Physics 689 (Section 602): Concepts of Modern Theoretical Physics

Instructor: R. E. Allen (Room 519 Engineering/Physics, 845-4341,

allen@tamu.edu, http://faculty.physics.tamu.edu/~allen)

This course meets MWF at 11:30-12:20 in Room 213 of the Engineering/Physics Building, starting Monday, September 1, 1997.

The material will mostly be drawn from about 50 books and review articles which are cited in a recent paper by the instructor. Only the most fundamental ideas in the extremely broad areas listed below will be discussed, but the treatment of these core ideas will usually be self-contained at the elementary level that is appropriate for this course. In a few cases, the treatment will be merely descriptive.

The purpose of this course is to survey the general principles of theoretical physics at the very end of the twentieth century. A major emphasis will be the unity of areas like condensed-matter and high-energy physics.

1. A Brief Overview of Fundamental Physics

1.1 Elementary Particles and Forces

1.2 Gravitation and Cosmology

1.3 Canonical and Path Integral Quantization

1.4 Statistical Mechanics and Euclidean Path Integrals

1.5 Superfluids and Order Parameters

1.6 Topology and Topological Defects

1.7 Grand-Unified and Higher-Dimensional Theories

1.8 Experimental and Observational Constraints

2. The Standard Model of Particle Physics

2.1 Quarks and Leptons

2.2 Vector Bosons and Gauge Interactions

2.3 The Higgs Boson and Symmetry-Breaking

2.4 Quantization via Path Integrals

2.5 Experimental Confirmation of the Standard Model

2.6 Unsolved Problems of the Standard Model

3. General Relativity and Its Implications

3.1 Classical Gravity within Einstein's Theory

3.2 The Standard Model of Cosmology

3.3 Inflation and Other Extensions of Standard Cosmology

3.4 Quantum Gravity and Quantum Cosmology

3.5 Observational Tests of General Relativity and Cosmological Models

3.6 Unsolved Problems in Gravity and Cosmology

4. Concepts from Differential Geometry and Topology

4.1 Topological Defects in Condensed Matter Physics

4.2 Vector Fields and Differential Forms

4.3 Connection and Curvature Forms

4.4 Topological Invariants

4.5 Topological Defects in Field Theory

5. Unsolved Problems in Fundamental Physics

5.1 The Cosmological Constant

5.2 The Dark Matter Problem

5.3 The Hubble Constant, Age of the Universe, and Structure in the Universe

5.4 Neutrino Masses

5.5 Quantization of Gravity

6. The Search for Unification

6.1 Grand-Unified Theories

6.2 Kaluza-Klein Theories

6.3 Supersymmetry

6.4 The Statistical Superfield