The goal of this course is introduction of students to one of most popular framewors of field theory that assures finitenes of the theory comprising the Standard model. In that sense the course is supplementation to the courses Field theory 1 and 2 which enables students to enter quickly to phenomenology and theory of large number presently popular "beyond Standard model" models. The course assures the basics and deep understanding of global supersymmetric theories. The stress is on methods necessary for finding the terms of a supersymmetric theory in terms of superfields, and for finding Lagrangians of the corresponding field theory. The course is also basis of one part of the course Physics beyond Standard model.
LEARNING OUTCOMES AT THE LEVEL OF THE PROGRAMME:
Upon completing the degree, students will be able to:
1. KNOWLEDGE AND UNDERSTANDING
1.1 formulate, discuss and explain the basic laws of physics including mechanics, electromagnetism and thermodynamics
1.2 demonstrate a thorough knowledge of advanced methods of theoretical physics including classical mechanics, classical electrodynamics, statistical physics and quantum physics
1.3 demonstrate a thorough knowledge of the most important physics theories (logical and mathematical structure, experimental support, described physical phenomena)
2. APPLYING KNOWLEDGE AND UNDERSTANDING
2.1 identify the essentials of a process/situation and set up a working model of the same or recognize and use the existing models
2.2 evaluate clearly the orders of magnitude in situations which are physically different, but show analogies, thus allowing the use of known solutions in new problems;
2.3 apply standard methods of mathematical physics, in particular mathematical analysis and linear algebra and corresponding numerical methods
3. MAKING JUDGEMENTS
3.2 develop a personal sense of responsibility, given the free choice of elective/optional courses
4. COMMUNICATION SKILLS
4.3 develop the written and oral English language communication skills that are essential for pursuing a career in physics
5. LEARNING SKILLS
5.1 search for and use physical and other technical literature, as well as any other sources of information relevant to research work and technical project development (good knowledge of technical English is required)
5.3 carry out research by undertaking a PhD
LEARNING OUTCOMES SPECIFIC FOR THE COURSE:
Upon completing the degree, students will be able to:
- write down superpotential, Kahler potential and gauge kinetic term for more or less any gauge supersymmetric field theory
- write down a Lagrangian which explicitly breaks supersymmetry
- write down a Lagrangian for amost any field theory in which supersymmetry is broken by soft terms
- evaluate tree level amplitudes using the knowledge attained at the course Field theory 1, and Lagrangians for theories with explicitly broken supersymmetry
- using the knowledge attained at the cours Field theory 2 evaluate the observables containing loops, that appear e.g. in MSSM at low energies, and that would strongly indicate that supersymmetry exists, if experimentaly confirmed
In the first part of the course the students get acknowledged with notation, basic theorems leading to the supersymmetric theories and basic notions convenient for building supersymmetric theories: Weyl spinors in Van der Waerden notation, Grassmann parameters and fields, fundamental algebra of SL(2,C) and Grassmann fields, Coleman-Mandula theorem, Haag-Sohnius-Lopuszanski theorem, supersymmetric algebra, on-mass-shell representations of supersymmetric algebra for massive and massless multiplets.
In the second part students get acquainted with the notions and formalism of supersymmetric field theory: supersymmetric field transformation, building supersymmetric multiplets, Lie algebra with Grassmann parameters, superspace, supersymmetric algebra in superspace, covariant derivative, scalar superfield, superpotential and kinetic term for scalar superfields, F-potential, vector superfield, supersymmetric gauge transformation, Wess-Zumino gauge, supersymmetric field strength, Yang-Mills kinetic term and corresponding Lagrangian, D-potential, gauge invariant interactions, Kahler potential, general Lagrangian for supersymmetric gauge theories, explicit breaking of sypersymmetry by soft terms.
In third part the applications of the formalism are made: supersymmetric electrodynamics, supersymmetric chromodynamics and minimal supersymmetric standard model (MSSM).
1. week: Experimental and theoretical motivation for supersymmetry
2. week: Covering group of Lorentz transformations SL(2,C), Weyl spinors in the Van der Waerden two-component notation and pertaining SL(2,L) algebra
3. week: Coleman-Mandula theorem and possible algebras of symmetry generators for general field theory
4. week: Haag-Sohnius-Lopuszanski theorem: supersymmetric and extended supersymmetric algebras of relativistic field theory
5. week: On mass shell particle representations for supersymmetric field theory: fermion number operator, supersymmetric vacuua and representations for massive and massless multiplets for supersymmetric and extended supersymmetric algebras.
6. week: Supersymmetric multiplets for a field theory: supersymmetric algebra in terms of Grassmann parameters, example of supersymmetric transformation leading to scalar multiplet with associated Lagrangian and supercurrent.
7. week: Superfields: Lie algebra with Grassmann variables, superspace, generators of supersymmetric transformations in superspace, covariant derivative, the notion of superfield and general supersymmetric transformation, scalar and vector superfield.
8. week: Scalar superfields: definition, product of scalar superfields, superpotential, kinetic terms for scalar superfields, Lagrangian for general renormalizable supersymmetric theory containing scalar superfields only, F-potential.
9. week: Vector superfields: definition, Abelian vector superfields: supersymmetric gauge transformation, Wess-Zumino gauge, supersymmetric field strength, supersymmetric Yang-Mills kinetic term and corresponding Lagrangian, D-potential.
10. week: Non-Abelian vector superfields: supersymmetric gauge transformation, Wess-Zumino gauge, superymmetric field strength, supersymmetric Yang-Mills kinetic term and corresponding Lagrangian, D-potential.
11. week: Gauge invariant interactions for Abelian theories: supersymmetric gauge transformation of a chiral superfield, Kahler's potential, general Lagrangian for Abelian supersymmetric theories, supersymmetric quantum electrodynamics in two and four component notation.
12. week: Gauge invariant non-Abelian theories: supersymmetric gauge transformation of a chiral superfield, Kahler potential, general Lagrangian for non-Abelian supersymmetric theories.
13. week: Supersymmetric quantum chromodynamics.
14. and 15. week: Minimal supersymmetric standard model (MSSM): explicit breaking of supersymmetry by soft terms, derivation of part of the MSSM Lagrangian.
REQUIREMENTS FOR STUDENTS:
Students have to attend the lectures and excercises regularly.
GRADING AND ASSESSING THE WORK OF STUDENTS:
The exam has three parts: solving homework problems, written examination and oral examination. Part of written examination points may be acheved through homeworks. The problems given on written examination are similar in logic and content as those passed through lectures and exercises. Through written examination the calculation techniques of the students are examined. Through oral examination the knowledge of the logical structures and notions are examined.