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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.
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.
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.
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 |