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Graduate Texts in Physics Edouard B. Manoukian Quantum Field Theory I Foundations and Abelian and Non-Abelian Gauge Theories
Graduate Texts in Physics Series editors Kurt H. Becker, Polytechnic School of Engineering, Brooklyn, USA Sadri Hassani, Illinois State University, Normal, USA Bill Munro, NTT Basic Research Laboratories, Atsugi, JapanRichard Needs, University of Cambridge, Cambridge, UKJean-Marc Di Meglio, Université Paris Diderot, Pa...
Graduate Texts in Physics Graduate Texts in Physics publishes core learning/teaching material for graduate- and advanced-level undergraduate courses on topics of current and emerging ﬁeldswithin physics, both pure and applied. These textbooks serve students at theMS- or PhD-level and their instructors as comprehensive ...
Edouard B. Manoukian Quantum Field Theory I Foundations and Abelian and Non-Abelian Gauge Theories 123
Edouard B. Manoukian The Institute for Fundamental StudyNaresuan UniversityPhitsanulok, Thailand ISSN 1868-4513 ISSN 1868-4521 (electronic) Graduate Texts in Physics ISBN 978-3-319-30938-5 ISBN 978-3-319-30939-2 (eBook)DOI 10.1007/978-3-319-30939-2 Library of Congress Control Number: 2016935720 © Springer International...
does not imply, even in the absence of a speciﬁc statement, that such names are exempt from the relevant protective laws and regulations an d therefore free for general use. The publisher, the authors and the editors are safe t o assume that the advice and information in this book are believed to be true and accurate a...
Preface to Volume I This textbook is based on lectures given in quantum ﬁeld theory (QFT) over the years to graduate students in theoretical and experimental physics. The writing of the book spread over three continents: North America (Canada), Europe (Ireland),and Asia (Thailand). QFT was born about 90 years ago, when...
do just that . Feynman’s statement is obviously more relevant today than it was then, since the recent common goal is t o provide a uniﬁed description of allthe fundamental interactions in nature. The book requires as background a good knowledge of quantum mechanics, including rudiments of the Dirac equation, as well a...
S. Weinberg, The Quantum Theory of Fields I (1995) & II (1996), Cambridge: Cambridge University Press; M. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory, NewYork: Westview Press (1995); B. D eWitt, The Globa l Approach to Quantum Field Theory, Oxford: Oxford University Press (2014). v
vi Preface to Volume I just touched upon, in standard references. Some notable differences are seen, partly, from unique features in the following material included in ours: The very elegant functional differential approach of Schwinger, referred to as the quantum dynamical (action) principle, and its underlying theo...
Particular emphasis is put on the concept of a quantum ﬁeld and its particle content, both physically and technically, as providing an appropriate descriptionof physical processes at sufﬁciently high energies, for which relativity becomesthe indispensable language to do physics and explains the exchange that takespla...
via ﬁeld variations of transformation functions and generators of ﬁeld variations.The introduction of such generators lead, self consistently, to the ﬁeld equations.Such questions are addressed as: “Why is the variation of the action, within the boundaries of transformation functions, set equal to zero which eventually...
studying abelian and non-abelian gauge theories anomalies. Moreover, an explicitexperimental test of the presence of an anomaly is shown by an example. Derivation of the Spin & Statistics connection and CPT symmetry, emphasizing for the latter that the invariance of the action under CPT transformation is notsufﬁcient...
Preface to V olume I vii The ﬁne-structure effective coupling ˛'1=128 at high energy corresponding to the mass of the neutral Z0vector boson based on all the charged leptons and all those contributing quarks of the three generations. Emphasis is put on renormalization theory, including its underlying general subtra...
