Gauge Theories in Particle Physics: a Practical Introduction, Volume 2: Non-Abelian Gauge Theories QCD and the Electroweak Theory, Fourth Edition

Name: Gauge Theories in Particle Physics: a Practical Introduction, Volume 2: Non-Abelian Gauge Theories QCD and the Electroweak Theory, Fourth Edition
Price: 90.97 USD
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ISBN: 9781466513075

ISBN-10: 1466513071

ISBN-13: 9781466513075

Edition: 4th 2013 (Revised)

Authors: Ian J. R. Aitchison, Anthony J. G. Hey

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Description:

The second volume of this updated fourth edition introduces global and local non-Abelian symmetries and develops simple ideas of group theory. It covers both perturbative and non-perturbative QCD, provides an extensive discussion of spontaneously broken symmetry, and includes an application to chiral symmetry breaking and chiral perturbation theory. The text also describes weak interaction phenomenology, the GWS theory, and condensed matter (many-body) systems, including the one-dimensional Ising model, the bosonic (Bogoliubov) superfluid, and the fermionic (BCS) superconductor.

Book details

Edition: 4th
Copyright year: 2013
Publisher: Taylor & Francis Group
Publication date: 12/17/2012
Binding: Hardcover
Pages: 524
Size: 6.26" wide x 9.33" long x 1.10" tall
Weight: 4.290
Language: English

Tony Hey is Vice President of Microsoft Research and has published over 150 research papers on particle physics, computer science and multi-disciplinary eScience. He is the co-author, with Ian Aitchison, of the graduate textbook Gauge Theories in Particle Physics (4th edition) and co-editor of Richard Feynman's Lectures on Computation. He is also co-author of popular science books on quantum mechanics and relativity, The New Quantum Universe and Einstein's Mirror. Most recently, he co-edited The Fourth Paradigm, a book about eScience and the new era of data-intensive science.



Preface



Non-Abelian Symmetries



Global Non-Abelian Symmetries



The Standard Model



The flavour symmetry SU(2)<sub>f</sub>



The nucleon isospin doublet and the group SU(2)



Larger (higher-dimensional) multiplets of SU(2) in nuclear physics



Isospin in particle physics: flavour SU(2)<sub>f</sub>



Flavour SU(3)<sub>f</sub>



Non-Abelian global symmetries in Lagrangian quantum field theory



SU(2)<sub>f</sub> and SU(3)<sub>f</sub>



Chiral symmetry


Problems



Local Non-Abelian (Gauge) Symmetries



Local SU(2) symmetry



The covariant derivative and interactions with matter



The non-Abelian field strength tensor



Local SU(3) Symmetry



Local non-Abelian symmetries in Lagrangian quantum field theory



Local SU(2) and SU(3) Lagrangians



Gauge field self-interactions



Quantizing non-Abelian gauge fields


Problems



QCD and the Renormalization Group



QCD I: Introduction, Tree Graph Predictions, and Jets



The colour degree of freedom



The dynamics of colour



Colour as an SU(3) group



Global SU(3)<sub>c</sub> invariance, and 'scalar gluons'



Local SU(3)<sub>c</sub> invariance: the QCD Lagrangian



The ï¿½-term



Hard scattering processes, QCD tree graphs, and jets



Introduction



Two-jet events in pp collisions



Three-jet events in pp collisions



3-jet events in e<sup>+</sup>e<sup>-</sup> annihilation



Calculation of the parton-level cross section



Soft and collinear divergences



Definition of the two-jet cross section in e<sup>+</sup>e<sup>-</sup> annihilation



Further developments



Test of non-Abelian nature of QCD in e<sup>+</sup>e<sup>-</sup> → 4 jets



Jet algorithms


Problems



QCD II: Asymptotic Freedom, the Renormalization Group, and Scaling Violations



Higher-order QCD corrections to ï¿½(e<sup>+</sup>e<sup>-</sup> → hadrons): large logarithms



The renormalization group and related ideas in QED



Where do the large logs come from?



