Книги: "Equivalence principles"

1

Molitor, Paul. Equivalence checking of digital circuits: Fundamentals, principles, methods. Boston: Kluwer Academic Publishers, 2004.

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2

United States. National Aeronautics and Space Administration., ed. Satellite Test of the Equivalence Principle STEP. [Washington, DC: National Aeronautics and Space Administration, 1994.

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3

United States. National Aeronautics and Space Administration., ed. Satellite Test of the Equivalence Principle STEP. [Washington, DC: National Aeronautics and Space Administration, 1994.

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4

Lyle, Stephen. Uniformly accelerating charged particles: A threat to equivalence principle. Berlin: Springer, 2008.

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5

Rowan-Robinson, Jeremy. The principle of equivalence and the limits of disturbance compensation. London: Sweet & Maxwell, 1994.

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6

Everitt, C. W. F. A preliminary study of a cryogenic equivalence principle experiment on shuttle: Final report. Stanford, CA: W.W. Hansen Laboratories of Physics, Stanford University, 1985.

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7

Colloquy on European Law (19th 1989 Luxembourg). Abuse of rights and equivalent concepts: The principle and its present day application : proceedings of the nineteenth colloquy on European law, Luxembourg 6-9 October 1989. Strasbourg: Council of Europe, 1988.

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8

Colloquy on European Law (19th 1989 Luxembourg). Abuse of rights and equivalent concepts: The principle and its present day application : proceedings of the nineteenth colloquy on European law, Luxembourg, 6-9 November 1989. Strasbourg: Council of Europe, 1990.

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9

Colloquy on European Law. (19th 1989 Luxembourg). Abuse of rights and equivalent concepts: The principle and its present day application : proceedings of the nineteenth Colloquy on European Law, Luxembourg, 6-9 November 1989. Strasbourg: Council of Europe, 1990.

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10

Frank, Abraham. Mi-tarbut shel beḥinot le-pedagogyah ʻakhshaṿit: From examination culture to current pedagogy : ha-maʻaśeh ha-ḥinukhi be-Yiśraʼel liḳrat shenat 2020. Tel-Aviv: Resling, 2013.

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11

Molitor, Paul. Equivalence Checking of Digital Circuits: "Fundamentals, Principles, Methods". Springer, 2010.

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12

Equivalence Checking of Digital Circuits: Fundamentals, Principles, Methods. Springer, 2004.

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13

Kennefick, Daniel. Three and a Half Principles: The Origins of Modern Relativity Theory. Edited by Jed Z. Buchwald and Robert Fox. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780199696253.013.27.

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This article explores the origins of modern relativity theory. In his 1905 paper On the Electrodynamics of Moving Bodies, Albert Einstein directly addressed one of the largest issues of the time. Electrodynamics aims to describe the motion of charged particles (usually thought of as electrons), whose interaction through the electromagnetic field, as described by Maxwell’s equations, affects their respective motions. The problem was so complex because the electromagnetic field theory was not an action-at-a-distance theory. This article begins with an overview of the principle of relativity and of the constancy of the speed of light, followed by a discussion on the relativity of simultaneity, the mass–energy equivalence, and experimental tests of special relativity. It also examines the principle of equivalence, the concepts of spacetime curvature and general covariance, and Mach’s principle. Finally, it considers experimental predictions of general relativity.

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14

Deruelle, Nathalie, and Jean-Philippe Uzan. The equivalence principle. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0041.

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This chapter recalls several relevant aspects of Newton’s theory of gravity, as well as Maxwell’s theory of electromagnetism, to describe the conceptual path that Albert Einstein followed in going from the theory of special relativity to general relativity. Looking at 1907 and beyond, the chapter shows that the ambition of Einstein was to construct a theory in which all reference frames (and therefore none) were privileged. Moreover, there were no longer any inertial forces, no ordering of Newton’s absolute space. Therefore, Einstein’s theory was one in which the laws of physics had the same form in all frames, inertial or not, so that no frame could be regarded as being privileged. In brief, he sought a theory of general relativity.

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15

Wittman, David M. The Equivalence Principle. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199658633.003.0013.

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The equivalence principle is an important thinking tool to bootstrap our thinking from the inertial coordinate systems of special relativity to the more complex coordinate systems that must be used in the presence of gravity (general relativity). The equivalence principle posits that at a given event gravity accelerates everything equally, so gravity is equivalent to an accelerating coordinate system.This conjecture is well supported by precise experiments, so we explore the consequences in depth: gravity curves the trajectory of light as it does other projectiles; the effects of gravity disappear in a freely falling laboratory; and gravitymakes time runmore slowly in the basement than in the attic—a gravitational form of time dilation. We show how this is observable via gravitational redshift. Subsequent chapters will build on this to show how the spacetime metric varies with location.

