Pub Date : 2021-10-25DOI: 10.1093/oso/9780192844200.003.0020
J. Iliopoulos, T. Tomaras
Neutrinos offered the greatest surprises in high energy physics during the last decades. In this chapter we review the main milestones of this passionate history: the first neutrino beams which established the separate neutrino identities, the Gargamelle discovery of the weak neutral currents, the LEP determination of three light neutrino species and the discovery of the intriguing phenomenon of neutrino oscillations. The experimental determination of the neutrino mass matrix elements is still in progress with several experiments either taking data or planned for the near future. We end with the present theoretical puzzles and the experiments which may help to solve them.
{"title":"Neutrino Physics","authors":"J. Iliopoulos, T. Tomaras","doi":"10.1093/oso/9780192844200.003.0020","DOIUrl":"https://doi.org/10.1093/oso/9780192844200.003.0020","url":null,"abstract":"Neutrinos offered the greatest surprises in high energy physics during the last decades. In this chapter we review the main milestones of this passionate history: the first neutrino beams which established the separate neutrino identities, the Gargamelle discovery of the weak neutral currents, the LEP determination of three light neutrino species and the discovery of the intriguing phenomenon of neutrino oscillations. The experimental determination of the neutrino mass matrix elements is still in progress with several experiments either taking data or planned for the near future. We end with the present theoretical puzzles and the experiments which may help to solve them.","PeriodicalId":285777,"journal":{"name":"Elementary Particle Physics","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128768253","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-25DOI: 10.1093/oso/9780192844200.003.0021
J. Iliopoulos, T. Tomaras
For many years strong interactions had a well-deserved reputation for complexity. Their apparent strength rendered perturbation theory inapplicable. However, in the late 1960s a series of experiments studying the deep inelastic electron–nucleon scattering showed that at a more fundamental level, the strong interactions among the constituent quarks can be described perturbatively by an asymptotically free gauge theory. We present the theory of quantum chromodynamics, the unbroken gauge theory of the colour SU(3) group. We show how we can compute its predictions in the kinematic regions in which perturbation theory is applicable, but also in the strong coupling regime through numerical simulations on a space-time lattice.
{"title":"The Strong Interactions","authors":"J. Iliopoulos, T. Tomaras","doi":"10.1093/oso/9780192844200.003.0021","DOIUrl":"https://doi.org/10.1093/oso/9780192844200.003.0021","url":null,"abstract":"For many years strong interactions had a well-deserved reputation for complexity. Their apparent strength rendered perturbation theory inapplicable. However, in the late 1960s a series of experiments studying the deep inelastic electron–nucleon scattering showed that at a more fundamental level, the strong interactions among the constituent quarks can be described perturbatively by an asymptotically free gauge theory. We present the theory of quantum chromodynamics, the unbroken gauge theory of the colour SU(3) group. We show how we can compute its predictions in the kinematic regions in which perturbation theory is applicable, but also in the strong coupling regime through numerical simulations on a space-time lattice.","PeriodicalId":285777,"journal":{"name":"Elementary Particle Physics","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125281359","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-25DOI: 10.1093/oso/9780192844200.003.0003
J. Iliopoulos, T. Tomaras
The purpose of this chapter is to recall the principles of Lagrangian and Hamiltonian classical mechanics. Many results are presented without detailed proofs. We obtain the Euler–Lagrange equations of motion, and show the equivalence with Hamilton’s equations. We derive Noether’s theorem and show the connection between symmetries and conservation laws. These principles are extended to a system with an infinite number of degrees of freedom, i.e. a classical field theory. The invariance under a Lie group of transformations implies the existence of conserved currents. The corresponding charges generate, through the Poisson brackets, the infinitesimal transformations of the fields as well as the Lie algebra of the group.
