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**BaDshaH** · 08-23-2023, 05:52 PM

[Image: 96a8e9320a6bc9bc57c182bee53d1c29.jpg]

Published 8/2023
MP4 | Video: h264, 1280x720 | Audio: AAC, 44.1 KHz
Language: English | Size: 4.69 GB | Duration: 6h 33m

Mathematics Behind the Standard Model and Particle Physics: Quarks, Leptons, Gauge Bosons, Baryons, Mesons, et al.

[b]What you'll learn[/b]
Quantum Chromodynamics
Electroweak Theory
Spontaneous Symmetry Breaking
The Higgs Mechanism
Understand the fundamentals of the Standard model
How quarks compose other particles such as baryons and mesons
Local gauge invariance and interactions
Neutral current interactions
Left and right handed fields
Special unitary group in N dimensions ( SU(N) )
basics of asymptotic freedom and confinement in QCD
Colour and flavour of quarks
W and Z bosons
Gauge covariant derivative
Weinberg angle
gluons

[b]Requirements[/b]
Lagrangian field theory
Covariant formulation of Classical electrodynamics
Basics of Quantum Field Theory
Tensors and Special Relativity
Familiarity with the Dirac equation would be beneficial (not strictly necessary, but if you comply with the other prerequisites above, chances are you have already come across the Dirac equation)

[b]Description[/b]
Master the Mathematics Behind Particle Physics!Welcome to a course that aims to demystify the math driving two essential particle physics theories: Quantum Chromodynamics (QCD) and Electroweak Theory.What You'll Learn:The Dirac Equation: Get comfortable with this vital equation, crucial for understanding particles like quarks and electrons. We will start from the classical field theory of a complex scalar field and generalize the theory to obtain the Dirac equation. SU(N) Basics: We'll kick off with a practical and theoretical exploration of SU(N) groups, a key concept in quantum physics and the foundation of the Standard model.Understanding Interactions: We'll break down particle interactions, uncovering the role of gauge covariant derivatives in deciphering quantum forces. Gauge invariance will be another essential topic related to particle interactions. For instance: we'll see how the local gauge invariance of the theory for electrically charged particles requires the existence of the photon and of the electromagnetic interaction ! This concept will also be applied to QCD and the Electroweak theory.Dive into QCD: Explore the strong force, a major player in particle physics, and its mathematical foundation for the description of quarks and gluons.Electroweak Theory: Understand how electromagnetism and the weak nuclear force come together in this simple, clear introduction. Its mathematical description will allow us to understand the behavior of leptons and quarks subjected to the electroweak force. The families of leptons and quarks will be discussed little by little during the course; the student will become more and more familiar as the course progresses.The Higgs Field: We'll examine the Higgs field, responsible for granting particles such as the Z and W bosons mass, and explore its mathematical aspects. This is a necessary step towards the equations of the standard model, since, in order to preserve a certain symmetry in the equations, the W and Z bosons are not allowed to have mass. The Higgs field, and in particular the so-called "Spontaneous Symmetry Breaking", will allow the Z and W bosons to acquire mass.Building Mathematical Intuition: Our approach prioritizes deep comprehension over complex formulas, ensuring you truly grasp the concepts.By the end of this course, you'll have a solid grasp of the mathematical framework supporting these advanced particle physics theories. Whether you're a physics enthusiast or a student seeking to strengthen your foundation, this course equips you with the tools to navigate the captivating world of Quantum Chromodynamics and Electroweak Theory.Enroll now and embark on your journey into the mathematical core of particle physics!

Overview
Section 1: Introduction
Lecture 1 Introduction
Lecture 2 Some material for the course
Section 2: Important properties of the Dirac equation, Charge conservation, and SU(N)
Lecture 3 Considerations on the Dirac equation and Dirac matrices
Lecture 4 Dirac equation derived from a lagrangian
Lecture 5 Charge conservation law from Dirac equation
Lecture 6 Important properties of unitary matrices and group theory
Section 3: Quantum Chromodynamics
Lecture 7 Special unitary group in 3 dimensions
Lecture 8 Why local gauge invariance
Lecture 9 Commutator of covariant derivatives
Lecture 10 QCD: the mathematics of quarks and gluons
Lecture 11 Lagrangian for QCD
Lecture 12 Considerations on the QCD Lagrangian: asymptotic freedom and confinement
Section 4: Electroweak theory
Lecture 13 Introduction to the Electroweak Theory
Lecture 14 Left and right handed spinors
Lecture 15 Local gauge invariance for the electroweak theory
Lecture 16 Field strengths in the electroweak theory
Lecture 17 Charged current interactions
Lecture 18 Neutral current interactions
Lecture 19 Derivation of the quark charges
Section 5: Spontaneous symmetry breaking and the Higgs mechanism
Lecture 20 Spontaneous symmetry breaking
Lecture 21 The Higgs mechanism part 1
Lecture 22 The Higgs mechanism part 2
Lecture 23 The Higgs mechanism part 3
Section 6: Appendix
Lecture 24 Conserved current in electromagnetism
physicists,master's level students in physics (or advanced undergraduates),mathematicians,physics enthusiasts,math enthusiasts,scientists,computational scientists,quantum engineers,anyone who is eager to discover the mathematical beauty of the universe

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