 semester of trigonometry. General background in physical concepts, principles, and methods for those who do not plan advanced study in physics or engineering. Mechanics, fluids, heat and thermodynamics, vibrations, waves, sound.
Phys 112. General Physics. (4-2) Cr. 4. F.S.SS. Prereq: 111. General background in physical concepts, principles, and methods for those who do not plan advanced study in physics or engineering. Electricity and magnetism, ray and wave optics, topics in modern physics.
Phys 198. Physics of Music. (2-2) Cr. 3. F. Introductory level course on sound for nonphysics majors. Properties of pure tones and harmonics; human perception of sound; room acoustics; scales; production, and analysis of musical by voice, string, woodwind, brass, and percussion instruments.
Phys 199. Introductory Seminar. Cr. R. F. Gain experience in key skills that physicists/astronomers use routinely, but are rarely explicitly taught in formal courses. Participate in faculty-led discussions on frontier areas and careers. Satisfactory-fail only.
Phys 221. Introduction to Classical Physics I. (4-1) Cr. 5. F.S.SS. Prereq: Credit or enrollment in Math 166. For engineering and science majors. 3 hours of lecture each week plus 3 recitations and 1 laboratory every 2 weeks. Elementary mechanics including kinematics and dynamics of particles, work and energy, linear and angular momentum, conservation laws, rotational motion, oscillations, gravitation. Electric forces and fields. Electrical currents; DC circuits.
Phys 222. Introduction to Classical Physics II. (4-2) Cr. 5. F.S.SS. Prereq: 221, Math 166. 3 hours of lecture each week plus 1 recitation and 1 laboratory each week. Magnetic forces and fields: LR, LC, LCR circuits; Maxwell's equations; waves and sound; ray optics and image formation; wave optics: heat, thermodynamics, kinetic theory of gases; topics in modern physics.
Phys 290. Independent Study. Cr. 1-4. Repeatable. Prereq: Permission of instructor.
Phys 298. Cooperative Education. Cr. R. F.S.SS. Prereq: Permission of the department cooperative education coordinator; sophomore classification. Required of all cooperative education students. Students must register for this course prior to commencing each work period.
Phys 302. The Challenge of Contemporary Physics. (3-0) Cr. 3. S. Prereq: Sophomore classification. A largely nonmathematical but intellectually challenging exploration of physics, which assumes no previous work in the field. Selected material from classical and modern physics establishes the conceptual framework for the study of major areas of contemporary physics, culminating in the discussion of topics at the frontier of present knowledge. Topics vary yearly and may include quarks, lasers, superconductivity, fission and fusion, solid state devices, gravitational waves, string theory, facilities, left handed materials, and quantum computing.
Phys 304. Thermal Physics. (3-0) Cr. 3. F. Prereq: 222, Math 266. Concepts of temperature, entropy, and other characteristic thermodynamic functions, with application to macroscopic properties of matter. The laws of thermodynamics. Introduction to statistical mechanics, including quantum statistics. Application to black body radiation, crystalline vibrations, magnetic ions in solids, electronic heat capacity of metals. Phase transformations and chemical reactions. Nonmajor graduate credit.
Phys 306. Physics of Wave Motion. (3-0) Cr. 3. S. Prereq: 222, credit or enrollment in Math 267. Oscillating systems including damped and forced oscillations; fluids, geometric optics, water waves, the wave equation, Fourier and Laplace transforms, non-uniform media, cylindrical and spherical waves, polarization, interference and diffraction, transmission lines, non-linear waves.
Phys 310. Electronic Instrumentation for Experimental Physics. (2-4) Cr. 4. F. Prereq: 222; Math 166. Common electrical instruments; power supplies; transducers; passive and active devices, analog integrated circuits, including filters and amplifiers; digital integrated circuits; signal transmission and enhancement. Nonmajor graduate credit.
Phys 311. Intermediate Laboratory. Cr. 1-2. Repeatable. S. Prereq: 322. Experiments in classical and modern physics performed independently by each student. Nonmajor graduate credit.
Phys 311T. Intermediate Laboratory. (0-6) Cr. 3. Repeatable. S. Prereq: 112 or 222. Experiments in classical and modern physics performed independently by each student. For students preparing for a career in high school teaching.
