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Titlebook: On Hilbert‘s Sixth Problem; Newton C. A. da Costa,Francisco Antonio Doria Book 2022 Springer Nature Switzerland AG 2022 Physics Formal Phi

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书目名称On Hilbert‘s Sixth Problem
编辑Newton C. A. da Costa,Francisco Antonio Doria
视频video
概述New work by two of the most renowned philosophers from Brazil.Explores which mathematical universe is required for the description of concrete physical events.Stresses that classical mechanics in its
丛书名称Synthese Library
图书封面Titlebook: On Hilbert‘s Sixth Problem;  Newton C. A. da Costa,Francisco Antonio Doria Book 2022 Springer Nature Switzerland AG 2022 Physics Formal Phi
描述This book explores the premise that a physical theory is an interpretation of the analytico–canonical formalism. Throughout the text, the investigation stresses that classical mechanics in its Lagrangian formulation is the formal backbone of theoretical physics. The authors start from a presentation of the analytico–canonical formalism for classical mechanics, and its applications in electromagnetism, Schrödinger‘s quantum mechanics, and field theories such as general relativity and gauge field theories, up to the Higgs mechanism..The analysis uses the main criterion used by physicists for a theory: to formulate a physical theory we write down a Lagrangian for it. A physical theory is a particular instance of the Lagrangian functional. So, there is already an unified physical theory. One only has to specify the corresponding Lagrangian (or Lagrangian density); the dynamical equations are the associated Euler–Lagrange equations. The theory of Suppes predicates as the main tool inthe axiomatization and examples from the usual theories in physics. For applications, a whole plethora of results from logic that lead to interesting, and sometimes unexpected, consequences..This volume look
出版日期Book 2022
关键词Physics Formal Philosophy; Foundation Physics Philosophy Hilbert; Gödel Theorem Philosophy; analytico–c
版次1
doihttps://doi.org/10.1007/978-3-030-83837-9
isbn_softcover978-3-030-83839-3
isbn_ebook978-3-030-83837-9Series ISSN 0166-6991 Series E-ISSN 2542-8292
issn_series 0166-6991
copyrightSpringer Nature Switzerland AG 2022
The information of publication is updating

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On Hilbert‘s Sixth Problem978-3-030-83837-9Series ISSN 0166-6991 Series E-ISSN 2542-8292
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Lagrangian FormulationLet’s consider the (very general) example. Consider the motion of a system of . material points.
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Hamilton’s EquationsAgain we meet our notational convention for the indices of vector-like objects that sort of behave like tangent vectors to a curve of coordinates ..(.) with components.
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From Classical to QuantumWe have sketched here how it is done: take a single particle in 3-space; its Hamilton–Jacobi equation is, from the general Hamilton–Jacobi equation.
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Field TheoryThe concept stems from a construction based on an infinite coupling of harmonic oscillators (and one later proves that quantized electromagnetism can be seen as a countable infinite collection of harmonic oscillators).
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