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16

Watson, Max, Caroline Lucas, Andrew Hoy, and Jo Wells. The management of pain. Oxford University Press, 2010. http://dx.doi.org/10.1093/med/9780199234356.003.0012.

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This chapter covers physical pain in patients with cancer, assessment of pain, pain classification, principles of pain management, breakthrough pain, step 1 analgesics, step 2 analgesics, and step 3 analgesics. The chapter also covers opioid equivalence for transdermal patches, approximate equivalent doses for opioid analgesics for adults, neuropathic pain, anaesthetic procedures in palliative care, chemical neurolysis for cancer pain, and pain and difficulties in communication.

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17

Tran, Thanh V., Tam Nguyen, and Keith Chan. Overview of Culture and Cross-Cultural Research. Oxford University Press, 2018. http://dx.doi.org/10.1093/acprof:oso/9780190496470.003.0001.

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Different academic disciplines and schools of thoughts often have different definitions and categorizations of culture. No agreement has ever been reached in defining culture. This chapter discusses the concept of culture and reviews the basic principles of multidisciplinary cross-cultural research. The readers are introduced to cross-cultural research in anthropology, psychology, political science, and sociology. These cross-cultural research fields offer social work both theoretical and methodological resources. The readers will find that all cross-cultural research fields share the same concern—that is, the equivalence of research instruments. One cannot draw meaningful comparisons of behavioral problems, social values, or psychological status between or across different cultural groups in the absence of cross-culturally equivalent research instruments. Although this book emphasizes the importance of measurement equivalence in cross-cultural social work research and evaluation, the issues of cultural sensitivity and cultural appropriateness are the foundation of all types of social work research and interventions.

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18

Lebed, Andrei G. Breakdown of Einstein's Equivalence Principle. WORLD SCIENTIFIC, 2022. http://dx.doi.org/10.1142/12759.

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19

STEP: Testing the equivalence principle in space : proceedings of an international symposium held in Pisa, Italy, 6-8 April 1993. Noordwijk, The Netherlands: ESA Publications Division, 1996.

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20

National Aeronautics and Space Administration (NASA) Staff. Test of the Equivalence Principle in an Einstein Elevator. Independently Published, 2018.

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21

National Aeronautics and Space Administration (NASA) Staff. Test of the Equivalence Principle in an Einstein Elevator. Independently Published, 2018.

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22

Lyle, Stephen. Uniformly Accelerating Charged Particles: A Threat to the Equivalence Principle. Springer, 2010.

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23

Mashhoon, Bahram. Introduction. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198803805.003.0001.

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This introductory chapter is mainly about the locality postulate of the standard relativity theory. The fundamental laws of microphysics have been formulated with respect to inertial observers. However, inertial observers do not in fact exist, since actual observers are accelerated. What do accelerated observers measure? Lorentz invariance is extended to accelerated observers by assuming that they are pointwise inertial. That is, an accelerated observer at each instant is equivalent to an otherwise identical momentarily comoving inertial observer. This hypothesis of locality, which underlies the special and general theories of relativity, is described in detail. The locality postulate fits perfectly together with Einstein’s local principle of equivalence to ensure that every observer in a gravitational field is pointwise inertial. When coupled with the hypothesis of locality, Einstein’s principle of equivalence provides a physical basis for a field theory of gravitation that is consistent with local Lorentz invariance.

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24

Weiss, Helen. Design issues in global mental health trials in low-resource settings. Oxford University Press, 2015. http://dx.doi.org/10.1093/med/9780199680467.003.0004.

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In this chapter we outline the key principles in design and analysis of trials for mental health. The chapter focuses on randomized controlled trials as these are the gold-standard trial design, which minimizes confounding due to other factors and enables us to draw conclusions about the effectiveness of the intervention. Other key principles of trial design discussed in the chapter include methods to develop a clearly stated, testable research hypothesis, definition of well-defined outcomes, appropriate choice of the control condition, masking of providers and participants where possible, realistic sample size estimates, and appropriate data monitoring and statistical analysis plans. The chapter also outlines alternatives to the parallel arm superiority trial design, such as equivalence and non-inferiority trials, cross-over, stepped wedge, fixed adaptive, and patient preference trial designs.

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25

Surowitz, Eugene J., and Engelbert L. Schucking. Einstein's Apple: Homogeneous Einstein Fields. World Scientific Publishing Co Pte Ltd, 2015.

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26

Einstein's Apple: Homogeneous Einstein Fields. World Scientific Publishing Co Pte Ltd, 2015.

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27

Voisin, Claire. Decomposition of the Diagonal. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691160504.003.0003.