Phys 321. Introduction to Modern Physics I. (3-0) Cr. 3. F. Prereq: 222, credit or enrollment in Math 266. Quantum nature of matter: photons, de Broglie's postulate: wave-like properties of matter; Bohr's model of hydrogen atom; Schrodinger equations in one dimension: energy quantization; detailed solutions for potential steps, barriers and wells; one-electron atoms, spin and magnetic interactions; ground states, optical and x-ray excitations of multi-electron atoms.
Phys 321L. Introductory Laboratory in Modern Physics. (0-2) Cr. 1. F. Prereq: Credit or enrollment in 321. Experiments related to the foundations of modern physics. The dual wave and particle character of electrons and photons, statistics, interferometry and x-ray spectroscopy.
Phys 322. Introduction to Modern Physics II. (3-0) Cr. 3. S. Prereq: 321. Quantum statistics; lasers; physics of molecules. Properties of solids, including electron band structure, superconductivity and magnetism. Nuclear physics, including nuclear sizes and masses, stability, decay modes, reactions, fission and fusion. Elementary particles, including strangeness, charm, and quarks. Fundamental forces of nature.
Phys 322L. Introductory Laboratory in Modern Physics II. (0-2) Cr. 1. S. Prereq: Credit or enrollment in 322. Experiments related to the foundations of modern physics. Radioactive decay, elementary particles, Hall effect, quantization, spectroscopy, statistics and instrumentation.
Phys 361. Classical Mechanics. (3-0) Cr. 3. F. Prereq: 222, Math 265, 266. Newtonian mechanics including forced oscillations, central forces and orbital motion, collisions, moving frames of reference, Lagrange's equations. Nonmajor graduate credit.
Phys 362. Intermediate Mechanics. (3-0) Cr. 3. S. Prereq: 361. Rigid body motion; small oscillations, normal modes. Special relativity including length contraction, time dilation, simultaneity, Lorentz transformation, 4-vector covariant formalism, relativistic mechanics. Nonmajor graduate credit.
Phys 364. Electricity and Magnetism I. (3-0) Cr. 3. F. Prereq: 222, Math 385 or Math 395. Static electric and magnetic fields, potential theory; electromagnetism, Maxwell's equations. Nonmajor graduate credit.
Phys 365. Electricity and Magnetism II. (3-0) Cr. 3. S. Prereq: 364. Relativistic electromagnetic theory; radiation and propagation of electromagnetic waves; interaction with matter. Nonmajor graduate credit.
Phys 389. Seminar. Cr. R. S. Required of all junior physics majors. Career opportunities: graduate school programs and application, job placement, alternative careers, basic skills needed for the job market competition. Satisfactory-fail only.
Phys 398. Cooperative Education. Cr. R. F.S.SS. Prereq: Permission of the department cooperative education coordinator; junior classification. Required of all cooperative education students. Students must register for this course prior to commencing each work period.
Phys 399. Seminar on Secondary School Physics. Cr. 1-2. Repeatable. F.S. Prereq: Permission of instructor. Review of materials and curricula for secondary school physics presented and discussed by members of the class. Required for approval to teach physics in secondary schools.
Phys 450. Undergraduate Research. Cr. 1-6. Repeatable. F.S.SS. Prereq: Permission of instructor. Theoretical research under supervision of physics faculty.
Phys 450L. Undergraduate Research. Cr. 1-6. Repeatable. F.S.SS. Prereq: 311, permission of instructor. Laboratory project under supervision of physics faculty.
Phys 470L. Applied Physics Laboratory. Cr. 2-5. Repeatable. F.S.SS. Prereq: 322 and permission of instructor. Studies in modern experimental techniques via experimentation and simulation in various areas of applied physics, e.g. superconductivity, optical spectroscopy, nuclear magnetic resonance, electron spin resonance, x-ray diffraction, and computation of electronic and structural properties of matter.
Phys 480. Quantum Mechanics I. (3-0) Cr. 3. F. Prereq: 322, Math 385. First semester of a full-year course. A systematic development of the formalism and applications of quantum mechanics. Solutions to the time independent Schrodinger equation for various one-dimensional potentials including the harmonic oscillator; operator methods; Heisenberg picture; angular momentum; the hydrogen atom; spin; symmetry properties. Nonmajor graduate credit.
Phys 481. Quantum Mechanics II. (3-0) Cr. 3. S. Prereq: 480. Continuation of 480. Addition of angular momentum; charged particles in electromagnetic fields; time-independent perturbation theory; variational principles; WKB approximation; interaction picture; time-dependent perturbation theory; adiabatic approximation; scattering; selected topics in radiation theory; quantum paradoxes. Nonmajor graduate credit.
