Quantum field theory : a quantum computation approach /

This book introduces quantum field theory models from a classical point of view. Practical applications are discussed, along with recent progress for quantum computations and quantum simulations experiments. New developments concerning discrete aspects of continuous symmetries and topological soluti...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Meurice, Yannick (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2021]
Colección:IOP (Series). Release 21.
IOP ebooks. 2021 collection.
Temas:
Quantum field theory.
Quantum computing.
Quantum physics (quantum mechanics & quantum field theory)
SCIENCE / Physics / Quantum Theory.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 1. Introduction
  • 1.1. Goals of the lecture notes
  • 1.2. Classical electrodynamics and its symmetries
  • 1.3. Field quantization
  • 1.4. The need for discreteness in quantum computing
  • 1.5. Symmetries and predictive models
  • 2. Classical field theory
  • 2.1. Classical action, equations of motion and symmetries
  • 2.2. Transition to field theory
  • 2.3. Symmetries
  • 2.4. The Klein-Gordon field
  • 2.5. The Dirac field
  • 2.6. Maxwell fields
  • 2.7. Yang-Mills fields
  • 2.8. Linear sigma models
  • 2.9. General relativity
  • 2.10. Examples of two-dimensional curved spaces
  • 2.11. Mathematica notebook for geodesics
  • 3. Canonical quantization
  • 3.1. A one-dimensional harmonic crystal
  • 3.2. The infinite volume and continuum limits
  • 3.3. Free KG and Dirac quantum fields in 3 + 1 dimensions
  • 3.4. The Hamiltonian formalism for Maxwell's gauge fields
  • 4. A practical introduction to perturbative quantization
  • 4.1. Overview
  • 4.2. Dyson's chronological series
  • 4.3. Feynman propagators, Wick's theorem and Feynman rules
  • 4.4. Decay rates and cross sections
  • 4.5. Radiative corrections and the renormalization program
  • 5. The path integral
  • 5.1. Overview
  • 5.2. Free particle in quantum mechanics
  • 5.3. Complex Gaussian integrals and Euclidean time
  • 5.4. The Trotter product formula
  • 5.5. Models with quadratic potentials
  • 5.6. Generalization to field theory
  • 5.7. Functional methods for interactions and perturbation theory
  • 5.8. Maxwell's fields at Euclidean time
  • 5.9. Connection to statistical mechanics
  • 5.10. Simple exercises on random numbers and importance sampling
  • 5.11. Classical versus quantum
  • 6. Lattice quantization of spin and gauge models
  • 6.1. Lattice models
  • 6.2. Spin models
  • 6.3. Complex generalizations and local gauge invariance
  • 6.4. Pure gauge theories
  • 6.5. Abelian gauge models
  • 6.6. Fermions and the Schwinger model
  • 7. Tensorial formulations
  • 7.1. Remarks about the discreteness of tensor formulations
  • 7.2. The Ising model
  • 7.3. O(2) spin models
  • 7.4. Boundary conditions
  • 7.5. Abelian gauge theories
  • 7.6. The compact abelian Higgs model
  • 7.7. Models with non-abelian symmetries
  • 7.8. Fermions
  • 8. Conservation laws in tensor formulations
  • 8.1. Basic identity for symmetries in lattice models
  • 8.2. The O(2) model and models with abelian symmetries
  • 8.3. Non-abelian global symmetries
  • 8.4. Local abelian symmetries
  • 8.5. Generalization of Noether's theorem
  • 9. Transfer matrix and Hamiltonian
  • 9.1. Transfer matrix for spin models
  • 9.2. Gauge theories
  • 9.3. U(1) pure gauge theory
  • 9.4. Historical aspects of quantum and classical tensor networks
  • 9.5. From transfer matrix functions to quantum circuits
  • 9.6. Real time evolution for the quantum ising model
  • 9.7. Rigorous and empirical Trotter bounds
  • 9.8. Optimal Trotter error
  • 10. Recent progress in quantum computation/simulation for field theory
  • 10.1. Analog simulations with cold atoms
  • 10.2. Experimental measurement of the entanglement entropy
  • 10.3. Implementation of the abelian Higgs model
  • 10.4. A two-leg ladder as an idealized quantum computer
  • 10.5. Quantum computers
  • 11. The renormalization group method
  • 11.1. Basic ideas and historical perspective
  • 11.2. Coarse graining and blocking
  • 11.3. The Niemeijer-van Leeuwen equation
  • 11.4. Tensor renormalization group (TRG)
  • 11.5. Critical exponents and finite-size scaling
  • 11.6. A simple numerical example with two states
  • 11.7. Numerical implementations
  • 11.8. Python code
  • 11.9. Additional material
  • 12. Advanced topics
  • 12.1. Lattice equations of motion
  • 12.2. A first look at topological solutions on the lattice
  • 12.3. Topology of U(1) gauge theory and topological susceptibility
  • 12.4. Mathematica notebooks
  • 12.5. Large field effects in perturbation theory
  • 12.6. Remarks about the strong coupling expansion.

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