Quantum Field Theory I: Basics in Mathematics and Physics

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. It bridges the gap between the different languages they use.

1 Daß ich erkenne, was die Welt im Innersten zusammenh¨ alt. Faust Concepts without intuition are empty, intuition without concepts is blind. Immanuel Kant (17241804) The greatest mathematicians like Archimedes, Newton, and Gauss have always been able to combine theory and applications into one. Felix Klein (18491925) The present comprehensive introduction to the mathematical and physical aspects of quantum ?eld theory consists of the following six volumes: Volume I: Basics in Mathematics and Physics Volume II: Quantum Electrodynamics Volume III: Gauge Theory Volume IV: Quantum Mathematics Volume V: The Physics of the Standard Model Volume VI: Quantum Gravity and String Theory. Since ancient times, both physicists and mathematicians have tried to und- stand the forces acting in nature. Nowadays we know that there exist four fundamental forces in nature: • Newton's gravitational force, • Maxwell's electromagnetic force, • the strong force between elementary particles, and • the weak force between elementary particles (e.g., the force responsible for the radioactive decay of atoms). In the 20th century, physicists established two basic models, namely, • the Standard Model in cosmology based on Einstein's theory of general relativity, and • the Standard Model in elementary particle physics based on gauge theory. 1 So that I may perceive whatever holds the world together in its inmost folds.

Excellent book for graduate students intending to learn the mathematics required for modern theoretical physics

Includes supplementary material: sn.pub/extras

Auteur

Prof. Dr. Dr. h.c. Eberhard Zeidler works at the Max Planck Institute for Mathematics in the Sciences in Leipzig (Germany). In 1996 he was one of the founding directors of this institute. He is a member of the Academy of Natural Scientists Leopoldina. In 2006 he was awarded the "Alfried Krupp Wissenschaftspreis" of the Alfried Krupp von Bohlen und Halbach-Stiftung.

The author wrote the following books.

(a) E. Zeidler, Nonlinear Functional Analysis and its Applications, Vols. I-IV,
Springer Verlag New York, 1984-1988 (third edition 1998).

(b) E. Zeidler, Applied Functional Analysis, Vol. 1:
Applications to Mathematical Physics, 2nd edition, 1997, Springer Verlag, New York.

(c) E. Zeidler, Applied Functional Analysis, Vol. 2:
Main Principles and Their Applications,
Springer-Verlag, New York, 1995.

(d) E. Zeidler, Oxford Users' Guide to Mathematics, Oxford University Press, 2004
(translated from German).

Contenu
Preface.- Part I. Introduction.- Prologue.- 1. Historical Introduction.- 2. Phenomenology of the Standard Model for Elementary Particles.- 3. The Challenge of Different Scales in Nature.- Part II. Basic Techniques in Mathematics.- 4. Analyticity.- 5. A Glance at Topology.- 6. Many-Particle Systems in Mathematics and Physics.- 7. Rigorous Finite-Dimensional Magic Formulas of Quantum Field Theory.- 8. Rigorous Finite-Dimensional Perturbation Theory.- 9. Fermions and the Calculus for Grassmann Variables.- 10. Infinite-Dimensional Hilbert Spaces.- 11. Distributions and Green's Functions.- 12. Distributions and Physics.- Part III. Heuristic Magic Formulas of Quantum Field Theory.- 13. Basic Strategies in Quantum Field Theory.- 14. The Response Approach.- 15. The Operator Approach.- 16. Peculiarities of Gauge Theories.- 17. A Panorama of the Literature.- Appendix.- Epilogue.- References.- List of Symbols.- Index.