Course Information

Course Department:

Department of Physics

Course Code:

PHY 435

Course Title:

Theoretical Physics

Number of ECTS:

Level of Course:

1st Cycle (Bachelor's Degree)

Year of Study (if applicable):

Semester/Trimester when the Course Unit is Delivered:

Spring Semester

Name of Lecturer(s):

Haralambos Panagopoulos

Lectures/Week:

2 (2 hours per lecture)

Laboratories/week:

Tutorials/Week:

1 (1 hours per lecture)

Course Purpose and Objectives:

Introduction to modern topics of Theoretical Physics.Special emphasis on the role of symmetries in Physics, on Relativistic Quantum Mechanics, on the Standard Model of Particle Physics, on Scattering Theory, and on the Feynman Path Integral. Familiarization with quantitative methods, appropriate to the study of physical systems with quantum behavior.

Learning Outcomes:

By the end of the course students are expected to:

Explain the physical concepts which led to the development of Relativistic Quantum Mechanics and critically discuss alternative formulations.
Compare the symmetries present in physical models, and determine the consequences of their violation.
Solve the Schroedinger, Klein-Gordon and Dirac equations for a wide spectrum of physical systems.
Analyze the symmetries of the Standard Model and some of its fundamental phenomenological features.
Use time-dependent and time-independent Perturbation Theory in the quantitative study of physical models.
Compute scattering amplitudes in nonrelativistic Quantum Mechanics.
Formulate algorithms for the evaluation of physical observables in Quantum Mechanics, via functional integration.

Prerequisites:

PHY326

Co-requisites:

Not Applicable

Course Content:

Symmetries: Definition, Types of symmetries, Physical consequences. Symmetries of Classical and Quantum Mechanics. Lorentz group, unitary groups. Noether's theorem.

Relativistic Quantum Mechanics: Klein-Gordon, Dirac equation. Relativistic spin. Relativistic study of hydrogen.

Classical Fields: Action of Electromagnetism. Gauge symmetry. Non-Abelian fields. Energy-momentum tensor.

Introduction to the Standard Model: Coupling of fermions to gauge fields. Chiral Lagrangians. Coupling to the Higgs field. Spontaneous violation of gauge symmetry.

Scattering theory: Green's functions. Asymptotic states. Potential scattering. Born approximation. Optical theorem.

Special topics in Perturbation Theory: Time-dependent perturbations. Radiation emission and absorption.

Functional integrals: Heisenberg ñ Schroedinger pictures. The propagator as a sum over paths. The role of functional integrals in the quantum description of particles and fields.

Teaching Methodology:

The 4 hours of weekly lectures typically consist of: Brief review of previous lectures, introduction to new concepts, historical and philosophical links where appropriate, discussion and questions by the instructor and the students, exercises and applications of increasing difficulty, problem solving with the active participation of students. Emphasis is placed on modern extensions and applications of the course material.

Lectures are delivered mostly on the blackboard, allowing for better comprehension, while descriptive elements or graphics are projected on a screen via a PC. Certain complex problems, whole quantitative investigation necessitates a numerical approach, are addressed interactively via the computer software Mathematica.

For each of the homework sets handed out during the semester, students are given one week's time to explore questions and problems of increasing difficulty. Students are encouraged to collaborate in their homeworks; however, each student much prepare their own write-up of the answers.

Past homeworks and exams, along with suggested solution sets, are uploaded on the course's website, and discussed in preparatory lectures before the final exam.

Bibliography:

J. J. Sakurai, Modern Quantum Mechanics, Addison-Wesley (1994).
J. S. Townsend, A Modern Approach to Quantum Mechanics, Univ. Science Books (2012).
S. Weinberg, Lectures on Quantum Mechanics, Cambridge University Press (2013).
Για εξειδικευμένα θέματα θα χρησιμοποιηθούν πρόσφατα άρθρα καθώς και αποσπάσματα από τα βιβλία:
M. E. Peskin, D. V. Schroeder, An Introduction to Quantum Field Theory, CRC Press (2015).
S. Weinberg, The Quantum Theory of Fields, Vols. I & II, Cambridge University Press (2005).

Assessment:

Homework sets (10%), Midterm exam (30%), Final exam (60%).

Language of Instruction:

Greek

Greek. The course is also offered in English for Erasmus students.

Delivery Mode:

Face-To-Face

Work Placement(s):

Not Applicable

Course Details