{"title":"Elements of Classical Field Theory","authors":"J. Iliopoulos, T. Tomaras","doi":"10.1093/oso/9780192844200.003.0003","DOIUrl":"https://doi.org/10.1093/oso/9780192844200.003.0003","url":null,"abstract":"The purpose of this chapter is to recall the principles of Lagrangian and Hamiltonian classical mechanics. Many results are presented without detailed proofs. We obtain the Euler–Lagrange equations of motion, and show the equivalence with Hamilton’s equations. We derive Noether’s theorem and show the connection between symmetries and conservation laws. These principles are extended to a system with an infinite number of degrees of freedom, i.e. a classical field theory. The invariance under a Lie group of transformations implies the existence of conserved currents. The corresponding charges generate, through the Poisson brackets, the infinitesimal transformations of the fields as well as the Lie algebra of the group.","PeriodicalId":285777,"journal":{"name":"Elementary Particle Physics","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115638798","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-25DOI: 10.1093/oso/9780192844200.003.0005
J. Iliopoulos, T. Tomaras
The mathematical language which encodes the symmetry properties in physics is group theory. In this chapter we recall the main results. We introduce the concepts of finite and infinite groups, that of group representations and the Clebsch–Gordan decomposition. We study, in particular, Lie groups and Lie algebras and give the Cartan classification. Some simple examples include the groups U(1), SU(2) – and its connection to O(3) – and SU(3). We use the method of Young tableaux in order to find the properties of products of irreducible representations. Among the non-compact groups we focus on the Lorentz group, its relation with O(4) and SL(2,C), and its representations. We construct the space of physical states using the infinite-dimensional unitary representations of the Poincaré group.
{"title":"Elements of Group Theory","authors":"J. Iliopoulos, T. Tomaras","doi":"10.1093/oso/9780192844200.003.0005","DOIUrl":"https://doi.org/10.1093/oso/9780192844200.003.0005","url":null,"abstract":"The mathematical language which encodes the symmetry properties in physics is group theory. In this chapter we recall the main results. We introduce the concepts of finite and infinite groups, that of group representations and the Clebsch–Gordan decomposition. We study, in particular, Lie groups and Lie algebras and give the Cartan classification. Some simple examples include the groups U(1), SU(2) – and its connection to O(3) – and SU(3). We use the method of Young tableaux in order to find the properties of products of irreducible representations. Among the non-compact groups we focus on the Lorentz group, its relation with O(4) and SL(2,C), and its representations. We construct the space of physical states using the infinite-dimensional unitary representations of the Poincaré group.","PeriodicalId":285777,"journal":{"name":"Elementary Particle Physics","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124918972","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-25DOI: 10.1093/oso/9780198805175.003.0005
J. Iliopoulos, T. Tomaras
The phenomenon of spontaneous symmetry breaking is a common feature of phase transitions in both classical and quantum physics. In a first part we study this phenomenon for the case of a global internal symmetry and give a simple proof of Goldstone’s theorem. We show that a massless excitation appears, corresponding to every generator of a spontaneously broken symmetry. In a second part we extend these ideas to the case of gauge symmetries and derive the Brout–Englert–Higgs mechanism. We show that the gauge boson associated with the spontaneously broken generator acquires a mass and the corresponding field, which would have been the Goldstone boson, decouples and disappears. Its degree of freedom is used to allow the transition from a massless to a massive vector field.
{"title":"Spontaneously Broken Symmetries","authors":"J. Iliopoulos, T. Tomaras","doi":"10.1093/oso/9780198805175.003.0005","DOIUrl":"https://doi.org/10.1093/oso/9780198805175.003.0005","url":null,"abstract":"The phenomenon of spontaneous symmetry breaking is a common feature of phase transitions in both classical and quantum physics. In a first part we study this phenomenon for the case of a global internal symmetry and give a simple proof of Goldstone’s theorem. We show that a massless excitation appears, corresponding to every generator of a spontaneously broken symmetry. In a second part we extend these ideas to the case of gauge symmetries and derive the Brout–Englert–Higgs mechanism. We show that the gauge boson associated with the spontaneously broken generator acquires a mass and the corresponding field, which would have been the Goldstone boson, decouples and disappears. Its degree of freedom is used to allow the transition from a massless to a massive vector field.","PeriodicalId":285777,"journal":{"name":"Elementary Particle Physics","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125607419","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-25DOI: 10.1093/oso/9780192844200.003.0010
J. Iliopoulos, T. Tomaras
We apply the canonical and the path integral quantisation methods to scalar, spinor and vector fields. The scalar field is a generalisation to an infinite number of degrees of freedom of the single harmonic oscillator we studied in Chapter 9. For the spinor fields we show the need for anti-commutation relations and introduce the corresponding Grassmann algebra. The rules of Fermi statistics follow from these anti-commutation relations. The canonical quantisation method applied to the Maxwell field in a Lorentz covariant gauge requires the introduction of negative metric states in the Hilbert space. The power of the path integral quantisation is already manifest. In each case we expand the fields in creation and annihilation operators.
