Lecture 5 | New Revolutions in Particle Physics: Standard Model

The first paragraph introduces gauge theories, emphasizing their importance in understanding natural phenomena. Quantum electrodynamics (QED) and quantum chromodynamics are highlighted as examples. The explanation begins with the fundamental concept of a gauge theory, using Maxwell's theory of electromagnetism as a starting point. Maxwell's equations are mentioned as the foundation for understanding electromagnetic waves, including their polarization and the role of electric and magnetic fields. The vector potential is introduced as a way to represent the electromagnetic field, and the significance of the electrostatic potential is discussed.

The second paragraph delves into the properties of electromagnetic waves, including their sources in charges and currents. The polarization of these waves and the role of the electric field in determining it are explained. The conservation of electric charge is discussed in the context of gauge theory, with an emphasis on the mathematical structure of Gauss's law and its implications. The concept of gauge fields, analogous to Maxwell's fields but with different sources, is introduced. The paragraph also touches on the idea of unphysical examples, like the baryon number, to illustrate the principles of gauge theory.

The third paragraph contrasts the classical description of electromagnetic waves with their quantum mechanical counterpart. The photon is introduced as the quantum of the electromagnetic field, characterized by its polarization. The process of emission and absorption of photons is described in the context of the Coulomb field. The paragraph also discusses the symmetries associated with conservation laws and how they are integral to gauge theories. The concept of gauge charges and their corresponding symmetries are explained, with an example from quantum chromodynamics provided.

The fourth paragraph provides a deeper look into quantum chromodynamics (QCD), focusing on the gauge fields labeled by indices. The structure of these fields as matrices transforming under the SU(3) group is explained. Quarks are introduced as objects with color indices, and their symmetry operation is described using unitary special unitary matrices. The concept of antiparticles and their transformation using complex conjugate matrices are also discussed. The representation of quarks and antiquarks in the fundamental representation of SU(3) is highlighted.

The fifth paragraph explores the properties of gluons, the gauge bosons in QCD, which have characteristics of both particles and antiparticles. The gluons' color is discussed, and their self-interaction through the emission of other gluons is introduced. The concept of flux tubes and the strong force between quarks, which prevents them from escaping each other, is explained. The paragraph also summarizes the key aspects of gauge theory, including Maxwell-like fields, sources, Gauss's law, conservation, and symmetries.

The sixth paragraph discusses the coupling constant in gauge theory, drawing parallels with the electric charge of an electron. The probabilistic nature of quantum mechanics is highlighted, with the square of the electric charge determining the likelihood of photon emission. The fine-structure constant, a dimensionless number, is introduced as a measure of this probability. The paragraph also provides a brief overview of units in physics, relating energy, time, and distance through fundamental constants.

The seventh paragraph establishes the relationship between energy, time, and distance in physics. It explains that these units are interconnected and can be set to simplify equations in quantum mechanics. The concept that large energies correspond to short time intervals is discussed, with examples provided to illustrate the size of atomic diameters and the transit time of light across an atom.

The eighth paragraph examines different time scales associated with atomic and subatomic processes. It discusses the time it takes for an electron to orbit an atom, the decay time for an excited atom, and the transit time across a hadron. The fine-structure constant is shown to play a crucial role in these time scales, with larger ratios between them due to its small value.

The ninth paragraph leads into the discussion of weak interactions, noting their slow decay rates despite the coupling constant being similar to that of electromagnetism. The paragraph sets up a puzzle to be solved in subsequent explanations, hinting that the reason for the slow decay rates in weak interactions is not due to the coupling constant but rather another factor to be explored.

The tenth paragraph introduces the concept of leptons and their relationship with quarks under the SU(2) symmetry. It outlines the different types of quarks and leptons, suggesting that the weak interactions involve horizontal symmetries that mix up and down quarks, as well as leptons. The potential group involved in these symmetries is speculated to be SU(2), acting on doublets.

The eleventh paragraph focuses on gauge bosons in the context of weak interactions. It proposes hypothetical gauge bosons that could allow for transitions between particles and antiparticles, such as an electron and an antineutrino. The W bosons, as gauge bosons, are suggested to facilitate these transitions, with the W- boson being negatively charged and capable of decaying into an electron and an anti-neutrino.

The twelfth paragraph elaborates on the role of W bosons in particle transitions, particularly in the context of quark transitions. It discusses how W bosons enable transitions between different types of quarks, such as a down quark to an up quark, and also between leptons. The paragraph also touches on the concept of flipping arrows and lines in diagrams to represent particle-antiparticle conversions and the decay of W bosons.

The thirteenth paragraph delves into the fundamental process governing beta decay, using the decay of a negatively charged pion as an example. It outlines how a pion can decay into an electron and an anti-neutrino through the emission of a W- boson, which subsequently decays. The paragraph also discusses the possibility of different decay paths and the role of the electron antineutrino in these processes.

The fourteenth paragraph discusses neutron decay as an example of a purely leptonic process involving weak interactions. It explains how a neutron, composed of two down quarks and an up quark, can decay into a proton, an electron, and an electron antineutrino through the emission of a W- boson. The paragraph also addresses why the neutron cannot decay into a muon and a neutrino due to energy constraints.

The fifteenth paragraph concludes the discussion by highlighting the puzzle of why weak interactions result in slow decay rates. It suggests that the coupling constant for weak interactions is not the reason for this, as it is similar to that of electromagnetism. The paragraph hints that the answer lies in a factor other than the coupling constant, setting the stage for further exploration in subsequent discussions.