Gauge theory: the standard model
Learning objectives
Referring to knowledge
Begin to develop an understanding of the technicalities and common characteristics of gauge theories, such as quantum electrodynamics (QED), quantum chromodynamics (QCD) and electroweak theory.
Understand and be able to easily use the characteristic techniques of field theories with gauge symmetry: Feynman diagram, dimensional regularisation, renormalisation groups.
Learn the fundamental principles of the standard model in elemental interactions: structure, symmetries, radiative corrections and renosmalisation.
Learn other key aspects of field theories in fundamental interactions.
Teaching blocks
Introduction: Gauge symmetry and spin-one particles
* Global symmetries of a theory with N Dirac fermions: covariant derivatives, massless vector fields and the Gauge principle
Quantum representations of the Lorentz group and one-particle states. Massless and massive spin-1 particles
Ward Identity in Compton scattering: One photon case (QED), and N photon case (YM)
Non-Abelian Gauge Theory
*
Connected Lie group of transformations: Structure constants and Lie Algebra. N-dimensional representations: Adjoint representation, Fundamental representation, and the case of SU(N). Complex, real and pseudo-real representations. Expressing a field in the adjoint representation of SU(N) as a linear combination of the generators in the fundamental representation.
Local SU(N) symmetry. Non abelian covariant derivative, Non-abelian Gauge fields, Feynman rules for YM coupled to fermions, and Gauge boson self-interactions. Theta term.
Extension to more general symmetry groups. U(1) subalgebras, Compact simple subalgebras, and the Cartan catalog. The covariant derivative in the Standard Model.
Spontaneous Symmetry Breaking (SSB) and Anomalies
*
SSB and the Linear Sigma Model: Goldstone’s theorem. Broken and unbroken generators. Flavor symmetry and Pions as Goldstone bosons.
SSB in gauge theories: the Higgs Mechanism: The U(1) case, photon mass terms, transversity of the vaccuum polarization and the unitarity gauge.The Non-Abelian case: broken generators and gauge-boson mass matrix.
Quantization of gauge theories with SSB: The U(1) case, Faddeev Popov, R_xi gauges and Ghosts. Fermion-antifermion scattering: Gauge-independence, the role of Goldstones, and the Unitarity gauge. Extension to the non-abelian case.
Anomalous Symmetries
Quantisation of gauge theories
*
Path integral quantization: Generating functional, correlation functions, Green’s functions and propagators.
Quantization of U(1) gauge theory and the Faddeev-Popov method.
Faddeev-Popov for Non-Abelian YM: Functional determinants, fermionic path integrals, functional determinants for fermions, and the Faddeev-Popov determinant in the non-abelian case, Gauge fixing and Ghosts. Feynman rules for YM theory.
Ward identity and unitarity in Non-Abelian YM theory: Optical theorem. The case of fermion-antifermion annihilation in YM theory: how Ghosts restore unitarity by cancelling unphysical gauge-boson polaizations.
Radiative corrections in gauge theories
* Divergent structure of gauge theories
Renormalisation and counter-terms in QCD
The meaning of the renormalisation procedure
Calculation of the beta function in QCD
The renormalisation group and fixed points
The R parameter and renormalisation ambiguities
Decoupling of heavy quarks
The limits of perturbation theory
* Confinement
Infrared divergences: inclusive and exclusive processes
The operator product expansion
Power corrections to R
Gauge structure of the electroweak theory
* Summary of known results: the origin of the SU(2)xU(1) weak group
Unitarity bounds and renormalization issues of Weak theories
Gauges and gauge fixing; Physical states
Mass generation and spontaneous symmetry breaking
Yukawa Interactions: Fermion masses and the CKM matrix.
Neutrino Mass and the see-saw mechanism and the PMNS matrix.
Anomaly Cancellation in Gauge Theories
The electroweak theory beyond tree level
* Custodial Symmetry and Higgs Effective Theory. Electroweak Precision observables: Delta rho.
FCNC transitions, the GIM mechanism, CP symmetry and CP violation in kaons and other neutral systems
Weak effective theories: Wilson Coefficient, Matching, Anomalous dimensions and Renormalization group equations
Teaching methods and general organization
Lecturers explain the different teaching blocks during face-to-face sessions.
Students solve weekly set exercises.
Official assessment of learning outcomes
Independent study: questions, activities, attitude in class, formality and quality of submitted exercises: 10%
Set exercises: 50%
Final examination: 40%
Repeat assessment criteria: repeat assessment follows the same criteria as regular assessment and consists of a final exam.
Examination-based assessment
Written final exam: 100%
Repeat assessment criteria: repeat assessment follows the same criteria as regular assessment and consists of a final exam.
Reading and study resources
Check availability in Cercabib
Book
Cheng, Ta-Pei ; Li, Ling-Fong. Gauge theory of elementary particle physics. Oxford : Clarendon Press ; New York : Oxford University Press, 2000 Enllaç
Ed. 1984 Enllaç
Georgi, Howard. Weak interactions and modern particle theory. Mineola, N.Y. : Dover Publications, 2009 Enllaç
Kaku, Michio. Quantum field theory : a modern introduction. New York [etc.] : Oxford University Press, 1993 Enllaç
Peskin, Michael E. ; Schroeder, Daniel V. An introduction to quantum field theory. Reading (Mass.) [etc.] : Addison-Wesley, cop. 1995 Enllaç
Ramond, Pierre. Field theory : a modern primer. Redwood City, Calif. [etc.] : Addison-Wesley Pub Co, cop. 1989 Enllaç
Taylor, John Clayton. Gauge theories of weak interactions. Cambridge : Cambridge University Press, 1976
More information at: http://grad.ub.edu/grad3/plae/AccesInformePDInfes?curs=2023&assig=568436&ens=M0D0B&recurs=pladocent&n2=1&idioma=ENG
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Gauge theory: the standard model
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