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This is the first volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists ranging from advanced undergraduate students to professional scientists. The book tries to bridge the existing gap between the different languages used by mathematicians and physicists. For students of mathematics it is shown that detailed knowledge of the physical background helps to motivate the mathematical subjects and to discover interesting interrelationships between quite different mathematical topics. For students of physics, fairly advanced mathematics is presented, which is beyond the usual curriculum in physics. It is the author's goal to present the state of the art of realizing Einstein's dream of a unified theory for the four fundamental forces in the universe (gravitational, electromagnetic, strong, and weak interaction). From the reviews: "… Quantum field theory is one of the great intellectual edifices in the history of human thought. … This volume differs from other books on quantum field theory in its greater emphasis on the interaction of physics with mathematics. … an impressive work of scholarship." (William G. Faris, SIAM Review, Vol. 50 (2), 2008)  "… it is a fun book for practicing quantum field theorists to browse, and it may be similarly enjoyed by mathematical colleagues. Its ultimate value may lie in encouraging students to enter this challenging interdisciplinary area of mathematics and physics. Summing Up: Recommended. Upper-division undergraduates through faculty." (M. C. Ogilvie, CHOICE, Vol. 44 (9), May, 2007).

Quantum field theory. --- Field theory (Physics) --- Relativistic quantum field theory --- Quantum theory --- Relativity (Physics) --- Classical field theory --- Continuum physics --- Physics --- Continuum mechanics --- Global analysis (Mathematics). --- Quantum theory. --- Mathematical physics. --- Functional analysis. --- Differential equations, partial. --- Theoretical, Mathematical and Computational Physics. --- Analysis. --- Elementary Particles, Quantum Field Theory. --- Mathematical Methods in Physics. --- Functional Analysis. --- Partial Differential Equations. --- Partial differential equations --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Physical mathematics --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Mechanics --- Thermodynamics --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Mathematics --- Mathematical analysis. --- Analysis (Mathematics). --- Elementary particles (Physics). --- Physics. --- Partial differential equations. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Elementary particles (Physics) --- High energy physics --- Nuclear particles --- Nucleons --- Nuclear physics --- 517.1 Mathematical analysis --- Mathematical analysis

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This is the second volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists ranging from advanced undergraduate students to professional scientists. This book seeks to bridge the existing gap between the different languages used by mathematicians and physicists. For students of mathematics it is shown that detailed knowledge of the physical background helps to discover interesting interrelationships between quite diverse mathematical topics. For students of physics fairly advanced mathematics, beyond that included in the usual curriculum in physics, is presented. The present volume concerns a detailed study of the mathematical and physical aspects of the quantum theory of light.

Condensed matter. --- Mathematical physics. --- Quantum field theory. --- Mathematics --- Physics --- Physical Sciences & Mathematics --- Calculus --- Electricity & Magnetism --- Quantum electrodynamics. --- Relativistic quantum field theory --- Electrodynamics, Quantum --- QED (Physics) --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Functional analysis. --- Partial differential equations. --- Geometry. --- Physics. --- Analysis. --- Partial Differential Equations. --- Mathematical Methods in Physics. --- Theoretical, Mathematical and Computational Physics. --- Functional Analysis. --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- Quantum field theory --- Schwinger action principle --- Global analysis (Mathematics). --- Differential equations, partial. --- Partial differential equations --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Euclid's Elements --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Physical mathematics --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- 517.1 Mathematical analysis --- Mathematical analysis

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Geometry --- Functional analysis --- Partial differential equations --- Mathematical physics --- differentiaalvergelijkingen --- functies (wiskunde) --- wiskunde --- fysica --- geometrie

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Functional analysis