Symmetries offer beautiful explanations for many otherwise incomprehensible physical phenomena in nature. Group theory is the underlying mathematical framework for studying symmetries, with far-reaching applications in many areas of physics, including solid-state physics, atomic and molecular physics, gravitational physics, and particle physics. We will discuss many of the fascinating mathematical aspects of group theory while highlighting its physics applications. The following topics will be covered: general properties of groups (definition, subgroups and cosets, quotient group, homo- and iso-morphism), representation theory (general group actions, direct sums and tensor products, Wigner-Eckart theorem, Young tablelaux), and discrete groups (cyclicity, characters, examples), Lie groups and Lie algebra (Cartan-Weyl basis, roots and weights, Dynkin diagrams, Casimir operators, Clebsch-Gordan coefficients, classification of simple Lie algebras), space-time symmetries (translation and rotation, Lorentz and Poincare groups, conformal symmetry, supersymmetry and superalgebra), and gauge symmetries (Abelian and non-Abelian, Standard Model, Grand Unified Theories). Interested undergraduates who have taken Physics 217 or similar can register for this course with prior approval.
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Stellar Astrophysics
PHYSICS 456
Stellar Astrophysics discusses the physical processes that play a role inside stars. Relevant physical processes include emission and absorption processes, radiation transfer, convective transfer, the weak and strong interactions, nuclear processes and nuclear burning, and the thermodynamics of equilibrium and non-equilibrium processes in stellar interiors. Subsequently, these processes are used to explain the structure and evolution of stars of different mass ranges. Finally, the course discusses endpoints of stellar evolution including white dwarfs, neutron stars, black holes, supernova explosions and gamma-ray bursts This course is also available for advanced undergraduates, with the prerequisites as noted. Prerequisites: Physics 411, 421, and 463, or permission of the instructor.This course is also available for advanced undergraduates, with the prerequisites as noted. Prerequisites: Physics 411, 421, and 463, or permission of the instructor.
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Physics of the Brain
PHYSICS 450
Contents are the same as Phys 350. Also intended for graduate students. Includes a more sophisticated term project than Phys 350. Prerequisite: Prerequisite: Physics 191 - 192 or Phys 193 - 194 or Physics 197-198 or Phys 205 - 206 or permission of instructor.
Course Attributes: FA NSM; EN TU; EN SU; BU SCI; AR NSM; AS NSM; EN BME T2
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Physics of the Brain
PHYSICS 350
Concepts and techniques of physics are applied to study the functioning of neurons and neuronal circuits in the brain. Neurons and neural systems are modeled at two levels: (i) at the physical level, in terms of the electrical and chemical signals that are generated and transmitted and (ii) at the information-processing level, in terms of the computational tasks performed. Specific topics include: neuronal electrophysiology, neural codes, neural plasticity, sensory processing, neural network architectures and learning algorithms, and neural networks as dynamical and statistical systems. Course grade is based primarily on an individualized term project. Prerequisite: Phys 191-192 or Phys 193-194 or Phys 197-198 or Phys 205-206, or permission of the instructor.
Course Attributes: FA NSM; EN TU; EN SU; BU SCI; AR NSM; AS NSM; EN BME T2
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Quantum Theory of Matter
PHYSICS 319
Students will learn how to apply quantum mechanics principles to atomic and molecular physics, solid-state physics, nuclear physics, and particle physics. A portion of the course will also be devoted to introducing Dirac notation and discussing its applications to simple systems.
Course Attributes: AS NSM; AS AN
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X-ray and Gamma-ray Astrophysics
PHYSICS 560
The final semester will provide an up to date coverage of x-ray and gamma-ray astronomy and astrophysics. Generation and observational techniques of energetic radiations from accreting neutron stars and black holes, supernova and supernova remnants, active galactic nuclei, interstellar and intergalactic matter, as well as related physics and model building will be discussed. The course will thus explore the most energetic phenomena in the universe and will also provide insight into diverse topics ranging from planetary exploration to dark matter and cosmology. This course is also available for advanced undergraduates, with the prerequisites as noted in 476/576.
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Gravitation and Cosmology
PHYSICS 557
Special relativity, equivalence principle, and fundamental experiments. Mathematics of curved spacetime. General structure of Einstein's equations. Observational tests. Applications of general relativity, relativistic stellar structure, gravitational collapse and black holes.
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Intro to Elementary Particle Physics
PHYSICS 547
An introduction to the "standard model" of elementary particle physics. The non-Abelian SU() X SU(2) X U (1) gauge theory and its relation to phenomenology and experiments.
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Classical Mechanics
PHYSICS 507
The culminating achievements in this classical discipline are presented: the Lagrangian and Hamiltonian formulation of the equations of motion, action principles and the Hamilton-Jacobi equation. Applications to constrained systems, many-body systems, continuous systems and classical fields are included. Perturbation theory and general relativity are discussed briefly.
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X-ray & Gamma-ray Astrophysics
PHYSICS 460
Observers started to use X-ray and gamma-rays in the sixties and seventies to explore the cosmos with high-energy photons. The sky looks dramatically different at these energies with bright flares from mass accreting black holes and gamma-ray bursts and large diffuse emission from supernova remnants and cosmic rays interacting with galactic matter and magnetic fields dominating the emission. This course gives a comprehensive overview of the underlying physics and observable phenomenology. Topics that will be covered include the history of X-ray and gamma-ray astronomy, high- energy radiation processes, particle heating and acceleration, accretion physics, blast waves and shocks, black holes, neutron stars, supernova remnants, gamma-ray bursts, and galaxy clusters. Prerequisite L31 312.
Course Attributes: AR NSM; AS NSM
