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Introduction to Hamiltonian formulation of QFT

Informacje ogólne

Kod przedmiotu: 1100-4IHFQFT Kod Erasmus / ISCED: (brak danych) / (brak danych)
Nazwa przedmiotu: Introduction to Hamiltonian formulation of QFT
Jednostka: Wydział Fizyki
Grupy: Fizyka, II stopień; przedmioty z listy "Wybrane zagadnienia fizyki współczesnej"
Fizyka; przedmioty prowadzone w języku angielskim
Physics (Studies in English), 2nd cycle; courses from list "Topics in Contemporary Physics"
Physics (Studies in English); 2nd cycle
Przedmioty do wyboru dla doktorantów;
Punkty ECTS i inne: 5.00
Język prowadzenia: angielski
Kierunek podstawowy MISMaP:


Założenia (opisowo):

Familiarity with elements of QFT.

Tryb prowadzenia:

w sali

Skrócony opis:

The lecture introduces students to advanced methods of constructing effective Hamiltonian operators for quantum field theory in application to particle, nuclear and condensed matter physics.

Pełny opis:

The purpose of the course is to discuss the advanced rules of constructing relativistic Hamiltonians for basic theories of particles and fields, including regularization, renormalization and description of bound states, for students who think about applying such rules in physics of hadrons and leptons or dynamically complex condense-matter systems as well as further development of the general theory. Such Hamiltonians include interactions that involve extraordinarily large range of scales, such as between the size of an electron and the size of a macroscopic chunk of matter, or literally infinity when one thinks about a point particle in an infinite space. Therefore, to manage the great number of variables in a computationally feasible way, trying to describe observables at the experimentally accessible scales, one is forced to construct equivalent effective Hamiltonians. The course aims at presenting methods of the required constructions using the renormalization group procedure for effective particles.

The lecture and exercises will provide participants with hands-on experience with practical application of the general principles to simple models. The course intends to cover:

1. Features of canonical Hamiltonians in QFT;

2. Renormalization group equations for Hamiltonians;

3. Model examples of triviality, asymptotic freedom and limit cycles;

4. The concept of universality on the example of a quartic oscillator;

5. Theory of effective particles in application to massive QED,

and may evolve as a result of questions in class.

Students work in small teams and become familiar with the subject matter by discussing and solving problems. Such work may lead to publications, e.g. see PLB 777, 260-264 (2017) or https://arxiv.org/abs/2012.11947.

Description by Stanisław Głazek, November 2021.

Time estimate:

Lecture = 45 hours (15 x 3)

Homework = 30 hours

Exam preparation = 30 hours

Total of about 105 hours

Research on issues of interest to students = unlimited


Original articles cited during the lecture, including:

P. A. M. Dirac, Forms of Relativistic Dynamics, Rev. Mod. Phys. 21, 392 (1949);

M. Gell-Mann, M. L. Goldberger, The Formal Theory of Scattering, Phys. Rev. 91, 398 (1953);

P. A. M. Dirac, Quantum Electrodynamics without Dead Wood, Phys. Rev. 139, B684 (1965);

K. G. Wilson, Model of Coupling-Constant Renormalization, Phys. Rev D 2, 1438 (1970);

S. D. Glazek, K. G. Wilson, Renormalization of Hamiltonians, Phys. Rev. D 48, 5863 (1993);

F. Wegner, Flow equations for Hamiltonians, Ann. Physik 506, 77 (1994),

and textbooks such as:

E. M. Henley and W. Thirring, Elementary quantum field theory (McGraw-Hill, 1962);

J. D. Bjorken and S. D. Drell, Relativistic Quantum Fields (McGraw-Hill, 1965);

C. Itzykson and J.-B. Zuber, Quantum Field Theory (McGraw-Hill,1980);

J. Collins, Renormalization (Cambridge University Press, 1984);

M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory (Perseus, 1995);

S. Weinberg, The Quantum Theory of Fields (Cambridge University Press, 1995);

S. Coleman, Quantum Field Theory Lectures of (World Scientific,2019).

Efekty uczenia się:

1. Student writes Hamiltonian operators for particles of the standard model

2. Student describes the concepts of renormalized energy and charge

3. Student describes the connection between fundamental and effective theories

4. Student describes the concepts of triviality, asymptotic freedom, fixed points and limit cycles

6. Student derives effective Hamiltonians for bound states in simple models

7. Student applies the relativistic concept of effective particle in perturbation theory

Metody i kryteria oceniania:

Assessment methods and assessment criteria:

Participation in class, a written document of work carried out during the semester, oral exam

Zajęcia w cyklu "Semestr letni 2021/22" (zakończony)

Okres: 2022-02-21 - 2022-06-15
Wybrany podział planu:

zobacz plan zajęć
Typ zajęć: Wykład, 45 godzin więcej informacji
Koordynatorzy: Stanisław Głazek
Prowadzący grup: Stanisław Głazek
Lista studentów: (nie masz dostępu)
Zaliczenie: Egzamin
Opisy przedmiotów w USOS i USOSweb są chronione prawem autorskim.
Właścicielem praw autorskich jest Uniwersytet Warszawski.