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Quantum Monte Carlo methods: algorithms for lattice models

This is a slim volume of around one hundred pages. In it, Prasenjit Saha and Paul Taylor take a unique approach introducing astrophysics through the most useful ‘back of the envelope’ calculations used in the field. Each set of calculations provide the essential description for a different key astrophysical concept. It is no surprise that this book emerged from a series of lectures. There is a strong logical, historical, mathematical and astrophysical flow through the concepts. Each chapter sets out the basic groundwork as a set of mathematical building blocks and poses problems that the reader canwork through to get a deeper understanding of the topic. The first chapter focuses on classical mechanics. It introduces the gravitational constant, and calculation of orbits. The following chapter expands this. It deals with more complex orbits and introduces Lagrangian and Hamiltonian mechanics. (An appendix provides a more detailed introduction to Hamiltonian dynamics.) Chapter three introduces relativity and uses Hamiltonians to describe the nature of space-time. This leads to a version of Schwarzschild’s formula for the impact of a spherical mass. This chapter also covers switching between Cartesian and Polar systems. It concludes by illustrating gravitational lensing by considering the effect of a highmass object on a beam of light passing nearby. The next section focuses on the structure of stars and their physical properties. It starts by considering an ideal ‘gas’ as a system of small identical particles. The book offers models for this first in classical and then in quantum mechanical terms. From here it is a short step to describing how within stars gravity and pressure create a hydrostatic equilibrium. This leads into modelling nuclear fusion in stars and approximating quantum tunnelling effects. Radiative transfer is introduced as a way to relate luminosity and effective temperature to the mass of the star. The discussion covers how the usefulness of this formula depends very much on the mass of the star. The final section explores the expanding Universe. The measuring of cosmology distances, time curvature and its consequences. Along the way it covers the ‘chirping’ of gravitational wave events and measuring redshift drift. The book concludes with amore cosmological section on cosmic microwave background radiation. This chapter discusses the nature of the ‘big bang’ and the implications of a hot early universe. It describes recombination and why local fluctuations in the cosmic microwave background are important. The authors make no claims that this is a comprehensive survey or textbook. The book’s virtues lie in being a coherent and accessible curation of topics. The topics covered being both useful to students, and well suited to this type of analysis. The focus of simplified approximations ‘back of the envelope’ calculations is refreshing. It is an accessible book – well peppered with historical tidbits, and links to powerful images from the ‘Astronomy Picture of the Day’ archive. I think it is a book I feel that will appeal to many mathematically minded students moving into astrophysics and looking for a straightforward introduction to the subject.