Equal importance is put on both abelian and non-abelian gauge theories, witnessing the wealth of information also stored in the abelian case.4 A most important, fairly detailed, and semi-technical introductory chapter is given which traces the development of QFT since its birth in 1926 without tears, in abelian and...
the reasonable agreement between gauge theories and experiments, the underlyingtheories are in pretty good shape. This volume is organized as follows. The ﬁrstintroductory chapter traces the subject of QFT since its birth, elaborating on many of its important developments which are conveniently described in a fairlysim...
book much earlier tha n the 2015 Nobel Prize in Physics was announced on neutri no oscilla tions. 4With the development of non-abelian gauge theories, unfortunately, it seems that some students are not even exposed to such derivations as of the “Lamb shift” and of the “anomalous magnetic moment of the electron” in QED.
viii Preface to V olume I in classical physics does not necessarily hold in the quantum world. Chapter 4,a critical one, deals with the concept of a quantum ﬁeld, the Poincaré algebra, and particle states. Particular attention is given to the stationary action principle aswell as in developing the solutions of QFT via ...
5Such important topics are included as “asymptotic freedom,” “deep inelastic” scattering, QCD jets, parton splittings, neutrino oscillations, the “seesawmechanism” and neutrino masses, Schwinge r-line integrals, Wilson loops, lattices, and quark conﬁnement. Uniﬁcation of c oupling parameters of the electroweak theory a...
of this volume, cover some additional important topics and/or technical details.In particular, I have included an appendix covering some aspects of the generaltheory of renormalization and its underlying subtractions scheme itself which isoften neglected in books on QFT. Fortunately, my earlier book, with proofs not ju...
I hope this book will be useful for a wide range of readers. In particular, I hope that physics graduate students, not only in quantum ﬁeld theory and high-energy physics, but also in other areas of specializations will also beneﬁt from itas, according to my experience, they seem to have been left out of this fundament...
Preface to Volume I ix In V olume II, the reader is introduced to quantum gravity, supersymmetry, and string theory,6which although may, to some extent, be independently read by a reader with a good background in ﬁeld theory, the present volume sets up the language, the notation, provid es additional background for i n...
Acknowledgements In the beginning of it all, I was introduced to the theoretical aspects of quantum ﬁeld theory by Theodore Morris and Harry C. S. Lam, both from McGill and toits mathematical intricacies by Eduard Prugove ˇcki from the University of Toronto. I am eternally grateful to them. Over the years, I was fortun...
as2/EM’s and other numerical factors, and, on top of this, is relatively easy to apply. Needless to say this has much inﬂuen ced my own approach to the subject. He had one of the greatest minds in theoretical physics of our time. I want to take this opportunity as well to thank Steven Weinberg, the late Abdus Salam, Ra...
and John Lewis from the Dublin Institute for Advanced Studies, and Jiri Pateraand Pavel Winternitz from the University of Montreal. For the ﬁnal developmentsof the project, I would like to thank Sujin Jinahyon, the President of Nare-suan University, Burin Gumjudpai, Seck son Sukhasena, Suchittra Sa-Nguansin, and Jiraph...
xii Acknowledgements Nattapong Yongram, Siri Sirininlakul, Tukkamon Vijaktanawudhi (aka Kanchana Limboonsong), Prasopchai Viriyasrisuwattana, and Seckson Sukhasena, whothrough their many questions, several discussions, and collaborations have beenvery helpful in my way of analyzing this subject. Although I have typed t...
team of Maria Bellantone and Mieke van der Fluit of Springer. I would like toexpress my deepest gratitude to them for their excellent guidance, caring, patience,and hard work in making this project possible and move forward toward itscompletion. I have exchanged more emails with Mieke than with anybody else onthe globe...
Contents 1 Introduction Donkey Electron, Bare Electron, Electroweak Frog, God Particle, “Colored” Quarks and Gluons, AsymptoticFreedom, Beyond Resonances into the Deep Inelastic Region, Partons, QCD Jets, Conﬁned Quarks, Bekenstein– Hawking Entropy of a Black Hole, Sparticles, Strings,Branes, Various Dimensions and eve...
Majorana Spinors ...................................................... 54 2.4 Differentiation and Integration with Respect to Grassmann Variables ............................................... 56 2.5 Fourier Transforms Involving Grassmann Variables ................. 60 2.6 Functional Differentiation a nd Integration;...
xiv Contents 3.2 The Dirac Quantum Field Concept, Particle Content, and C, P, T Tansformations ............................................ 78 3.2.1 Charge Conjugation (C), Parity Transformation (T), and Time Reversal (T) of the Dirac Quantum Field ............................. 83 3.3 Re-Discovering the Positron and Ev...
