No Nonsense Quantum Field Theory A Student Friendly Introduction 1st Edition by Jakob Schwichtenberg ISBN 3948763011 9783948763015

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Product details:

ISBN 10:    3948763011  
ISBN 13: 978-3948763015
Author:       Jakob Schwichtenberg

Learning quantum field theory doesn’t have to be hard

What if there were a book that allowed you to see the whole picture and not just tiny parts of it?

Thoughts like this are the reason that No-Nonsense Quantum Field Theory now exists.

What will you learn from this book?

• Get to know all fundamental concepts — Grasp what a quantum field is, why we use propagators to describe its behavior, and how Feynman diagrams help us to make sense of field interactions.
• Learn to describe quantum field theory mathematically — Understand the meaning and origin of the most important equations: the Klein-Gordon equation, the Dirac equation, the Proca equation, the Maxwell equations, and the canonical commutation/anticommutation relations.
• Master important quantum field theory interactions — Read fully annotated, step-by-step calculations and understand the general algorithm we use to particle interactions.
• Get an understanding you can be proud of —Learn about advanced topics like renormalization and regularization, spontaneous symmetry breaking, the renormalization group equations, non-perturbative phenomena, and effective field models.

No-Nonsense Quantum Field Theory is one the most student-friendly book on quantum field theory ever written.

Here’s why.

• First of all, it’s nothing like a formal university lecture. Instead, it’s like a casual conservation with a more experienced student. This also means that nothing is assumed to be “obvious” or “easy to see”.
• Each chapter, each section, and each page focuses solely on the goal to help you understand. Nothing is introduced without a thorough motivation and it is always clear where each equation comes from.
• The book ruthlessly focuses on the fundamentals and makes sure you’ll understand them in detail.

The primary focus on the readers’ needs is also visible in dozens of small features that you won’t find in any other textbook

• In total, the book contains more than 100 illustrations that help you understand the most important concepts visually.
• In each chapter, you’ll find fully annotated equations and calculations are done carefully step-by-step. This makes it much easier to understand what’s going on.
• Whenever a concept is used that was already introduced previously there is a short sidenote that reminds you where it was first introduced and often recites the main points.
• In addition, there are summaries at the beginning of each chapter that make sure you won’t get lost.

No Nonsense Quantum Field Theory A Student Friendly Introduction 1st Table of contents:

 

Bird’s-Eye View of Quantum Field Theory

Part 0: Preliminaries

1. Spacetime

   • The Arena of Physics
   • Maximum Speed
   • The Speed of Light
   • Time Dilation
   • Proper Time
   • The Minkowski Metric and Four-Vectors
   • The Relativistic Energy-Momentum Relation
   • Lorentz and Poincare Transformations
   • Summary

2. Fields

   • Scalar Fields
   • Vector Fields
   • Polarization
   • Scalars, Vectors, Tensors, and Spinors
   • Spinor Fields
   • Spinor Formalism
   • Spin
   • Chirality
   • Field Dynamics
   • Waves
   • Wave Packets
   • Field Spaces
   • Local Coordinate Systems
   • Gauge Fields

3. The Lagrangian Formalism

   • The Euler-Lagrange Equation
   • Intermezzo: Variational Calculus
   • Deriving the Euler-Lagrange Equation
   • The Meaning of the Euler-Lagrange Equation
   • The Lagrangian Formalism in Field Theory
   • Noether’s Theorem
   • Spacetime Symmetries
   • Internal Symmetries

4. The Behavior of Free Fields

   • Free Scalar fields and the Klein Gordon Equation
   • The Meaning of the Klein-Gordon Equation
   • Solutions of the Klein-Gordon Equation
   • Free Spinor Fields and the Dirac Equation
   • The Meaning of the Dirac Equation
   • Free Gauge Fields and the Proca/Maxwell equations
   • Meaning of the Proca and Maxwell Equations
   • Solutions of the Proca and Maxwell Equations

