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Renormalization
This monograph is the first to present the recently discovered renormalization techniques for the Schrödinger and Dirac equations, providing a mathematically rigorous, yet simple and clear introduction to the subject. It develops field-theoretic techniques such as Feynman graph expansions and renormalization, taking pains to make all proofs as simple as possible by using generating function techniques throughout. Renormalization is performed by using an exact renormalization group differential equation, a technique that provides simple but complete proofs of the theorems.
Renormalization
This monograph is the first to present the recently discovered renormalization techniques for the Schrödinger and Dirac equations, providing a mathematically rigorous, yet simple and clear introduction to the subject. It develops field-theoretic techniques such as Feynman graph expansions and renormalization, taking pains to make all proofs as simple as possible by using generating function techniques throughout. Renormalization is performed by using an exact renormalization group differential equation, a technique that provides simple but complete proofs of the theorems.
Nuclear Lattice Effective Field Theory
This primer begins with a brief introduction to the main ideas underlying Effective Field Theory (EFT) and describes how nuclear forces are obtained from first principles by introducing a Euclidean space-time lattice for chiral EFT. It subsequently develops the related technical aspects by addressing the two-nucleon problem on the lattice and clarifying how it fixes the numerical values of the low-energy constants of chiral EFT. In turn, the spherical wall method is introduced and used to show how improved lattice actions render higher-order corrections perturbative. The book also presents Monte Carlo algorithms used in actual calculations. In the last part of the book, the Euclidean time pr...
Astroparticle Physics and Cosmology
Cosmology and astroparticle physics have seen an avalanche of discoveries in the past decade (IceCube - high energy neutrinos, LIGO - gravitational waves, Fermi- gamma-ray telescope, Xenon-1T - dark matter detection, PLANCK- cosmic microwave radiation, EHT picture of black hole, SDSS -galaxy surveys), all of which require a multidisciplinary background for analyzing the phenomena. The arena for testing particle physics models is in the multimessenger astronomical observations and at the same time cosmology now requires a particle physics basis for explaining many phenomena. This book discusses the theoretical tools of particle physics and general relativity which are essential for understanding and correlating diverse astronomical observations.
Tensor Network Contractions
Tensor network is a fundamental mathematical tool with a huge range of applications in physics, such as condensed matter physics, statistic physics, high energy physics, and quantum information sciences. This open access book aims to explain the tensor network contraction approaches in a systematic way, from the basic definitions to the important applications. This book is also useful to those who apply tensor networks in areas beyond physics, such as machine learning and the big-data analysis. Tensor network originates from the numerical renormalization group approach proposed by K. G. Wilson in 1975. Through a rapid development in the last two decades, tensor network has become a powerful ...
Theoretical Fluid Dynamics
This textbook gives an introduction to fluid dynamics based on flows for which analytical solutions exist, like individual vortices, vortex streets, vortex sheets, accretions disks, wakes, jets, cavities, shallow water waves, bores, tides, linear and non-linear free-surface waves, capillary waves, internal gravity waves and shocks. Advanced mathematical techniques ("calculus") are introduced and applied to obtain these solutions, mostly from complex function theory (Schwarz-Christoffel theorem and Wiener-Hopf technique), exterior calculus, singularity theory, asymptotic analysis, the theory of linear and nonlinear integral equations and the theory of characteristics. Many of the derivations, so far contained only in research journals, are made available here to a wider public.
Quantum Optical Processes
This book is a self-contained guide to the world of quantum optical processes which addresses different aspects relevant in quantum optics and quantum information. The basic descriptions, measurement techniques, possible sources, nonclassical features, practical implications and applications of the quantization of light and its interaction with matter, are explored. The observed quantum properties such as coherent superposition, entanglement, nonlocality, decoherence and no-cloning, are discussed. The quantum optical processes such as continuous variable entanglement swapping, teleportation and telecloning from which follow the practical aspects such as quantum gate operations, cryptography ...
Physics of Dusty Plasmas
Colloidal plasmas - a still emerging field of plasma physics - enable the study of basic plasma properties on a microscopic kinetic level and allow the visualization of collective plasma phenomena, like oscillations and waves. Moreover, a vast number of novel phenomena are found in these systems, ranging from Coulomb crystallization to new types of forces and waves. Last but not least, they shed a new light on various traditional aspects of plasma physics such as shielding or the mechanism of acoustic waves in plasmas, thus providing new insight into the basic foundations of plasma physics.These course-based and self-contained lecture notes provide a general introduction to this active and growing field to students and nonspecialists, requiring only basic prior knowledge in plasma physics.
Host Stars and their Effects on Exoplanet Atmospheres
Like planets in our solar system, exoplanets form, evolve, and interact with their host stars in many ways. As exoplanets acquire material and grow to the final size, their atmospheres are subjected to intense UV and X-radiation and high-energy particle bombardment from the young host star. Whether a planet can retain its atmosphere and the conditions for significant mass loss both depend upon the strength of the host star's high-energy radiation and wind, the distance of the exoplanet from its host star, the gravitational potential of the exoplanet, and the initial chemical composition of the exoplanet atmosphere. This introductory overview describes the physical processes responsible for t...
