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4300 results in General and Classical Physics

Page 34 of 215

  • 12 - Statistics, Symmetry, and the Spin-Statistics Theorem

  • from Part I - General Properties of Fields; Scalars and Gauge Fields
  • Horaƫiu Năstase, Universidade Estadual Paulista, São Paulo
  • Book:
    Classical Field Theory
    Published online:
    04 March 2019
    Print publication:
    14 March 2019, pp 108-117

  • Summary

    We define statistics of quantum mechanical particles, obtaining the Bose–Einstein and Fermi–Dirac varieties of indistinguishable particles. After finding the rotation and Lorentz matrices in different Lorentz representations, we describe the spin-statistics theorem, relating fermions with half-integer spin and bosons with integer spin. We explain two simple proofs and say some words on two others. We end by discussing symmetries in more generality, and we discuss the fact that internal symmetries must commute with spacetime ones, due to the Coleman–Mandula theorem.

  • 44 - Dimensional Reduction: The Domain Wall, Cosmic String, and BTZ Black Hole Solutions

  • from Part III - Other Spins or Statistics; General Relativity
  • Horaƫiu Năstase, Universidade Estadual Paulista, São Paulo
  • Book:
    Classical Field Theory
    Published online:
    04 March 2019
    Print publication:
    14 March 2019, pp 418-432

  • Summary

    We consider “dimensionally reduced” gravitational solutions. We write a domain wall ansatz and solve the Einstein equations for it, first for a perturbative nonrelativistic solution, and then for a nonperturbative relativistic one. We write a cosmic string ansatz and solve Einsein's equations by dimensional reduction to 2+1 dimensions, and alternatively in the weak field limit. We define the cosmological constant and write an ansatz for a 2+1 dimensional black hole in a space with cosmological constant, obtaining the BTZ black hole solution. Anti–de Sitter space is defined in general, starting from the BTZ black hole for M = –1.

  • 38 - General Relativity: Metric and General Coordinate Invariance

  • from Part III - Other Spins or Statistics; General Relativity
  • Horaƫiu Năstase, Universidade Estadual Paulista, São Paulo
  • Book:
    Classical Field Theory
    Published online:
    04 March 2019
    Print publication:
    14 March 2019, pp 356-366

  • Summary

    We define general relativity. We first consider intrinsically curved spaces and the notion of metric. Einstein's theory of general relativity is defined, based on the two physical assumptions, that gravity is geometry, and that matter sources gravity, and leading to general coordinate invariance and the equivalence principle. Kinematics, specifically tensors, Christoffel symbol and covariant derivatives, is defined. The motion of a free particle in a gravitational field is calculated.

  • 2 - Symmetries, Groups, and Lie algebras; Representations

  • from Part I - General Properties of Fields; Scalars and Gauge Fields
  • Horaƫiu Năstase, Universidade Estadual Paulista, São Paulo
  • Book:
    Classical Field Theory
    Published online:
    04 March 2019
    Print publication:
    14 March 2019, pp 14-23

  • Summary

    In this chapter, we introduce the basic concepts of symmetries and symmetry groups. After describing groups in general, we focus on Lie groups and their associated Lie algebras. We discuss representations of groups and Lie algebras, in particular irreducible representations, and when representations are equivalent.

Classical Field Theory
  • Horaƫiu Năstase
  • Published online:
    04 March 2019
    Print publication:
    14 March 2019
  • Classical field theory predicts how physical fields interact with matter, and is a logical precursor to quantum field theory. This introduction focuses purely on modern classical field theory, helping graduates and researchers build an understanding of classical field theory methods before embarking on future studies in quantum field theory. It describes various classical methods for fields with negligible quantum effects, for instance electromagnetism and gravitational fields. It focuses on solutions that take advantage of classical field theory methods as opposed to applications or geometric properties. Other fields covered includes fermionic fields, scalar fields and Chern–Simons fields. Methods such as symmetries, global and local methods, Noether theorem and energy momentum tensor are also discussed, as well as important solutions of the classical equations, in particular soliton solutions.

Modern Electrodynamics
  • Andrew Zangwill
  • Published online:
    01 February 2019
    Print publication:
    24 December 2012
  • An engaging writing style and a strong focus on the physics make this comprehensive, graduate-level textbook unique among existing classical electromagnetism textbooks. Charged particles in vacuum and the electrodynamics of continuous media are given equal attention in discussions of electrostatics, magnetostatics, quasistatics, conservation laws, wave propagation, radiation, scattering, special relativity and field theory. Extensive use of qualitative arguments similar to those used by working physicists makes Modern Electrodynamics a must-have for every student of this subject. In 24 chapters, the textbook covers many more topics than can be presented in a typical two-semester course, making it easy for instructors to tailor courses to their specific needs. Close to 120 worked examples and 80 applications boxes help the reader build physical intuition and develop technical skill. Nearly 600 end-of-chapter homework problems encourage students to engage actively with the material. A solutions manual is available for instructors at www.cambridge.org/Zangwill.

Electricity and Magnetism
  • 3rd edition
  • Edward M. Purcell, David J. Morin
  • Published online:
    01 February 2019
    Print publication:
    21 January 2013
  • For 50 years, Edward M. Purcell's classic textbook has introduced students to the world of electricity and magnetism. The third edition has been brought up to date and is now in SI units. It features hundreds of new examples, problems, and figures, and contains discussions of real-life applications. The textbook covers all the standard introductory topics, such as electrostatics, magnetism, circuits, electromagnetic waves, and electric and magnetic fields in matter. Taking a nontraditional approach, magnetism is derived as a relativistic effect. Mathematical concepts are introduced in parallel with the physics topics at hand, making the motivations clear. Macroscopic phenomena are derived rigorously from the underlying microscopic physics. With worked examples, hundreds of illustrations, and nearly 600 end-of-chapter problems and exercises, this textbook is ideal for electricity and magnetism courses. Solutions to the exercises are available for instructors at www.cambridge.org/Purcell-Morin.

Page 34 of 215