Phys 490. Independent Study. Cr. 1-4. Repeatable. Prereq: 6 credits in physics, permission of instructor. No more than 9 credits of Phys 490 may be counted toward graduation.
Phys 496. Modern Optics. (Cross-listed with E E). (3-0) Cr. 3. Alt. S., offered 2008. Prereq: Credit or enrollment in Phys 322 and 365. Review of wave and electromagnetic theory; topics selected from: reflection/refraction, interference, geometrical optics, Fourier analysis, dispersion, coherence, Fraunhofer and Fresnel diffraction, holography, quantum optics, nonlinear optics. Nonmajor graduate credit.
Phys 498. Cooperative Education. Cr. R. F.S.SS. Prereq: Permission of the department cooperative education coordinator; senior classification. Required of all cooperative education students. Students must register for this course prior to commencing each work period.
Courses primarily for graduate students, open to qualified undergraduate students
Phys 501. Oral Communication of Physics Seminar. (2-0) Cr. 1. Repeatable. S. A practical introduction to communication methods in physics and astronomy classrooms and professional settings. For graduate physics majors only. Satisfactory-fail only.
Phys 502. Introductory Research Seminar. Cr. R. F. Discussion by research staff of their research areas, expected thesis research work, and opportunities in the field. For graduate physics majors only. Satisfactory-fail only.
Phys 511. Condensed Matter Physics I. (3-0) Cr. 3. S. Prereq: 304, credit or enrollment in 481. First semester of a full-year course. Free electron model; crystal symmetry; band theory of solids; transport properties; Fermi surface; phonons; semiconductors; crystal surfaces; magnetism; superconductivity.
Phys 512. Condensed Matter Physics II. (3-0) Cr. 3. F. Prereq: 511. Continuation of 511. Free electron model; crystal symmetry; band theory of solids; transport properties; Fermi surface; phonons; semiconductors; crystal surfaces; magnetism; superconductivity.
Phys 526. Particle and Nuclear Physics. (4-0) Cr. 4. S. Prereq: Credit or enrollment in 481. Basic properties and structures of nuclei, hadrons, and elementary particles; weak and strong interactions; the Standard Model; accelerators and detectors; nuclear models; nuclear decay and stability; nuclear astrophysics; the Higgs mechanism; the CKM matrix; running coupling constants; relativistic heavy-ion collisions; selected topics beyond the standard model such as SUSY and grand unification.
Phys 531. Statistical Mechanics. (3-0) Cr. 3. S. Prereq: 304 and credit or enrollment in 481, Math 465, credit or enrollment in Math 365 or 426. Thermodynamic properties of systems of many particles obeying Boltzmann, Fermi-Dirac, and Bose-Einstein statistics; microcanonical, canonical, and grand canonical ensembles and their application to physical problems; density matrices; introduction to phase transitions; renormalization group theory; kinetic theory and fluctuations.
Phys 534. Symmetry and Group Theory in Physics. (3-0) Cr. 3. S. Prereq: Credit or enrollment in 481. Theory of groups and group representations; introduction to both point and continuous groups, and their applications in physics.
Phys 535. Physics of Semiconductors. (Cross-listed with E E). (3-3) Cr. 4. Prereq: EE 311 and EE 332. Basic elements of quantum theory, Fermi statistics, motion of electrons in periodic structures, crystal structure, energy bands, equilibrium carrier concentration and doping, excess carriers and recombination, carrier transport at low and high fields, phonons, optical properties, amorphous semiconductors, heterostructures, and surface effects. Laboratory experiments on optical properties, carrier lifetimes, mobility, defect density, doping density.
Phys 536. Physics of Semiconductor Devices. (Cross-listed with E E). (3-0) Cr. 3. Prereq: EE 535. P-n junctions, band-bending theory, tunneling phenomena, Schottky barriers, heterojunctions, bipolar transistors, field-effect transistors, negative-resistance devices and optoelectronic devices.
Phys 541. General Relativity. (3-0) Cr. 3. F. Prereq: 362 or Math 465. First offered Fall 2008. Tensor analysis and differential geometry developed and used to formulate Einstein field equations. Schwarzschild and Kerr solutions. Other advanced topics may include gravitational radiation, particle production by gravitational fields, alternate gravitational theories, attempts at unified field theories, cosmology.