3.8 Pair Creation by a Constant Electric Field ........................... 109 3.9 Fermions and Anomalies in Field Theory: Abelian Case ............ 111 3.9.1 Derivation of the Anomaly .................................. 112 3.9.2 Experimental Veriﬁcation of the Anomaly: /EM0!/CR/CRDecay ...................................
Renormalization ....................................................... 135 4.2 PoincarKe Algebra and Particle States ................................. 139 4.3 Principle of Stationary Action of Quantum Field Theory: The Rationale Of ............................................. 146 4.3.1 A Priori Imposed Variations of ...
4.5.2 The Hamiltonian ............................................. 166 4.5.3 Constraints ................................................... 167
Contents xv 4.6 Quantum Dynamical Principle (QDP) of Field Theory .............. 168 4.6.1 Summary ..................................................... 175 4.7 A Panorama of Fields .................................................. 176 4.7.1 Summary of Salient Features of Some Basic Fields ........ 177 4.7.2 Spin 0 .....
Appendix A: Basic Equalities Involving the CPT Operator ................. 217 Problems ....................................................................... 219 References ..................................................................... 221 Recommended Reading .......................................................
Up the Solution ........................................................ 241 5.7.1 The Differential Formalism (QDP) and Solution of QED in Covariant Gauges ...................... 241 5.7.2 From the Differential Formalism to the Path Integral Expression for h0Cj0/NULi........................... 246 5.8 Low Order Contrib...
5.11 Vertex Part ............................................................. 283 5.11.1 Charge renormalization and External lines ................. 287 5.11.2 Anomalous Magnetic Moment of the Electron ............. 290
xvi Contents 5.12 Radiative Correction to Coulomb Scattering and Soft Photon Contribution ................................................... 290 5.13 Lamb Shift ............................................................. 293 5.14 Coulomb Gauge Formulation ......................................... 304 5.14.1h0Cj0/NUL...
Potential in Full QED, Unordered Products of Currents ... 323 5.16.4 Integral Equation for the Vacuum Polarization Tensor ..... 333 5.17 The Full Renormalized Theory ....................................... 335 5.18 Finiteness of the Renormalized Theory; Renormalized Vertex Function and Renormalized Propagators ...........
and Spontaneous Symmetry Breaking ................................ 355 5.20.1 Change of Real Field Variables of Integration in a Path Integral ............................................. 356 5.20.2 Goldstone Bosons and Spontaneous Symmetry Breaking ...................................................... 357 Problems ....
Contents xvii 6.3 Functional Fourier Transform and Transition to Covariant Gauges; BRS Transformations and Renormalization of Gauge Theories ............................. 388 6.3.1 Functional Fourier Transform and The Coulomb Gauge .............................................. 388 6.3.2 Trasformation Law from the Coul...
6.7 Renormalization Constants, Effective Coupling, Asymptotic Freedom, and What is Responsible for the Latter? ..... 419 6.7.1 What Part of the Dynamics is Responsible for Asymptotic Freedom? ....................................... 423 6.8 Renormalization Group and QCD Corrections to eCe/NUL Annihilation .................
and How the latter Emerges ........................................... 457 6.13 Lattices and Quark Conﬁnement ...................................... 463 6.14 The Electroweak Theory I ............................................. 469 6.14.1 Development of the Theory: From the Fermi Theory to the Electroweak Theory ........
xviii Contents Problems ....................................................................... 504 References ..................................................................... 506 Recommended Reading ....................................................... 511 General Appendices .......................................
Solutions to the Problems ....................................................... 551 Index ............................................................................... 583
Notation and Data ıLatin indices i;j;k;::: are generally taken to run over 1,2,3, while the Greek indices/SYN;/ETB;::: over0;1;2;3 in 4D. Variations do occur when there are many different types of indices to be used, and the meanings should be evident from the presentations. ıThe Minkowski metric /DC1/SYN/ETBis deﬁned ...