{"title":"From Classical to Quantum Fields. Free Fields","authors":"J. Iliopoulos, T. Tomaras","doi":"10.1093/oso/9780192844200.003.0010","DOIUrl":"https://doi.org/10.1093/oso/9780192844200.003.0010","url":null,"abstract":"We apply the canonical and the path integral quantisation methods to scalar, spinor and vector fields. The scalar field is a generalisation to an infinite number of degrees of freedom of the single harmonic oscillator we studied in Chapter 9. For the spinor fields we show the need for anti-commutation relations and introduce the corresponding Grassmann algebra. The rules of Fermi statistics follow from these anti-commutation relations. The canonical quantisation method applied to the Maxwell field in a Lorentz covariant gauge requires the introduction of negative metric states in the Hilbert space. The power of the path integral quantisation is already manifest. In each case we expand the fields in creation and annihilation operators.","PeriodicalId":285777,"journal":{"name":"Elementary Particle Physics","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117054075","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The most important milestones in particle physics are put in a historical perspective. We follow a century of scattering experiments, from Rutherford to LHC. We introduce successively the concept of the atomic nucleus, the study of β-decay and the proposal of the neutrino, the first internal symmetries, the Fermi theory and the Yukawa meson. In parallel we present the technical achievements in accelerator and detector technologies which made these advances possible. We end with the discovery of strange particles, the flavour SU(3) unitary symmetry, and the introduction of the quarks. This chapter follows a descriptive rather than a deductive approach and summa- rises many aspects of particle physics phenomenology which preceded the discovery of the Standard Model.
{"title":"Particle Physics Phenomenology","authors":"J. Iliopoulos, T. Tomaras","doi":"10.1142/3485","DOIUrl":"https://doi.org/10.1142/3485","url":null,"abstract":"The most important milestones in particle physics are put in a historical perspective. We follow a century of scattering experiments, from Rutherford to LHC. We introduce successively the concept of the atomic nucleus, the study of β-decay and the proposal of the neutrino, the first internal symmetries, the Fermi theory and the Yukawa meson. In parallel we present the technical achievements in accelerator and detector technologies which made these advances possible. We end with the discovery of strange particles, the flavour SU(3) unitary symmetry, and the introduction of the quarks. This chapter follows a descriptive rather than a deductive approach and summa- rises many aspects of particle physics phenomenology which preceded the discovery of the Standard Model.","PeriodicalId":285777,"journal":{"name":"Elementary Particle Physics","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114410348","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-25DOI: 10.1093/oso/9780192844200.003.0009
J. Iliopoulos, T. Tomaras
In Chapter 2 we presented the method of canonical quantisation which yields a quantum theory if we know the corresponding classical theory. In this chapter we argue that this method is not unique and, furthermore, it has several drawbacks. In particular, its application to constrained systems is often problematic. We present Feynman’s path integral quantisation method and derive from it Schroödinger’s equation. We follow Feynman’s original approach and we present, in addition, more recent experimental results which support the basic assumptions. We establish the equivalence between canonical and path integral quantisation of the harmonic oscillator.