Phys 551. Computational Physics. (0-4) Cr. 2. S. Prereq: 365, credit or enrollment in 481. Use of modern computational techniques to analyze topics in classical and modern physics. Satisfactory-fail only.
Phys 564. Advanced Classical Mechanics. (3-0) Cr. 3. F. Prereq: 362, Math 426, 465. Variational principles, Lagrange's equations, Hamilton's canonical equations, canonical transformations, Hamilton-Jacobi theory, infinitesimal transformations, classical field theory, canonical perturbation theory, classical chaos.
Phys 571. Electricity and Magnetism I. (3-0) Cr. 3. F. Prereq: 365, Math 426. Electrostatics, magnetostatics, boundary value problems, Maxwell's equations, wave phenomena in macroscopic media, wave guides.
Phys 572. Electricity and Magnetism II. (3-0) Cr. 3. S. Prereq: 571. Special theory of relativity, least action and motion of charged particles in electromagnetic fields, radiation, collisions between charged particles, multipole fields, radiation damping.
Phys 590. Special Topics. Cr. arr. Repeatable. Prereq: Permission of instructor. Topics of current interest.
Phys 591. Quantum Physics I. (4-0) Cr. 4. F. Prereq: 481. First semester of a full-year course. Postulates of quantum mechanics; time-dependent and time-independent Schrodinger equations for one-,two-, and three-dimensional systems; theory of angular momentum; Rayleigh-Schrodinger time-independent perturbation theory.
Phys 592. Quantum Physics II. (4-0) Cr. 4. S. Prereq: 591. Continuation of 591. Variational theorem and WKB method; time-dependent perturbation theory; method of partial waves and Born approximation for scattering by central potentials; identical particles and symmetry; Dirac and Klein-Gordon equation for free particles; path integral formalism.
Phys 599. Creative Component. Cr. arr. Prereq: Permission of instructor. Individually directed study of research-level problems for students electing the nonthesis M.S. degree option.
Courses for graduate students
Phys 611. Quantum Theory of Condensed Matter. (3-0) Cr. 3. S. Prereq: 512, 681. Quasiparticles in condensed matter: phonons, magnons, photons, electrons. Quantum theory of interacting many body systems: Green's functions and diagrammatic techniques.
Phys 624. Advanced Nuclear Physics. (3-0) Cr. 3. Alt. F., offered 2007. Prereq: 526 and 592. Microscopic few-body and many-body theory; theory of effective Hamiltonians; relativistic nuclear physics; nuclear effects in hadron-nucleus, lepton-nucleus, and nucleus-nucleus reactions.
Phys 625. Physics of Strong Interactions. (3-0) Cr. 3. Alt. S., offered 2008. Prereq: 681. Quark model; Quantum Chromodynamics IQCD); perturbation methods for QCD; effective field theories for pions and nucleons; finite temperature field theories; quark-gluon plasma; phase transitions in QCD.
Phys 637. Elementary Particle Physics I. (3-0) Cr. 3. Alt. F., offered 2007. Prereq: 526 and 592. First semester of a full year course. Properties of leptons, bosons, and quarks and their interactions; quantum chromodynamics, Glashow-Weinberg-Salam model, grand unification theories, supersymmetry; modern theoretical techniques and tests of the Standard Model.
Phys 638. Elementary Particle Physics II. (3-0) Cr. 3. Alt. S., offered 2008. Prereq: 637. Continuation of 637. Properties of leptons, bosons, and quarks and their interactions; quantum chromodynamics, Glashow-Weinberg-Salam model, grand unification theories, supersymmetry, and superstring theory; modern theoretical techniques.
Phys 650. Advanced Seminar. (1-0) Cr. 1. Repeatable. F.S. Topics of current interest. Satisfactory-fail only.
Phys 660. Advanced Topics in Physics. Cr. 1-3. Repeatable. F.S. Courses on advanced topics and recent developments.
Phys 681. Quantum Field Theory I. (3-0) Cr. 3. F. Prereq: 564, 572, 592. Quantization of fields (canonical and path integral); Feynman rules; introduction to gauge theories; Quantum Electrodynamics; radiative corrections; renormalization and renormalization group.
Phys 682. Quantum Field Theory II. (3-0) Cr. 3. Alt. S., offered 2008. Prereq: 681. Continuation of 681. Systematics of renormalization; renormalization group methods; symmetries; spontaneous symmetry breaking; non-abelian gauge theories; the Standard Model and beyond; special topics.
Phys 699. Research. Cr. arr. Repeatable.