Quantum Mechanics and Quantum Field Theory from Algebraic and Geometric Viewpoints

Beschreibung

This book offers a non-standard introduction to quantum mechanics and quantum field theory, approaching these topics from algebraic and geometric perspectives. Beginning with fundamental notions of quantum theory and the derivation of quantum probabilities from decoherence, it proceeds to prove the expression for the scattering matrix in terms of Green functions (LSZ formula), along with a similar expression for the inclusive scattering matrix. The exposition relies on recent findings by the author that provide a deeper understanding of the structure of quantum theory and extend beyond its traditional boundaries. The book is suitable for graduate students and young researchers in mathematics and theoretical physics seeking to delve into innovative concepts within quantum theory. The book contains  many recent results therefore it should be interesting also to accomplished physicists and mathematicians.

Autor*in

Albert Schwarz

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geometric approach to QFT inclusive scattering matrix deterministic physical theories particle and quasiparticle solitons

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“The book is structured into four chapters and an appendix. ... This monograph offers an original perspective on the foundations of quantum theory. It will be of particular interest to researchers in mathematical physics, especially those engaged in algebraic formulations of quantum mechanics, operator algebras, and geometric approaches to QFT. While further development is required to assess the physical applicability of the proposed models, the formal innovations presented here suggest a promising direction for foundational inquiry.” (Marcelo Santos Guimaraes, Mathematical Reviews, November 7, 2025)

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