ıThe symbol "is used in dimensional regularization (see Appendix III)./SIis used in deﬁning the boundary condition in the denominator of a propagator.Q 2Cm2/NULi/SI/and should not be confused with "used in dimensional regularization. We may also use either one when dealing with an inﬁnitesimalquantity, in general, with...
xx Notation and Data 1JD6:242/STX109GeV cD2:99792458/STX1010cm/s (exact) „D 1:055/STX10/NUL34Js „cD197:33 MeV fm 1fmD 10/NUL13cm (Masses) MpD938:3 MeV=c2,MnD939:6 MeV=c2, MWD80:4 GeV=c2,MZD91:2 GeV=c2, meD0:511 MeV=c2,m/SYND105:66 MeV=c2,m/FSD1777 MeV=c2. Mass of/ETBe<2eV=c2,M a s s o f/ETB/SYN<0:19 MeV=c2,M a s s o f/...
1. Beringer, J., et al. (2012). Particle data group. Physical Review D, 86 , 010001. 2. Olive, K. A., et al. (2014). Particle data group. Chinese Physics C, 38, 090001.
Chapter 1 Introduction Donkey Electron, Bare Electron, Electroweak Frog, God Particle, “Colored” Quarks and Gluons, Asymptotic Freedom, Beyond Resonances into the Deep InelasticRegion, Partons, QCD Jets, Conﬁned Quarks, Bekenstein – Hawking Entropyof a Black Hole, Sparticles, Strings, Branes, Various Dimensions and eve...
way, and has been struggling to provide us with a coherent description of naturein spite of the “patchwork” of seemingly different approaches that have appearedduring the last 40 years or so, but still all, with the common goal of uniﬁcation. As mentioned in our Preface, Feynm an, in his 1958 Cornell, 1959–1960 Cal Tec...
nature. With this in mind, let us trace the development of this very rich subject fromthe past to the present, and see what the theory has been telling us all these years. When the energy and momentum of a quantum particle are large enough, one is
confronted with the requirement of developing a formalism, as imposed by nature,which extends quantum theory to the relativistic regime. A relativistic theory, asa result of the exchange that takes place between energy and matter, allows thecreation of an unlimited number of particles and the number of particles in a g...
2 1 Introduction Field Theory” or just “Quantum Field Theory” . Quantum Electrodynamics is an example of a quantum ﬁeld theory and is the most precise theory devised by man when confronted with experiments. The essence of special relativity is that allinertial frames are completely equivalent in explaining a physical t...
described concisely above, by marrying quantum theory and relativity, was spelledout and applied consistently to physical processes in the quantum world in therelativistic regime. An appropriate place to start in history is when Dirac [47 –49] developed his relativistic equation of spin 1/ 2, from which one learns quit...
lower and lower negative energy states emitting radiation of arbitrary large energiesleading eventually to the collapse of the atom with the release of an inﬁnite amountof energy. Historically, a relativistic equation for spin 0, was developed earlier byKlein and Gordon in 1926, 1referred to as the Klein-Gordon equatio...
energy electron in the Dirac sea, may absorb radiation of sufﬁcient energy so asto overcome an energy gap arising from the level /NULmc 2toCmc2,w h e r e mis the mass of an electron, thus making such a negative energy electron jump to apositive energy state, leaving behind a su rplus of positive energy and a surplus of...
1 Introduction 3 positive chargeCjejrelative to the Dirac sea. This has led Dirac eventually,3in 1931 [ 52], to interpret the “hole” left behind by the transition of the negative energy electron to a positive energy state, as a particle that has the same mass as the electron but of opposite charge. It is interesting to...
an electron may make a transition to such a state releasing radiation giving rise to thephenomenon of pair annihilation. A Pair created, as described above, in the vicinity of a positively charged nucleus, would lead to a partial screening of the charge ofthe nucleus as the electron within the pair would be attracted b...
2of the electron, the ﬁne-structure of the atom, and eventually anti-matter was discovered such as antiprotons. 8It was thus tremendously successful. Apparently,9 Dirac himself remarked in one of his talks that his equation was more intelligent than its author .10 Thus the synthesis of relativity and quantum physics, l...