{"title":"From Classical to Quantum Mechanics","authors":"J. Iliopoulos, T. Tomaras","doi":"10.1093/oso/9780192844200.003.0009","DOIUrl":"https://doi.org/10.1093/oso/9780192844200.003.0009","url":null,"abstract":"In Chapter 2 we presented the method of canonical quantisation which yields a quantum theory if we know the corresponding classical theory. In this chapter we argue that this method is not unique and, furthermore, it has several drawbacks. In particular, its application to constrained systems is often problematic. We present Feynman’s path integral quantisation method and derive from it Schroödinger’s equation. We follow Feynman’s original approach and we present, in addition, more recent experimental results which support the basic assumptions. We establish the equivalence between canonical and path integral quantisation of the harmonic oscillator.","PeriodicalId":285777,"journal":{"name":"Elementary Particle Physics","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132779041","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-25DOI: 10.1093/oso/9780192844200.003.0008
J. Iliopoulos, T. Tomaras
The Klein–Gordon and the Dirac equations are studied as candidates for a relativistic generalisation of the Schrödinger equation. We show that the first is unacceptable because it admits solutions with arbitrarily large negative energy and has no conserved current with positive definite probability density. The Dirac equation on the other hand does have a physically acceptable conserved current, but it too suffers from the presence of negative energy solutions. We show that the latter can be interpreted as describing anti-particles. In either case there is no fully consistent interpretation as a single-particle wave equation and we are led to a formalism admitting an infinite number of degrees of freedom, that is a quantum field theory. We can still use the Dirac equation at low energies when the effects of anti-particles are negligible and we study applications in atomic physics.
{"title":"Towards a Relativistic Quantum Mechanics","authors":"J. Iliopoulos, T. Tomaras","doi":"10.1093/oso/9780192844200.003.0008","DOIUrl":"https://doi.org/10.1093/oso/9780192844200.003.0008","url":null,"abstract":"The Klein–Gordon and the Dirac equations are studied as candidates for a relativistic generalisation of the Schrödinger equation. We show that the first is unacceptable because it admits solutions with arbitrarily large negative energy and has no conserved current with positive definite probability density. The Dirac equation on the other hand does have a physically acceptable conserved current, but it too suffers from the presence of negative energy solutions. We show that the latter can be interpreted as describing anti-particles. In either case there is no fully consistent interpretation as a single-particle wave equation and we are led to a formalism admitting an infinite number of degrees of freedom, that is a quantum field theory. We can still use the Dirac equation at low energies when the effects of anti-particles are negligible and we study applications in atomic physics.","PeriodicalId":285777,"journal":{"name":"Elementary Particle Physics","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123927455","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-25DOI: 10.1093/oso/9780192844200.003.0023
J. Iliopoulos
We review the fundamental physics questions left unanswered by the Standard Model, and we explain why, despite its great successes, the search for physics beyond the Standard Model is a very active field of research. We briefly review the theories of Grand Unification which assume that the SU(3) × SU(2) x U(1) group of the Standard Model is the remnant of a larger, simple or semi-simple group, spontaneously broken at very high energies. These theories predict the phenomenon of proton decay and we discuss possible cosmological consequences of such an instability. We end with the theory of supersymmetry which postulates the existence of an approximate fermion-boson symmetry.
{"title":"Beyond the Standard Model","authors":"J. Iliopoulos","doi":"10.1093/oso/9780192844200.003.0023","DOIUrl":"https://doi.org/10.1093/oso/9780192844200.003.0023","url":null,"abstract":"We review the fundamental physics questions left unanswered by the Standard Model, and we explain why, despite its great successes, the search for physics beyond the Standard Model is a very active field of research. We briefly review the theories of Grand Unification which assume that the SU(3) × SU(2) x U(1) group of the Standard Model is the remnant of a larger, simple or semi-simple group, spontaneously broken at very high energies. These theories predict the phenomenon of proton decay and we discuss possible cosmological consequences of such an instability. We end with the theory of supersymmetry which postulates the existence of an approximate fermion-boson symmetry.","PeriodicalId":285777,"journal":{"name":"Elementary Particle Physics","volume":"266 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122547574","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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