Quantum Field Theory: A Quantum Computation Approach

PRELIMS.pdf
	Preface
	Acknowledgements
	Author biography
		Yannick Meurice
CH001.pdf
	Chapter 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
		References
CH002.pdf
	Chapter 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
		References
CH003.pdf
	Chapter 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
CH004.pdf
	Chapter 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
		References
CH005.pdf
	Chapter 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
		References
CH006.pdf
	Chapter 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
		References
CH007.pdf
	Chapter 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
		References
CH008.pdf
	Chapter 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
		References
CH009.pdf
	Chapter 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
		References
CH010.pdf
	Chapter 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
		References
CH011.pdf
	Chapter 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
		References
CH012.pdf
	Chapter 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
		References
APP1.pdf
	Chapter
APP2.pdf
	Chapter
		Reference