7The presence of the nucleus is to conserve energy and momentum. 8Chamberlain et al. [30 ]. 9Weisskopf [ 242]. 10For a systematic treatment of the intricacies of Dirac’s theory and of the quantum description of relativistic particles, in general, see Manoukian [ 151], Chapter 16.
4 1 Introduction multi-particle aspect became necessary. The so-called “hole” theory although it gave insight into the nature of fundamental processes involving quantum particles in the relativistic regime, and concepts such as vacuum polarization, turned out to be alsonot complete. For example, in the “hole” theory, t...
in a nucleus for the latter process. Finally, Dirac’s argument of a sea of negativelycharged bosons did not work with the Klein-Gordon equation because of the verynature of the Bose statistics of the particles. A new description to meet all of theabove challenges including the creation and annihilation of particles, me...
description of how photons emerge in the quantization of the electromagnetic ﬁeld.This paper is considered to mark the birthdate of “Quantum Electrodynamics”, aname coined by Dirac himself, and provided a prototype for the introduction ofﬁeld operators for other particles with spin, such as for spin 1/2, where in the l...
the (Dirac) ﬁeld operator and its adjoint were expanded in terms of appropriatecreation and annihilation operators for the electron and positron, thus providinga uniﬁed description for the particle and its antiparticle. The method had a directgeneralization to bosons. The old “hole” theory became unnecessary and obsole...
1 Introduction 5 similar methods by Pauli and Weisskopf in 1934 [170 ]. The ﬁelds thus introduced from these endeavors have become operators for creation and annihilation of particles and antiparticles, rather than probability amplitudes.12 The explanation that interactions are generated by the exchange of quanta was c...
scalar particle is exchanged in describing the strong interaction (as understood inthose days), with the particle necessarily being massive to account for the shortrange nature of the strong force unlike the electromagnetic one which is involvedwith the massless photon describing an interaction of inﬁnite range. The ma...
in these computations, came from integrations that one had to carry out overenergies of photons exchanged in describing the interaction of the combinedsystem of electrons and the electromagnetic ﬁeld to arbitrary high-energies. By formally restricting the energies of photons exchanged, as just described, to beless than...
states and the vacuum naturally lead to amplitudes of particles creation by the ﬁelds and to the concept of wavefunction renormalization (see Sect. 4.1) independently of any perturbation theories. 13The corresponding expression occurs with higher powers of the logarithm for higher orders in the ﬁne-structure constant e...
6 1 Introduction e+ e−e−e−e−γ γ γ) b ( ) a ( Fig. 1.1 Processes leading to an electron self-energy correction, and vacuum polarization, respec- tively be of no surprise as one is assuming that our theories are valid up to inﬁnite energies!15 The2S1=2,2P1=2states of the Hydrogen atom are degenerate in Dirac’s theory. In...
He obtained a shift of the order of 1000 megacycles which was in pretty good agreement with the Lamb-Retherford experiment. Very accurate computations were then ma de, within the full relativistic quantum electrodynamics, and positron theory. Notably, Schwinger17in 1948 [ 192], com- puted the magnetic moment of the ele...
electron as shown below in Fig. 1.1a. Similarly, the electromagnetic ﬁeld ( /CR)m a y lead to the creation of an electron-positron pair eCe/NUL, which in turn annihilate each other re-producing an electromagnetic ﬁeld, a process referred to as vacuum- polarization, shown in part (b). Because of these processes, the par...
1 Introduction 7 e−e− p p E=p2+m2, E=p2+m2, Fig. 1.2 As a result of the self-energy correction in Fig. 1.1a, where an electron emits and re- absorbs a photon, the mass parameter m0, one initially starts with, doe s not represent the physical mass of the electron determined in the lab. Here this is emphasized by the ene...
process shown in Fig. 1.2, where the dashed lines represent other particles (such as /CR;e/NUL;eC), where the total charge as well as the total energy and momentum are conserved in the scattering process. Similarly, the potential energy betw een two widely separated electrons, by a distance r, turned up to be not e20=4...
measurements made on the electron from sufﬁciently large distances. One thus, in turn, may generate parameters, corresponding to a wide spectrum of scales running from the very small to the very large. Here one already notices that inquantum ﬁeld theory, one encounters so-called effective parameters which are func-tion...
