Open AccessMathematical Tools to Understand the Field Theories of the Standard Model and Beyond
Author(s) -
Philippe Durand
Publication year - 2021
Publication title -
international journal of mathematics and computers in simulation
Language(s) - English
Resource type - Journals
ISSN - 1998-0159
DOI - 10.46300/9102.2021.15.10
Subject(s) - string theory , manifold (fluid mechanics) , operator algebra , quantum gravity , space (punctuation) , euclidean geometry , algebra over a field , mathematics , field (mathematics) , euclidean space , quantum field theory , theoretical physics , loop quantum gravity , topology (electrical circuits) , pure mathematics , computer science , quantum , physics , geometry , quantum mechanics , mechanical engineering , combinatorics , engineering , mathematical physics , operating system
Since Isaac Newton the understanding of the physical world is more and more complex. The Euclidean space of three dimensions , independent of time is replaced in Enstein’s vision by the Lorentzian space-time at first, then by four dimensions manifold to unify space and matter. String theorists add to space more dimensions to make their theory consistent. Complex topological invariants which characterize different kind of spaces are developed. Space is discretized at the quantum scale in the loop quantum gravity theory. A non-commutative and spectral geometry is defined from the theory of operator algebra by Alain Connes. In this review, our goal is to enumerate different approaches implementing algebra and topology in order to understand the standard model of particles and beyond