國立高雄大學圖資館 |

Language: English

Back

On Hilbert's sixth problem

Record Type:	Electronic resources : Monograph/item
Title/Author:	On Hilbert's sixth problemby Newton C. A. da Costa, Francisco Antonio Doria.
Author:	Costa, Newton C. A. da.
other author:	Doria, Francisco Antonio.
Published:	Cham :Springer International Publishing :2022.
Description:	xiii, 191 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Mathematical physics.
Online resource:	https://doi.org/10.1007/978-3-030-83837-9
ISBN:	9783030838379$q(electronic bk.)

On Hilbert's sixth problem
Costa, Newton C. A. da.

On Hilbert's sixth problem[electronic resource] /by Newton C. A. da Costa, Francisco Antonio Doria. - Cham :Springer International Publishing :2022. - xiii, 191 p. :ill., digital ;24 cm. - Synthese library, studies in epistemology, logic, methodology, and philosophy of science,v. 4412542-8292 ;. - Synthese library, studies in epistemology, logic, methodology, and philosophy of science ;v.375..

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.

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 in the 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.

ISBN: 9783030838379$q(electronic bk.)

Standard No.: 10.1007/978-3-030-83837-9doiSubjects--Topical Terms:

190854
Mathematical physics.

LC Class. No.: QC20

Dewey Class. No.: 530.15

On Hilbert's sixth problem
LDR:03237nmm a2200337 a 4500 001 619971
003 DE-He213
005 20220125150505.0
006 m d
007 cr nn 008maaau
008 221103s2022 sz s 0 eng d
020 $a 9783030838379$q(electronic bk.)
020 $a 9783030838362$q(paper)
024 7 $a 10.1007/978-3-030-83837-9 $2 doi
035 $a 978-3-030-83837-9
040 $a GP $c GP
041 0 $a eng
050 4 $a QC20
072 7 $a PDA $2 bicssc
072 7 $a SCI075000 $2 bisacsh
072 7 $a PDA $2 thema
082 0 4 $a 530.15 $2 23
090 $a QC20 $b .D111 2022
100 1 $a Costa, Newton C. A. da. $3 664194
245 1 0 $a On Hilbert's sixth problem $h [electronic resource] / $c by Newton C. A. da Costa, Francisco Antonio Doria.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2022.
300 $a xiii, 191 p. : $b ill., digital ; $c 24 cm.
490 1 $a Synthese library, studies in epistemology, logic, methodology, and philosophy of science, $x 2542-8292 ; $v v. 441
505 0 $a 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.
520 $a 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 in the 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.
650 0 $a Mathematical physics. $3 190854
650 1 4 $a Philosophy of Science. $3 277156
650 2 4 $a Philosophical Foundations of Physics and Astronomy. $3 913461
650 2 4 $a Mathematical Logic and Foundations. $3 274479
700 1 $a Doria, Francisco Antonio. $3 806875
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Synthese library, studies in epistemology, logic, methodology, and philosophy of science ; $v v.375. $3 739403
856 4 0 $u https://doi.org/10.1007/978-3-030-83837-9
950 $a Religion and Philosophy (SpringerNature-41175)