Table Of ContentQuantum Field Theory Quantum
An Arcane Setting for Explaining the World Field T
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About the Author
Roberto Iengo is a professor at the PhD Graduate School SISSA (Trieste, Italy), now
retired but still affiliated to the Theoretical Particle Physics group. He is author (also
spelt as Jengo) of many scientific publications in various aspects of Quantum Field
Theory and String Theory. He has taught for years a course in Quantum Field Theory
for PhD students. He has also been Director of the SISSA Interdisciplinary Laboratory of
Humanities and Science and of the Master in Science Communication.
About Concise Physics
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Quantum Field Theory
An arcane setting for explaining the world
Quantum Field Theory
An arcane setting for explaining the world
Roberto Iengo
Morgan & Claypool Publishers
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ISBN 978-1-6432-7053-1(ebook)
ISBN 978-1-6432-7050-0(print)
ISBN 978-1-6432-7051-7(mobi)
DOI 10.1088/978-1-6432-7053-1
Version:20180701
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ISSN2053-2571(online)
ISSN2054-7307(print)
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A formulae-free guided tour for curious persons
With all its imperfections, modern science is a technique
that is sufficiently well tuned to nature so that it works
Steven Weinberg, in:
ToExplaintheWorld.TheDiscoveryofModernScience.
(Harper Perennial 2015)
This book is written in physicists’ ‘English’.
Indeed,mostphysicistsarenotatallofEnglishmothertongue.Theyarecitizens
of the world and ‘English’ is their international language. It resembles the Greek
language used in the Mediterranean area during the Hellenistic epoch and the
Roman empire; indeed it was not even called Greek but rather κoινη‵ meaning:
commonlanguage.Itwasnotsuchasophisticatedlanguageascomparedtothatof
the great Greek of poetry or theatre; similarly, one cannot compare the physicists’
‘English’ to the great English of poetry or theatre.
Contents
Introduction x
Acknowledgements xii
Author biography xiii
1 Interaction at a distance? Rather, the propagation of a field 1-1
1.1 Static fields perhaps well known 1-2
1.2 Time dependent fields perhaps less well known 1-2
1.2.1 Signals in spacetime 1-3
1.2.2 The four-vector potential 1-3
1.2.3 Waves 1-4
1.3 Bibliography 1-5
2 The messengers of the interactions: the ‘quanta’ of the field 2-1
2.1 The revenge of the integers 2-1
2.2 Quanta as particles 2-2
2.2.1 Photons 2-2
2.2.2 Zero mass for the photon 2-3
2.3 Quanta as waves 2-4
2.4 Two other, less familiar, fundamental fields and their quanta 2-4
2.5 Weak interactions 2-4
2.6 Strong interactions 2-5
2.7 Radiation fields: a collective name 2-5
2.8 Bibliography 2-6
3 Matter fields, of an uncommon self-avoiding kind 3-1
3.1 The need for new unusual anti-commuting numbers 3-1
3.2 Matter quanta. An interlude 3-2
3.2.1 Particles and antiparticles 3-3
3.2.2 Left or right spinning 3-3
3.2.3 The Dirac equation 3-3
3.2.4 The number of matter particles cannot change 3-4
3.3 Matter fields 3-4
vii
QuantumFieldTheory
3.4 Supersymmetry 3-5
3.5 The love affair with anticommuting numbers 3-5
3.6 Bibliography 3-6
4 Whatever is happening makes an action 4-1
4.1 The action and the motion 4-1
4.2 The action of the fields 4-2
4.3 Action in quantum field theory 4-2
4.4 Time is real but it helps treating it as imaginary 4-3
4.5 Bibliography 4-4
5 The vacuum: the stage of the fields’ play 5-1
5.1 A metaphysical vacuum? 5-1
5.2 Feynman graphs 5-2
5.2.1 Lines and vertices 5-2
5.2.2 Coupling constants 5-5
5.3 The vacuum has a physical content, to be seen 5-5
5.4 Bibliography 5-5
6 The symmetric shape of the action 6-1
6.1 Are there other fields in nature? 6-1
6.2 Symmetry and invariance: the gauge invariance 6-1
6.3 Other kinds of gauge invariance 6-3
6.4 Why gauge invariance 6-3
6.5 The mass looks forbidden by gauge invariance 6-4
6.6 The rescue of the mass (thanking Professor Higgs for a nice suggestion) 6-4
6.7 Other possibilities of spontaneously broken gauge invariance 6-6
6.8 Bibliography 6-6
7 Everything fluctuates 7-1
7.1 Violating energy conservation? 7-1
7.2 Picturing by Feynman graphs 7-2
7.3 Sometimes the quantum corrections are a bit too large, actually infinite 7-3
7.4 The coupling constant runs like Achilles’ tortoise 7-5
7.5 The picture changes when observed at a distance 7-7
7.6 Bibliography 7-8
viii