Changing the renormalization scale



The RGE and large -q<sup>2</sup> behaviour in QED



Back to QCD: asymptotic freedom



One loop calculation



Higher-order calculations, and experimental comparison



ï¿½(e<sup>+</sup>e<sup>-</sup> → hadrons) revisited



A more general form of the RGE: anomalous dimensions and running masses



QCD corrections to the parton model predictions for deep inelastic scattering: scaling violations



Uncancelled mass singularities at order ï¿½<sub>s</sub>



Factorization, and the order ï¿½<sub>s</sub> DGLAP equation



Comparison with experiment


Problems



Lattice Field Theory, and the Renormalization Group Revisited



Introduction



Discretization



Scalar fields



Dirac fields



Gauge fields



Representation of quantum amplitudes



Quantum mechanics



Quantum field theory



Connection with statistical mechanics



Renormalization, and the renormalization group, on the lattice



Introduction



Two one-dimensional examples



Connections with particle physics



Lattice QCD



Introduction, and the continuum limit



The static qq potential



Calculation of ï¿½(M<sub>Z</sub><sup>2</sup>)



Hadron masses


Problems



Spontaneously Broken Symmetry



Spontaneously Broken Global Symmetry



Introduction



The Fabri-Picasso theorem



Spontaneously broken symmetry in condensed matter physics



The ferromagnet



The Bogoliubov superfluid



Goldstone's theorem



Spontaneously broken global U(1) symmetry: the Goldstone model



Spontaneously broken global non-Abelian symmetry



The BCS superconducting ground state


Problems



Chiral Symmetry Breaking



The Nambu analogy



Two flavour QCD and SU(2)<sub>f L</sub> ï¿½ SU(2)<sub>f R</sub>



Pion decay and the Goldberger-Treiman relation



Effective Lagrangians



The linear and non-linear ï¿½-models



Inclusion of explicit symmetry breaking: masses for pions and quarks



Extension to SU(3)<sub>f L</sub> ï¿½ SU(3)<sub>f R</sub>



Chiral anomalies


Problems



Spontaneously Broken Local Symmetry



Massive and massless vector particles



The generation of 'photon mass' in a superconductor: Ginzburg-Landau theory and the Meissner effect



Spontaneously broken local U(1) symmetry: the Abelian Higgs model



Flux quantization in a superconductor



't Hooft's gauges



Spontaneously broken local SU(2) ï¿½ U(1) symmetry


Problems



Weak Interactions and the Electroweak Theory



Introduction to the Phenomenology of Weak Interactions



Fermi's 'current-current' theory of nuclear ï¿½-decay, and its generalizations



Parity violation in weak interactions, and V-A theory



Parity violation



V-A theory: chirality and helicity



Lepton number and lepton flavours



The universal current ï¿½ current theory for weak interactions of leptons



Calculation of the cross section for ï¿½<sub>ï¿½</sub> + e<sup>-</sup> → ï¿½<sup>-</sup> + ï¿½<sub>e</sub>



Leptonic weak neutral currents



Quark weak currents



Two generations



Deep inelastic neutrino scattering



Three generations



Non-leptonic weak interactions


Problems



CP Violation and Oscillation Phenomena



Direct CP violation in B decays'



CP violation in B meson oscillations



Time-dependent mixing formalism



Determination of the angles ï¿½(ï¿½<sub>2</sub>) and ï¿½( ï¿½<sub>1</sub>) of the unitarity triangle



CP violation in neutral K-meson decays



Neutrino mixing and oscillations



Neutrino mass and mixing



Neutrino oscillations: formulae



Neutrino oscillations: experimental results



Matter effects in neutrino oscillations



Further developments


Problems



The Glashow-Salam-Weinberg Gauge Theory of Electroweak Interactions



Difficulties with the current-current and 'naive' IVB models



Violations of unitarity



The problem of non-renormalizability in weak interactions



The SU(2) ï¿½ U(1) electroweak gauge theory



Quantum number assignments; Higgs, W and Z masses



The leptonic currents (massless neutrinos): relation to current-current model



The quark currents



Simple (tree-level) predictions



The discovery of the W<sup>ï¿½</sup> and Z<sup>0</sup> at the CERN pp collider



Production cross sections for W and Z in pp colliders



Charge asymmetry in W<sup>ï¿½</sup> decay



Discovery of the W<sup>ï¿½</sup> and Z<sup>0</sup> at the pp collider, and their properties



Fermion masses



One generation



Three-generation mixing



Higher-order corrections



The top quark



The Higgs sector



Introduction



Theoretical considerations concerning m<sub>H</sub>



Higgs boson searches and the 2012 discovery


Problems



Group Theory



Definition and simple examples



Lie groups



Generators of Lie groups



Examples



SO (3) and three-dimensional rotations



SU(2)



SO(4): The special orthogonal group in four dimensions



The Lorentz group



SU(3)



Matrix representations of generators, and of Lie groups



The Lorentz group



The relation between SU(2) and SO(3)



Geometrical Aspects of Gauge Fields



Covariant derivatives and coordinate transformations



Geometrical curvature and the gauge field strength tensor



Dimensional Regularization



Grassmann Variables



Feynman Rules for Tree Graphs in QCD and the Electroweak Theory



QCD



External particles



Propagators



Vertices



The electroweak theory



External particles



Propagators



Vertices


References


Index