Quantum field theory : a quantum computation approach /
Saved in:
Author / Creator: | Meurice, Yannick, author. |
---|---|
Imprint: | Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2021] |
Description: | 1 online resource (various pagings) : illustrations (some color). |
Language: | English |
Series: | IOP ebooks. [2021 collection] IOP ebooks. 2021 collection. |
Subject: | |
Format: | E-Resource Book |
URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/12558116 |
Table of Contents:
- 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.