00431 - Theoretical Physics

Learning outcomes

Elementary introduction to the features which Quantum Mechanics must
possess in order to be compatible with Special Relativity;
a discussion of Dirac's equation for spin one-half particles.

Course contents

Symmetries and unitary transformations in Quantum Mechanics.
Outline od group theory; BCH formula, generators, their algebra,
linear representations and infinitesimal transformations.
The angular momentum operators as generators of the group of the
rotations O(3); the group O(3) and the group SU(2).
The group O(4) and its equivalence to SU(2) x SU(2).
Spinorial representations L and R.
The Lorentz group as group O(3,1). 4 components Dirac spinors as
finite dimensional but not unitary representation of the Lorentz
group.The Dirac gamma matrices and the matrix gamma5; traces of products
of gamma matrices.
Bilinear forms of Dirac spinors and their transformation properties.
The relativistic Lagrangian for spin 1/2 particles and Dirac's
equation; free solutions, plane waves and spinors.
Spin eigenstates; projectors on states of definite energy and spin
and their algebra.
Sums on polarization states.
Transformation properties under P, C and T.
Antiparticle states.

Minimal electromagnetic interaction, non relativistic limit and
gyromagnetic ratio of the electron.
Outline of perturbation theory; propagators, Feynman rules,
radiative corrections, regularization and renormalization.

The success of QED and the anomalous magnetic moment of the electron.

Readings/Bibliography

Given the introductory nature of the course, the subjects of the program
can be studied on the first chapters of any of the many existing excellent
textbooks on relativistic quantum field theory and elementary particles;
the students are invited to choose freeley following their preferences.
As an example, see for instance
1) S. Weinberg, The Quantum Theory of Fields, I, (Cambridge, 1995);
2) P. Ramond, Field Theory, A Modern Primer,
Frontier in Physics: A Lecture Note and Reprint Series, (Benjamin 1981).

Teaching methods

The course is theoretical only, with exercises and discussions with
the students.

Assessment methods

oral examination

Teaching tools

The course is theoretical only, with exercises and discussions with
the students.

Office hours

See the website of Ettore Remiddi