8 1 Introduction A process was, in turn, then carried out , referred to as “renormalization”, to eliminate the initial parameters in the theory in favor of physically observed ones. This procedure related the theory at very small distances to the theory at sufﬁciently large distances at which particles emerge on their ...
In classic papers, Dyson [59 ,60] has shown not only the equivalence of the Schwinger, Feynman, and Tomonaga approaches,21and the ﬁniteness of the so- called renormalized quantum electrodynamics, but also developed a formalism forcomputations that may be readily applied to other interacting quantum ﬁeld theories.Theori...
cannot have too many derivatives of the ﬁelds, describing interactions, as everyderivative necessitates involving a coupling of dimensionality reduced by one inunits of mass.) The photon as the agent for t ransmitting the interaction between charged parti- cles, is described by a vector – the vector potential. In quant...
second diagram in the latter part, two photons emerge locally from the same point. 19This is well described in their Nobel lectures: Schwinger [ 201], Feynman [ 75], Tomonaga [ 225], as well as in the collection of papers in Schwinger [ 198,201]. 20Stueckelberg and Peterman [ 209], Gell-Mann and Low [ 93], Bogoliubov a...
1 Introduction 9 e e eγ(a) ϕ e ϕγ(b) ϕ e2 ϕγ γ Fig. 1.3 Local couplings for photon emission by an electron, and by a spin 0 charged particle described by the ﬁeld ', respectively Quantum Electrodynamics, was not only the theory of interest. There was also the weak interaction. The preliminary theory of weak interaction...
with this type of interaction may be somehow improved by introducing, in theprocess, a vector Boson 23W/NULwhich mediates an interaction24between the two pairs (so-called currents), .n;p/and.e/NUL;Q/ETBe/, with both necessarily described by entities carrying (Lorentz) vector indices, t o ensure the invariance of the un...
22It is interesting to point out as one goes to higher and higher orders in the Fermi coupling constant G F, the divergences increase (Sect. 6.14) without any bound and the theory becomes uncontrollable. 23A quantum relativistic treatment of a problem, implies that a theory involving the W/NULparticle, must also includ...
10 1 Introduction (a) (b) (x) (x) (x)GF g gn np p e− e− ˜νe ˜νeW− Fig. 1.4 (a) The old Fermi theory with a coupling G Fis replaced by one in ( b)w h e r et h e interaction is mediated by a vector boson with a dimensionless coupling g necessarily a vanishingly small range of the interaction.25Upon comparison of both dia...
.2/EM/4eik/ETB.x/ETB/NULx0/ETB/4/SYN/ETBC.k/; .d k/Ddk0dk1dk1dk3; (1.2) 4/SYN/ETBC.k/D1 .k2CM2 W/NULi0//DC2 /DC1/SYN/ETBCk/SYNk/ETB M2W/DC3 ; (1.3) 25Here/DC1/SYN/ETBis the Minkowski metric. 26This expression will be derived in Sect. 4.7. For a so-called virtual particle k2Dk2/NUL.k0/2¤ /NULM2 W.T h e/NULi0in the denom...
1 Introduction 11 where k0is its energy, and kD.k1;k2;k3/its momentum. Formally for M2 W! 1,4/SYN/ETB C.k/!/DC1/SYN/ETB=M2 W, leading from (1.2 )t o 4/SYN/ETB C.x/NULx0/!/DC1/SYN/ETB M2 WZ.dk/ .2/EM/4eik/ETB.x/ETB/NULx0/ETB/D/DC1/SYN/ETB M2Wı4.x/NULx0/; (1.4) signalling, in a limiting sense, a short range interaction f...
perturbation theory the number of integra tion variables, over energy and momenta arising in the theory, increase, and the divergences in turn increase without bound and the theory becomes uncontrollable.27On the other hand, an inherited property of quantum electrodynamics is gauge symmetry due to the masslessness of t...
28This has led Gershtein and Zel’dovich [ 95], Feynman and Gell-Mann [77], Sudarshan and Marshak [ 210], and Sakurai [ 178], to express the currents 27The damping provided by the propagators of a massless vector particle, a spin 1/2 particle, and a spin 0 particle, for example, in the ultraviolet region vanish like 1/e...
