From Classical Mechanics to Quantum Field Theory

January 3, 2020 9:10 From Classical Mechanics to Quantum Field Theory 9in x 6in b3742-main page xi

  - 2.2.1 Hilbertspaces x From Classical Mechanics to Quantum Field Theory. A Tutorial

  - 2.2.2 Typesofoperators......................

  - 2.2.3 Criteria for (essential) selfadjointness

  - 2.2.4 Spectrumofanoperator

  - 2.2.5 Spectralmeasures

  - 2.2.6 Spectral decomposition andrepresentation theorems

  - 2.2.7 Measurablefunctionalcalculus...............

  - 2.2.8 Elementary formalism for the infinite dimensional case

  - 2.2.9 Technical interemezzo: threeoperator topologies

• 2.3 More Fundamental Quantum Structures
  
  
  • 2.3.1 TheBooleanlogicofCM
    
    
    • areselfadjointoperators................... 2.3.2 The non-Boolean logic of QM, the reason why observables
    
    
    
    
  
  
  • 2.3.3 Recovering the Hilbert spacestructure
  
  
  • 2.3.4 States as measures onL(H): Gleason’s theorem
    
    
    • rules.............................. 2.3.5 von Neumann algebra of observables, superselection
    
    
    • representations........................ 2.3.6 Quantum symmetries: unitary projective
    
    
    
    
  
  
  
  


• 2.4 Just Few Words about the Algebraic Approach
  
  
  • 2.4.1 Algebraicformulation....................
  
  
  
  


• Bibliography.................................


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  3. A Concise Introduction to Quantum Field Theory
  
  
  
  
  
  
  • 3.1 Introduction..............................
  
  
  • 3.2 QuantumMechanicsandRelativity.................
    
    
    • 3.2.1 Quantummechanics.....................
    
    
    • 3.2.2 Relativity and the Poincar ́egroup.............
    
    
    
    
  
  
  • 3.3 QuantumFieldTheory........................
    
    
    • 3.3.1 Canonicalquantization
    
    
    
    
  
  
  • 3.4 TheQuantumVacuum........................
    
    
    • 3.4.1 Renormalization of vacuum energy
    
    
    • 3.4.2 Momentumoperator.....................
    
    
    • 3.4.3 Casimireffect
    
    
    
    
  
  
  • 3.5 FieldsversusParticles
    
    
    • 3.5.1 Fockspace
    
    
    • 3.5.2 Wicktheorem
    
    
    
    
  
  
  • 3.6 FieldsinInteraction
    
    
    • 3.6.1 Renormalization of excited states
    
    
    
    
  
  
  • 3.7 CovariantApproach Contents xi
    
    
    • 3.7.1 Euclideanapproach
    
    
    
    
  
  
  • 3.8 ConformalInvariantTheories
    
    
    • 3.8.1 Functional integral approach
    
    
    
    
  
  
  • 3.9 WhatisBeyond?...........................
  
  
  • 3.10 Appendix1.Casimireffect
  
  
  • 3.11 Appendix2.Gaussianmeasures...................
  
  
  • 3.12 Appendix3.Peierlsbrackets
  
  
  • Bibliography.................................
  
  
  
  


• Index