2020/2021

2020/2021

DM270

FIS/02 (THEORETICAL PHYSICS, MATHEMATICAL MODELS AND METHODS)

DEPARTMENT OF PHYSICS

Fisica teorica

1°

2nd semester (01/03/2021 - 11/06/2021)

6

48 lesson hours

Italian

ORAL TEST

DAPPIAGGI CLAUDIO (titolare) - 6 ECTS

It is required mastery of the concepts and tools learned during the math courses of the batchelor studies in physics. The student is strongly advised to have studied the content of the course of Electrodynamics and Relativity.

Introduction to the mathematical methods of theoretical physics with a particular emphasis for those related to realtivistic and to gauge theories.

Fiber and principal bundles: structural aspects with particular emphasis on the applications to Yang-Mills field theories. Differential forms on R^n and on manifold as a starting point to discuss de Rham and singular coohmologies as tools to study topological aspects of field theories.

Teaching consists in blackboard lectures, during which the teacher describes the mathematical objects the course deals with, shows their properties, and proves the main theorems involving them.

1) J. M. Lee, Introduction to smooth manifolds, 2nd ed. (2013) Springer, 708p.

2) S. Morita, The geometry of differential forms, (2001) AMS, 321p.

3) R. Bott and L. W. Tu, Differential Forms in Algebraic Topology (1982) Springer, 331p.

The student has to give an oral exam aimed at verifying that he/she has learned the topics presented during the lectures. Special emphasis will be given to the verification of the ability of the student to present rigorously and with an appopriate technical language all concepts learned.

The student has to give an oral exam aimed at verifying that he/she has learned the topics presented during the lectures. Special emphasis will be given to the verification of the ability of the student to present rigorously and with an appopriate technical language all concepts learned.