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Quantum Field Theory An Introduction

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Lingua: Inglese


Pubblicazione: 11/2023
Edizione: 1st ed. 2023


This book is a pedagogical introduction to quantum field theory, suitable for a students’ first exposure to the subject. It assumes a minimal amount of technical background and it is intended to be accessible to a wide audience including students of theoretical and experimental high energy physics, condensed matter, optical, atomic, nuclear and gravitational physics and astrophysics. It includes a thorough development of second quantization and the field theoretic approach to nonrelativistic many-body physics as a step in developing a broad-based working knowledge of the basic aspects of quantum field theory.  It presents a logical and systematic first principles development of relativistic field theory and of functional techniques and perturbation theory with Feynman diagrams, renormalization, and basic computations in quantum electrodynamics.


1Many Particle Physics as a Quantum Field Theory

1.1   Introduction                           

1.2   Non-relativistic particles                       

1.2.1   Identical particles 

1.2.2   Spin 

1.3   Second Quantization 

1.4   The Heisenberg picture 

2 Degenerate Fermi and Bose Gases

2.1The limits of large volume and weakly interacting particles

2.2Degenerate Fermi gas and the Fermi surface 

 2.2.1  The ground state |O > 

2.2.2  Particle and holes 

2.2.3  The grand canonical ensemble

2.3 Bosons 

3 Classical field theory and the action principle

 3.1The Action Principle                                                 

3.1.1  The Action                     

3.1.2  The action principle and the Euler-Lagrange equations

3.1.3  Canonical momenta, Poisson brackets and Commutation relations                       

3.2Noether’s theorem                                               

        3.2.1 Conservation laws and continuity equations

        3.2.2 Definition of symmetry                

        3.2.3 Examples of symmetries

            3.2.4    Proof of Noether’s Theorem 



3.3Phase symmetry and the conservation of particle number

4 Non-relativistic space-time symmetries


4.1Translation invariance and the stress tensor       


4.2Galilean symmetry                                               


4.3Scale invariance                                                 

4.3.1  Improving the stress tensor                     

4.3.2  The consequences of scale invariance    

4.4Special Schrödinger symmetry

5 Space-time symmetry and relativistic field theory

5.1Quantum mechanics and special relativity         


5.3Scalars, vectors, tensors 

5.4The metric                              

5.5Symmetry of space-time          

 5.6The symmetries of Minkowski space            

6 Emergent relativistic symmetry


6.2The free scalar field theory           

 6.3The Debye theory of solids                 

 6.4Relativistic Fermions in Graphene         

7The Dirac Equation

 7.1The Dirac equation                        

 7.2Natural units                              

7.3Solving the Dirac equation     

7.4Lorentz Invariance of the Dirac equation         

 7.5Spin of the Dirac field            

7.6 Phase symmetry and the conservation of particle number


7.6.1 Conserved number current

7.6.2 Relativistic Noether’s Theorem for the Dirac equation

7.6.3 Alternative Proof of Noether’s Theorem

7.7 Spacetime symmetries of the Dirac theory

7.7.1 Translation Invariance and the Stress Tensor

7.7.2 Lorentz Transformations

7.7.3 Stress Tensor and Killing Vectors

8 Photons                                                                                         

8.1 Relativistic Classical Electrodynamics

8.1.1 The Photon Hamiltonian

8.1.2 Massive photon (Optional reading)

8.2 Space-time symmetries of the photon

8.3 Quantum Electrodynamics

9 Functional methods                                                                      

9.1 Functional derivative

9.2 Functional integral

9.3 Real Scalar Field

9.3.1 Generating functional for free scalar fields

9.3.2 Wick’s theorem for scalar fields

9.3.3 Generating functional as a functional in


Gordon W. Semenoff is Professor at The University of British Columbia in Vancouver, Canada. His research examines the nature at its most fundamental level. His recent interests have been in superstring theory and duality of string theories with strongly coupled gauge field theories and in quantum gravity.  He is also interested in quantum information theoretic questions in quantum field theory.

Altre Informazioni



Condizione: Nuovo
Collana: Graduate Texts in Physics
Dimensioni: 235 x 155 mm Ø 863 gr
Formato: Copertina rigida
Illustration Notes:X, 403 p. 40 illus., 5 illus. in color.
Pagine Arabe: 403
Pagine Romane: x

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