5. Interacting Classical Fields

   • Green’s Functions
   • Delta Decomposition
   • Green’s Function of the Klein-Gordon Equation
   • Self-Interactions
   • Yukawa Interactions
   • Gauge Interactions

---

Part I: What Everybody Ought to Know About Quantum Field Theory

6. Quantum Mechanics

   • The Quantum Formalism
   • Group Theory
   • Quantum Operators
   • The Canonical Commutation Relation
   • The Schrödinger Equation
   • Time Evolution
   • Quantum Waves
   • de Broglie Relations
   • The Stationary Schrödinger Equation
   • The Quantum Harmonic Oscillator

7. Quantum Fields

   • Quantum Fields vs. Classical Fields
   • The Canonical Commutation Relations
   • Field Operators
   • Creation and Annihilation Operators
   • Particle States
   • Plane Waves
   • The Uncertainty Relation
   • Dealing with Non-Normalizable States
   • Wave Packets
   • Propagators
   • Dynamical Propagators
   • Advanced and Retarded Propagators
   • The Feynman Propagator
   • Complex Scalar Fields
   • Antiparticles
   • Complex Scalar Field Propagators
   • Quantized Spinor Fields
   • Spinor Hamiltonian
   • Spinor Particles
   • Spinor Propagator
   • Quantized Gauge Fields
   • Quantized Massive Gauge Fields
   • Quantized Massless Gauge Fields

8. Interacting Quantum Fields

   • Transition Amplitudes and Time Evolution
   • The Interaction Picture
   • The Dyson Series
   • Time-Ordering
   • Ground State Energy in the Presence of Interactions

---

Part II: Essential Applications

9. Scattering – a First Look

   • Zeroth-Order Approximation
   • First-Order Approximation

10. Amplitude Technology

• Contractions
• Wick’s Theorem
• Important Contractions
• Scattering – a Second Look
• Zeroth-Order Approximation
• First-Order Approximation
• Feynman Diagrams
• Scattering – a Third Look
• Zeroth order Approximation
• First order Approximation
• Second-Order Approximation
• Summary

11. Elementary Models

• Yukawa Interactions
• Important Contractions
• Zeroth-Order Approximation
• First-Order Approximation
• Second-Order Approximation
• The Non-Relativistic Limit
• Further Comments
• Gauge Interactions
• The Non-Relativistic Limit
• Further Examples

12. Scattered Comments

• Virtual Particles
• Loops and Legs
• Scattering Conventions
• Regularization
• The Renormalization Group
• The Meaning of the Renormalization Group Equation

---

Part III: Get an Understanding of Quantum Field Theory You Can Be Proud Of

13. The Living Vacuum

• Symmetry Breaking
• Explicit Symmetry Breaking
• Spontaneous Symmetry Breaking
• Spontaneous Mass Generation

14. The Path Integral Formulation

• The Path Integral in Quantum Mechanics
• The Classical Path
• The Path Integral in Quantum Field Theory

15. Non-Perturbative Phenomena

• Instantons

16. Effective Field Models and the Origin of Simplicity

• Dimensional Analysis
• The Origin of “Fundamental” Lagrangians

17. Outlook

18. Further Reading Recommendations

---

Part IV: Appendices

A. Cumbersome Calculations from Part 0 and Part 1

• Rewriting the Proca Lagrangian
• Noether Current for a Complex Field
• Rewriting the General Solution of the Klein-Gordon Equation
• Verifying the a(k), a+(k) commutation relations
• Rewriting the Scalar Field Energy
• Rewriting the Scalar Field Momentum
• Demonstration that the Feynman Propagator is a Green’s Function
• Total Charge in Terms of Creation and Annihilation Operators

B. Cumbersome Calculations from Part II and Part III

• Validating Wick’s Theorem For Three Field Products
• Work in the Vicinity of an Infinitely Long Wire
• Fourier Transform of the Yukawa Potential

C. Wave Properties

• Advanced properties

D. Gauge Symmetry in Classical Electrodynamics

• Partial Gauge Fixing

E. Delta Distribution

• Integral Representation of the Delta Distribution

F. Statistics

• Mean

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