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An introduction to how the mathematical tools from quantum field theory can be applied to economics and finance, providing a wide range of quantum mathematical techniques for designing financial instruments. The ideas of Lagrangians, Hamiltonians, state spaces, operators and Feynman path integrals are demonstrated to be the mathematical underpinning of quantum field theory, and which are employed to formulate a comprehensive mathematical theory of asset pricing as well as of interest rates, which are validated by empirical evidence. Numerical algorithms and simulations are applied to the study of asset pricing models as well as of nonlinear interest rates. A range of economic and financial topics are shown to have quantum mechanical formulations, including options, coupon bonds, nonlinear interest rates, risky bonds and the microeconomic action functional. This is an invaluable resource for experts in quantitative finance and in mathematics who have no specialist knowledge of quantum field theory.

Economics --- Finance --- Quantum field theory. --- Relativistic quantum field theory --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- Economics, Mathematical --- Mathematical models.

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Scheck’s successful textbook presents a comprehensive treatment, ideally suited for a one-semester course. The textbook describes Maxwell's equations first in their integral, directly testable form, then moves on to their local formulation. The first two chapters cover all essential properties of Maxwell's equations, including their symmetries and their covariance in a modern notation. Chapter 3 is devoted to Maxwell's theory as a classical field theory and to solutions of the wave equation. Chapter 4 deals with important applications of Maxwell's theory. It includes topical subjects such as metamaterials with negative refraction index and solutions of Helmholtz' equation in paraxial approximation relevant for the description of laser beams. Chapter 5 describes non-Abelian gauge theories from a classical, geometric point of view, in analogy to Maxwell's theory as a prototype, and culminates in an application to the U(2) theory relevant for electroweak interactions. The last chapter 6 gives a concise summary of semi-Riemannian geometry as the framework for the classical field theory of gravitation. The chapter concludes with a discussion of the Schwarzschild solution of Einstein's equations and the classical tests of general relativity. The new concept of this edition presents the content divided into two tracks: the fast track for master's students, providing the essentials, and the intensive track for all wanting to get in depth knowledge of the field. Cleary labeled material and sections guide students through the preferred level of treatment. Numerous problems and worked examples will provide successful access to Classical Field Theory.

Physics. --- Gravitation. --- Classical Electrodynamics. --- Classical and Quantum Gravitation, Relativity Theory. --- Field theory (Physics) --- Optics. --- Electrodynamics. --- Matter --- Physics --- Antigravity --- Centrifugal force --- Relativity (Physics) --- Dynamics --- Light --- Properties

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Composite materials. --- Continuum mechanics. --- Mechanics of continua --- Elasticity --- Mechanics, Analytic --- Field theory (Physics) --- Composites (Materials) --- Multiphase materials --- Reinforced solids --- Solids, Reinforced --- Two phase materials --- Materials

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This thesis sheds valuable new light on the second-order cosmological perturbation theory, extensively discussing it in the context of cosmic microwave background (CMB) fluctuations. It explores the observational consequences of the second-order vector mode, and addresses magnetic field generation and the weak lensing signatures, which are key phenomena of the vector mode. The author demonstrates that the second-order vector mode, which never appears at the linear-order level, naturally arises from the non-linear coupling of the first-order scalar modes. This leads to the remarkable statement that the vector-order mode clearly contributes to the generation of cosmological magnetic fields. Moreover, the weak lensing observations are shown to be accessible to the vector mode. On the basis of ongoing and forthcoming observations, the thesis concludes that the second-order vector mode is detectable.

Perturbation (Astronomy) --- Physics. --- Gravitation. --- Astrophysics. --- Cosmology. --- Astrophysics and Astroparticles. --- Classical and Quantum Gravitation, Relativity Theory. --- Celestial mechanics --- Perturbation (Mathematics) --- Field theory (Physics) --- Matter --- Physics --- Antigravity --- Centrifugal force --- Relativity (Physics) --- Astronomical physics --- Astronomy --- Cosmic physics --- Deism --- Metaphysics --- Properties

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Following the approach of Lev Landau and Evgenii Lifshitz, this book introduces the theory of special and general relativity with the Lagrangian formalism and the principle of least action. This method allows the complete theory to be constructed starting from a small number of assumptions, and is the most natural approach in modern theoretical physics. The book begins by reviewing Newtonian mechanics and Newtonian gravity with the Lagrangian formalism and the principle of least action, and then moves to special and general relativity. Most calculations are presented step by step, as is done on the board in class. The book covers recent advances in gravitational wave astronomy and provides a general overview of current lines of research in gravity. It also includes numerous examples and problems in each chapter.

Physics. --- Gravitation. --- Astronomy. --- Astrophysics. --- Cosmology. --- Classical and Quantum Gravitation, Relativity Theory. --- Astronomy, Astrophysics and Cosmology. --- General relativity (Physics) --- Astronomical physics --- Astronomy --- Cosmic physics --- Physics --- Field theory (Physics) --- Matter --- Antigravity --- Centrifugal force --- Relativity (Physics) --- Properties