Fundamental physics, year 1 (Teknisk fysik, årskurs 4)

Lecturer: Bengt E W Nilsson

This is an introductory course in string theory/M theory. The course home page can be found at http://fy.chalmers.se/~tfebn/StringTheoryMSc2009.html.

- Tuesday 2009-03-17
- Introduction to the course.
**Unifications**in the history of physics: Earthly and celestial mechanics; Maxwell's equations (light, electricity, magnetism); Special relativity (space and time unified, mechanics and electromagnetism unified, mass and energy unified); Nordström; Kaluza; Klein; Electroweak theory; Grand Unified Theories (GUT's).**Group theory:**SO(3), SU(2), SU(n). The classical matrix groups, and five exceptional cases. Quantum Mechanics as a framework. Many string theories, unified into M-theory. Theory of everyting — or a frame work. Forces and particles are vibrational modes. Quantum gravity. No free dimensionless parameters. Many solutions. Extra dimensions are looked for at CERN. The size of a string. - Wednesday 2009-03-18
- Special relativity and extra dimensions. Units: The SI system, Gaussian units, natural units. Lorentz transformations. Light-cone coordinates. Four-velocity and four-momentum. Extra dimensions. Compact extra dimensions. Fundamental domain. Coordinates on a circle. Fixpoints. Making a cone by indentifying points. Square well potential with an extra circle dimension.
- Thursday 2009-03-19
- Electromagnetism and gravity in various dimensions. Maxwell's
equations
in Lorentz-Heaviside
units. The electromagnetic force (the Lorentz force) in
Lorentz-Heaviside units. The victor potential
. The scalar potential**A***φ*. The role of the potentials in classical and quantum mechanics, respectively. Gauge transformations. Different potentials in different patches of a manifold. Electromagnetism in 2+1 dimensions. Manifestly relativistic electromagnetism. Spheres and balls in*d*dimensions. Electric fields in higher dimensions. Gravitation and the Planck length. Gravitational waves. Planck time, Planck mass, Planck energy. The gravitational potential. The*D*dimensional analogue to Newton's constant*G*. The Planck length in various dimensions. - Monday 2009-03-23
- Gravitational potentials. The Planck length in various
dimensions. The gravitational constant and compactification. The
compactification scale
*l*_{c}. Relating*l*_{c}to the Planck length. Large extra dimensions (Brane World scenarios). Non-relativistic strings. A fundamental string cannot oscillate longitudinally. Tension and mass density (independent in the non-relativistic case, dependent relativistically). The wave velocity. Equation of motion for a non-relativistic string. Boundary conditions: Dirichlet and Neumann. The coordinates*x*^{±}. The Lagrangian. The Action. Variational calculus, with bulk term and boundary term. Deriving Newton's second law from a variational principle and a Lagrangian. The non-relativistic string Lagrangian. Lagrangian versus Lagrangian density. - Tuesday 2009-03-24
- Non-relativistic strings. The relativistic point particle: The
Lagrangian, action, canonical momenta and
Hamiltonian. Reparametrisation invariance. Equations of motion. A
4-vector in Minkowski space that is a scalar on the world
line. Relativistic particles with charge. Relativistic strings. The
soap film. World surface and target
space. The metric
*g*_{i j}. Area element and metric determinant. - Thursday 2009-03-26
- Th relativistic point particle. Spatial soap films. Induced
metric (pull-back). The invariant measure (volume) from general
relativity. Wedge products. Area functional for space-time
surfaces. String coordinate. Any small but finite section of the
string moves with velocity
*v*<*c*. The Numbu–Goto action. Equations of motion. Free end condition becomes Neumann after gauge fixing. D-branes and boundary conditions. The static gauge. Tension and energy. Action in terms of transverse velocity. The endpoints of open strings. - Monday 2009-03-30
- (
*Images not yet uploaded. My camera broke down.*) String parametrisation and string motion. Static gauge. The free end condition.*σ*parametrisation. 7.2. ... - Tuesday 2009-03-31
- Electric charge conservation. Conserved currents. Lagrangian symmetries and Noether's theorem. Current on the string world sheet. The complete momentum current.
- Friday 2009-04-03
- The light-cone relativistic string.
- Monday 2009-04-20
- Light-cone fields and particles.
- Tuesday 2009-04-21
- The relativistic quantum point particle.
- Thursday 2009-04-23
- The relativistic quantum open string.
- Monday 2009-04-27
- The relativistic quantum open string, continuation.
- Tuesday 2009-04-28
- Closed strings.
- Monday 2009-05-04
- Superstrings.
- Tuesday 2009-05-05
- Superstrings. D-branes and gauge fields.
- Thursday 2009-05-07
- String charge and electric charge.
- Monday 2009-05-11
- T-duality of closed strings
- Tuesday 2009-05-12
- T-duality of open strings
- Monday 2009-05-18
- String theory and particle physics.
- Tuesday 2009-05-19
- The connection between type IIA string theory and M theory.

Barton
Zwiebach. *A
First Course in String Theory*, second edition. Cambridge
university press, 2009. ISBN
978-0-521-88032-9. An
older edition is available as an e-book
through Chalmers library.

Christian von Schultz <forelant@vonschultz.se>