On Hilbert's Sixth Problem | Buch

Cover: 9783030838362 | On Hilbert's Sixth Problem | Francisco Antonio Doria (u. a.) | Buch

Rückseite: 9783030838362 | On Hilbert's Sixth Problem | Francisco Antonio Doria (u. a.) | Buch

Dekorationsartikel gehören nicht zum Leistungsumfang.

Sprache: Englisch

91,40 €

UVP 106,99 €

inkl. MwSt.

Versandkostenfrei per Post / DHL

Lieferzeit 1-2 Wochen

Kategorien:

Beschreibung

This book explores the premise that a physical theory is an interpretation of the analyticöcanonical 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 analyticöcanonical 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 looks at where our physics happen and which mathematical universe we require for the description of our concrete physical events. It also explores if we use the constructive universe or if we need set¿theoretically generic spacetimes.

Über den Autor

Francisco Antonio Doria is Professor Emeritus, UFRJ. PhD (mathematical physics, advisor Leopoldo Nachbin, 1977, CBPF, Rio Brazil). With Newton da Costa settled the 1976 Arnol'd Hilbert Symposium Problems; proved that chaos in dynamical systems theory is undecidable.

Newton C. A. da Costa is a well-known expert in the field of nonclassical logics, developed the theory of paraconsistent logics.

Zusammenfassung

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 Lagrangian formulation is the formal backbone of theoretical physics

Inhaltsverzeichnis

Foreword.- 1. Preliminary.- Part I. Physics: A Primer. 2. Classical mechanics.- 3. Variational calculus.- 4. Lagrangian formulation.- 5. Hamilton's equations.- 6. Hamilton-Jacobi theory.- 7. Where the action is.- 8. From classical to quantum.- 9. Field theory.- 10. Electromagnetism.- 11. Special relativity.- 12. General relativity.- 13. Gauge field theories.- Part II. Axiomatics. 14. Axiomatizations in ZFC.- Part III. Technicalities. 15. Hierarchies.- Part IV. More applications. 16. Arnol'd's 1974 problems.- 17. Forcing and gravitation.- 18. Economics and ecology.- Part V. Computer science. 19. Fast-growing functions.- Part VI. Hypercomputation. 20. Hypercomputation.- References.

Details

Erscheinungsjahr:	2022
Fachbereich:	Allgemeines
Genre:	Geisteswissenschaften , Kunst , Musik , Philosophie
Jahrhundert:	Antike
Rubrik:	Geisteswissenschaften
Thema:	Lexika
Medium:	Buch
Inhalt:	xiii 191 S. 1 s/w Illustr. 191 p. 1 illus.
ISBN-13:	9783030838362
ISBN-10:	3030838366
Sprache:	Englisch
Einband:	Gebunden
Autor:	Doria, Francisco Antonio da Costa, Newton C. A.
Auflage:	1st edition 2022
Hersteller:	Springer Nature Switzerland Springer International Publishing
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	241 x 160 x 17 mm
Von/Mit:	Francisco Antonio Doria (u. a.)
Erscheinungsdatum:	26.01.2022
Gewicht:	0,483 kg