An Introduction to the Standard Model of Particle Physics for the Non-Specialist

Gerald E Marsh

• Publisher: WSPC
• Year: 2017
• eBook ISBN:
  9789813232600
• Topic: Physical Sciences
• Subtopic: Nuclear Physics

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This book takes the reader from some elementary ideas about groups to the essence of the Standard Model of particle physics along a relatively straight and intuitive path. Groups alone are first used to arrive at a classical analog of the Dirac equation. Using elementary quantum mechanics, this analog can be turned into the actual Dirac equation, which governs the motion of the quarks and leptons of the Standard Model. After an introduction to the gauge principle, the groups introduced in the beginning of the book are used to give an introduction to the Standard Model. The idea is to give an Olympian view of this evolution, one that is often missing when absorbing the detailed subject matter of the Standard Model as presented in an historical approach to the subject.

--> Contents:

• Preface
• Groups
• A Semblance of the Dirac Equation From Groups
• Minimalist Quantum Mechanics
• Gauge Principle
• Standard Model Beginnings
• Particles of the Standard Model and QCD
• Appendix A: The Particle Enigma
• Appendix B: Spinor Representations of the Lorentz Group
• Appendix C: The Schwinger Term
• Appendix D: The Cosmic Microwave Background Radiation
• A Few Reference Books
• Index

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--> Readership: Undergraduate students and academics interested in the Standard Model. -->
Keywords:Standard Model?? Particle Physics;Standard Model?? QCDReview: Key Features:

• Presents the Standard Model not only using an historical approach, but also with some philosophical aspects, discussing some recent research on the nature of a "particle"

Appendix A: The Particle Enigma

What is a particle? We all know that the concept of a particle comes from Democritus’ idea of atoms. His conception, and what today we would call Brownian motion, was related by Lucretius to the origin of all motion in his poem On the Nature of Things (50 B.C.E.):

Whence Nature all creates, and multiplies

And fosters all, and whither she resolves

Each in the end when each is overthrown.

This ultimate stock we have devised to name

Procreant atoms, matter, seeds of things,

Or primal bodies, as primal to the world.

• • •

For thou wilt mark here many a speck, impelled

By viewless blows, to change its little course,

And beaten backwards to return again,

Hither and thither in all directions round.

Lo, all their shifting movement is of old,

From the primeval atoms; for the same

Primordial seeds of things first move of self,

And then those bodies built of unions small

And nearest, as it were, unto the powers

Of the primeval atoms, are stirred up

By impulse of those atoms' unseen blows,

And these thereafter goad the next in size;

Thus motion ascends from the primevals on,

And stage by stage emerges to our sense,

Until those objects also move which we

Can mark in sunbeams, though it not appears

What blows do urge them.

With a little license, Lucretius’ “Procreant atoms, matter, seeds of things, Or primal bodies” formed the basis of physical thought until quite late into modern times. In the ancient world, however, while it was accepted there might be different kind of atoms, the number of types was small and sometimes related to geometrical shapes. The advent of modern chemistry and spectroscopy in the 19^th century began the formation of the current understanding of the nature of atoms.

Today, it is believed that the elementary building blocks of matter are leptons and quarks, all of which are called fermions and obey the Dirac equation for a particle of spin of ½ In addition, there is electromagnetic radiation carrying a spin of 1. Lucretius’ understanding of atoms has been carried over into the modern conception of “particle” in the sense that the basic fermions are thought to be “structureless” or “point” particles. This can be seen in the attempts to construct “classical” models for the electron. Examples are the de Broglie-Bohm interpretation of quantum mechanics [1] and the work of David Hestenes. [2] But retaining the idea of a massive charged point particle requires that both mass and charge be renormalized, a process that has never rested comfortably with many physicists.

The greatest challenge to the ancient idea of a particle came from the work of de Broglie, who introduced in 1924 the idea that each particle had associated with it an internal clock of frequency m₀c²/h. From this idea he found his famous relation showing particles of matter were associated with a wave. [3] He did not believe a particle like the electron was a point particle, but rather that the energy of an electron was spread out over all space with a strong concentration in a very small region: “L’électron est pour nous le type du morceau isolé d’énergie, celui que nous croyons, peut-être à tort, le mieux connaître; or, d’après les conceptions reçues, l’énergie de l’électron est répandue dans tout l’espace avec une très forte condensation dans une région de très petites dimensions dont les propriétés nous sont d’ailleurs fort mal connues.” [4]

A1. The de Broglie Relation: Theory and Experiment

De Broglie, in his 1929 Nobel lecture used the following argument:

Identifying the energy of the massive particle with E = hv gives

De Broglie then assumed that c² / V corresponds to a phase velocity via vV = c², so that

Using V = vλ, he obtains his relation λp = h.

Note that by assuming that c² / V corresponds to a phase velocity de Broglie is introducing waves having neighboring frequencies so that he can define both phase and group velocities. The phase velocity so introduced is, in Max Born’s words, “a purely artificial conception, inasmuch as it cannot be determined experimentally.” [5]

The existence of de Broglie’s internal clock has recently been directly subject to experiment. The experimental approach used is known as “electron channeling”, a phenomenon observed in silicon crystals. [6], [7] In the experiments, a stream of electrons is aligned along a major axis of a thin single crystal corresponding to a row of atoms. Th...

Table of contents

• Cover
• Halftitle
• Title
• Copyright
• Dedication
• Preface
• Contents
• Groups
• A Semblance of the Dirac Equation From Groups
• Minimalist Quantum Mechanics
• Gauge Principle
• Standard Model Beginnings
• Particles of the Standard Model and QCD
• Appendix A: The Particle Enigma
• Appendix B: Spinor Representations of the Lorentz Group
• Appendix C: The Schwinger Term
• Appendix D: The Cosmic Microwave Background Radiation
• A Few Reference Books
• Index