12 1 Introduction constructed out of the pairs of ﬁelds: .n;p/,.e/NUL;Q/ETBe/;::: in the Fermi theory to reﬂect, in particular, this property dicta ted by nature. The various currents were eventually expressed and conveniently parametrized in such a way that the theory was described by the universal coupling parameter ...
transformations, encountered in quantum electrodynamics, to a non-abelian29gauge theory, described by the group SU .2/,30and turned out to be a key ingredient in the development of the modern theory of weak interactions. This necessarily requiredthe introduction, in addition to the charged bosons W ˙, a neutral one. Wh...
boson description, respectively. In a uniﬁed description of electromagnetism and theweak interaction, one expects these couplings to be comparable, i.e., g 2/EMe2D4/EM˛; where˛/EM1 137;GF/EM1:166/STX10/NUL5=.GeV/2:(1.7) in units„D1;cD1.F r o m ( 1.1), we may then estimate the mass of the Wbosons to be MW/EMs 4/EM˛ GF/E...
1 Introduction 13 re-inserting the constant c for convenience, in good agreement with the observed mass. We may also estimate the range of the weak interaction to be RW/EM„c MWc2/EM2:2/STX10/NUL16cm: (1.9) Glashow, a former graduate student of Schwinger, eventually realized [ 96]31the important fact that the larger gro...
which the group SU .2//STXU.1/is spontaneously broken to the group U .1/with the latter associated with the photon, and, in the process, the other bosons, calledW ˙;Z0, acquiring masses, thanks to the Higgs boson, and renormalizability may be achieved. The latter particle has been also called the “God Particle”.36The m...
33Some key papers showing how spontaneous symmetry breaking using spin 0 ﬁeld may generate masses for vector bosons are: Englert and Brout [ 63], Englert et al. [ 64], Guralnik et al. [ 110], and Kibble [ 127]. 34Apparently the Legendary Victor Weisskopf was not impressed by this way of generating masses. In his CERN p...
theory of weak interactions but did not include electromagnetic interactions. 38Hasert et al. [ 112, 113] and Benvenuti et al. [ 15]. 39See, e.g., C. Rubbia’s Nobel Lecture [ 176].
14 1 Introduction Fig. 1.5 A process involving the exchange of the neutral vector boson Z0 e−e−Z0˜νμ ˜νμ the resulting theory with massive vector bosons. Proofs of renormalizability were given by ’t Hooft [ 216,217].40It seems that Sydney Coleman used to say that ’t Hooft’s proof has turned the Weinberg-Salam frog into...
extension to the one described as a point-like particle. With a one photon exchangedescription, the form factors in the differential cross section are seen to vanishrapidly for large momentum transfer (squared) Q 2of the photon imparted to the proton. As Q2is increased further one reaches the so-called resonance region...
these point-like particles within the proton are free and the virtual photon interacts 40See also ’t Hooft and Veltman [ 221], Lee and Zinn-Justin [ 139–142], and Becchi et al. [13 ]. 41See Salam [ 183], p. 529. 42The basic idea of the renormalizability of the theory rests on the fact that renormalizability may be esta...
1 Introduction 15 } nucleon leptonleptonAnything Fig. 1.6 In the process, “Anything” denotes anything that may be created in the process consistent with the underlying conservation laws. The wavy line denotes a neutral particle (/CR ,Z0, ...)o fl a r g e momentum transfer (a) (b) Fig. 1.7 (a) If interactions between qu...
CC, which is described in terms of three identical quarks (the so-called u quarks) as a low lying state with no orbital angular momentum between the quarks, behavesas a symmetric state under the exchange of two of its quarks and would violate theSpin & Statistics connection without this additional quantum number. The c...
16 1 Introduction photons in quantum electrodynamics since photons do not carry a charge. These gluon-gluon interactions turn out to have an anti-screening effect on a source ﬁeldwhich dominate over the screening effect of quark/antiquark interactions leading tothe interesting fact that the effective coupling of quark ...

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