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Advanced Concepts in Particle and Field Theory



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Author: Tristan Hübsch

Publisher: Cambridge University Press

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Publish Date: August 31, 2015

ISBN-10: 1107097487

Pages: 575

File Type: Epub

Language: English

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Book Preface

PHYSICS MAY BE DEFINED AS THE DISCIPLINE OF UNDERSTANDING NATURE. This definition is about as good as any other I can think of, although – or perhaps exactly because – much of the material in the following chapters is required even just to more precisely describe what it is we are to understand under discipline, understanding and Nature. That is, what is the nature of disciplining our understanding of something of which we ourselves are a part: Nature.

True to the meaning of the Greek original , physics is indeed concerned with all aspects of Nature. Molecular phenomena are the objects of study in both chemistry and physics, which disciplines are separate but tightly related through quantum physics [477]. The science with which we study phenomena of continental proportions is called geology (but areology on Mars), whereas (planetary, stellar, galactic, cosmic) events that are at least a few orders of magnitude larger are labeled as astrophysics. Living things and events are the object of study in biology, but life itself and its characteristics quite probably derive from quantum physics [477]. Extending this point of view, phenomena of thought and feeling (commonly labeled as “psychology”) may well be shown to be caused and determined by definite physical processes in the brain, so that social phenomena may be regarded as the “psychology of large ensembles of people,” just as thermodynamics is the “mechanics of large ensembles of particles.”1

Of course, a mere reduction of all phenomena to a common denominator achieves very little other than irking those who would rather keep up the appearance of separateness or those who insist on “irreducible wholeness.” Hoping that this has nudged the Reader to think along (or against) such sweepingly unifying avenues of human understanding of Nature, let us turn to the real focus of this tome: to the fundamental physics of elementary particles.

Subject This book represents an attempt of a compact but comprehensive review of some of the key questions in contemporary fundamental physics, traditionally called both elementary particle physics and high energy physics. The correlation between these concepts is not at all accidental: The voyage towards an idealized but also pragmatically useful fundamental understanding of Nature really does lead through the world of ever smaller objects, the study of which requires ever larger energies in a complementary way.

The concept of “elementary particles” is in this sense a Democritean ideal, but it is also an evolving idea: On one hand, we follow this twenty-five-century hypothesis that the World around us may be understood as a complex system, ultimately consisting of certain basic and indivisible objects – elementary particles. On the other hand, the past two centuries of the history of science warn us that concrete things (and ideas) in Nature, which we at times identify as elementary, not infrequently later turn out to be themselves composed of more elementary things (and ideas). In this sense, the list of elementary particles was very short in the first third of the twentieth century. Everything in Nature was understood to consist of either the elementary particles (matter) the electron image, the proton image, the neutron image and (hypothetically) the neutrino image – or a form of their interaction, which could also be represented in terms of exchanging elementary particles such as the photon γ. Soon enough, however, hundreds of new particles were discovered. Already their unrelentingly growing number vanquished all hope that all these particles could really be elementary. Indeed, even the proton and the neutron were soon shown to be consistently describable as composite systems; they both consist of more elementary quarks.

Contents

Preface
I Preliminaries
1 The nature of observing Nature
1.1 Fundamental physics as a natural science
1.2 Measurement units and dimensional analysis
1.3 The quantum nature of Nature and limits of information
2 Fundamental physics: elementary particles and processes
2.1 The subject matter
2.2 Elementary particles: detection and predisposition in experiments
2.3 A historical inventory of the fundamental ingredients of the World
2.4 Lessons
II The Standard Model
3 Physics in spacetime
3.1 The Lorentz transformations and tensors
3.2 Relativistic kinematics: limitations and consequences
3.3 Feynman’s diagrams and calculus
4 The quark model: combinatorics and groups
4.1 Bound states
4.2 Finite symmetries
4.3 Isospin
4.4 The eightfold way, the group and the quarks
5 Gauge symmetries and interactions
5.1 The non-relativistic example
5.2 Electrodynamics with leptons
5.3 Quantum electrodynamics with leptons
5.4 Quantum electrodynamics of hadrons
6 Non-abelian gauge symmetries and interactions
6.1 The gauge symmetry of color
6.2 Concrete calculations
6.3 Non-perturbative comments
7 The Standard Model
7.1 Boundary conditions and solutions of symmetric equations
7.2 The weak nuclear interaction and its consequences
7.3 The Standard Model
III Beyond the Standard Model
8 Unification: the fabric of understanding Nature
8.1 Indications
8.2 Grand unified models
8.3 On the formalism and characteristics of scientific systems
9 Gravity and the geometrization of physics
9.1 Einstein’s equivalence principle and gauge symmetry
9.2 Gravity vs. Yang–Mills interactions
9.3 Special solutions
10 Supersymmetry: boson–fermion unification
10.1 The linear harmonic oscillator and its extensions
10.2 Supersymmetry in descriptions of Nature
10.3 Supersymmetric field theory
10.4 Classification of off-shell supermultiplets
11 Strings: unification of all foundations of reality
11.1 Strings: recycling, recycling…
11.2 The theoretical system of (super)strings
11.3 Towards realistic string models
11.4 Duality and dual worldviews
11.5 Instead of an epilogue: unified theory of everything
IV Appendices
A Groups: structure and notation
A.1 Groups: definitions and applications
A.2 The group
A.3 The group
A.4 The group
A.5 Orthogonal and groups
A.6 Spinors and Dirac -matrices
B A lexicon
B.1 The jargon
B.2 Tensor calculus basics
B.3 A telegraphic introduction to Gödelian incompleteness
C A few more details
C.1 Nobel Prizes
C.2 Some numerical values and useful formulae
C.3 Answers to some exercises
References

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