"Version: 20210201"--Title page verso.

Includes bibliographical references.

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.

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 solutions in tensorial formulations of gauge theories are also reported. Quantum Field Theory: A Quantum Computation Approach requires no prior knowledge beyond undergraduate quantum mechanics and classical electrodynamics. With exercises involving Mathematica and Python with solutions provided, the book is an ideal guide for graduate students and researchers in high-energy, condensed matter and atomic physics.

Upper level undergraduate/graduate.

Also available in print.

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.

Yannick Meurice is a Professor at the University of Iowa. He obtained his PhD at U. C. Louvain-la-Neuve in 1985 under the supervision of Jacques Weyers and Gabriele Veneziano. He was a postdoc at CERN and Argonne National Laboratory and a visiting professor at CINVESTAV in Mexico City. He joined the faculty of the Department of Physics and Astronomy at the University of Iowa in 1990. His current work includes lattice gauge theory, tensor renormalization group methods, near conformal gauge theories, critical machine learning, quantum simulations with cold atoms and quantum computing. He is the PI of a multi-institutional DOE HEP QuantISED grant.

Title from PDF title page (viewed on March 17, 2021).