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This chapter explains the method initiated by Bloch and Srinivas, which leads to statements of the following: if a smooth projective variety has trivial Chow groups of k-cycles homologous to 0 for k ≤ c − 1, then its transcendental cohomology has geometric coniveau ≤ c. This result is a vast generalization of Mumford's theorem. A major open problem is the converse of this result. It turns out that statements of this kind are a consequence of a general spreading principle for rational equivalence. Consider a smooth projective family X → B and a cycle Z → B, everything defined over C; then, if at the very general point b ∈ B, the restricted cycle Z𝒳b ⊂ X𝒳b is rationally equivalent to 0, there exist a dense Zariski open set U ⊂ B and an integer N such that NZsubscript U is rationally equivalent to 0 on Xsubscript U.

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28

STEP, satellite test of the equivalence principle: Report on the phase A study. [Paris]: European Space Agency, 1993.

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29

Linnebo, Øystein. Dynamic Abstraction. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199641314.003.0003.

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Any abstractionist approach to thin objects faces the threat of paradox, as illustrated by Frege’s inconsistent Basic Law V. The neo-Fregeans Hale and Wright respond by severely restricting the class of acceptable abstraction principles. Their approach is static in the sense that they hold the domain fixed. This approach to abstraction is criticized, and an alternative approach is developed which permits abstraction on a vast class of equivalence relations. This alternative approach is dynamic in the sense that abstraction on an extensionally specified domain (i.e. a domain specified by means of a plurality of objects) may result in a larger such domain. A form of absolute generality is nevertheless possible, provided that the associated domain is understood in an intensional sense (i.e. it cannot be specified by means of a plurality).

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30

Tran, Thanh, Tam Nguyen, and Keith Chan. Developing Cross-Cultural Measurement in Social Work Research and Evaluation. Oxford University Press, 2018. http://dx.doi.org/10.1093/acprof:oso/9780190496470.001.0001.

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Given the demographic changes and the reality of cultural diversity in the United States and other parts of the world today, social work researchers are increasingly aware of the need to conduct cross-cultural research and evaluation, whether for hypothesis testing or for outcome evaluation. This book’s aims are twofold: to provide an overview of issues and techniques relevant to the development of cross-cultural measures and to provide readers with a step-by-step approach to the assessment of cross-cultural equivalence of measurement properties. There is no discussion of statistical theory and principles underlying the statistical techniques presented in this book. Rather, this book is concerned with applied theories and principles of cross-cultural research, and draws information from existing work in the social sciences, public domain secondary data, and primary data from the author’s research. In this second edition, several changes have been made throughout the book and a new chapter on item response theory has been added. The chapter on developing new cross-cultural instrument has also been expanded with a concrete example.

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31

Bhugra, Dinesh, Antonio Ventriglio, and Kamaldeep S. Bhui. Assessment tools and cultural formulation. Oxford University Press, 2018. http://dx.doi.org/10.1093/med/9780198723196.003.0005.

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Assessment tools can support clinical assessments but cannot replace them. They can be used for a number of purposes. They are standardized tools but may require some adjustments if they are being used in cultures other than those in which they were developed. If they have been translated into other languages, it is essential that translation be carried out with proper conceptual equivalence rather than simple literal translation. The experiences of migration and acculturation need to be assessed carefully. Furthermore, for the first time DSM-5 includes concepts of cultural formulation; the key features include cultural identity of individuals, cultural explanations of their illnesses, cultural factors related to their environment and levels of functioning, various cultural elements of relationship between the clinician and the individual, and overall cultural assessment. At the heart of cultural formulation lie the principles of cultural sensitivity.

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32

Lyle, Stephen. Uniformly Accelerating Charged Particles. Springer, 2008.

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33

Solymar, L., D. Walsh, and R. R. A. Syms. Principles of semiconductor devices. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198829942.003.0009.

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p–n junctions are examined initially and the potential distribution in the junction region is derived based on Poisson’s equation. Next the operation of the transistor is discussed, both in terms of the physics and of equivalent circuits. Potential distributions in metal–semiconductor junctions are derived and the concept of surface states is introduced. The physics of tunnel junctions is discussed in terms of their band structure. The properties of varactor diodes are described and the possibility of parametric amplification is touched upon. Further devices discussed are field effect transistors, charge-coupled devices, controlled rectifiers, and the Gunn effect. The fabrication of microelectronic circuits is discussed, followed by the more recent but related field of micro-electro-mechanical systems. The discipline of nanoelectronics is introduced including the role of carbon nanotubes. Finally, the effect of the development of semiconductor technology upon society is discussed.

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34

Eisenberg, Melvin A. The Specific-Performance Principle. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199731404.003.0024.

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Chapter 24 considers the most prominent alternative to expectation damages—specific performance. Specific performance is a judicial decree that orders a promisor to render the performance she agreed to render, on pain of a penalty for contempt of court if she does not. The principle that should govern specific-performance—the Specific-Performance Principle—is as follows: actual specific performance should be awarded unless a special moral, policy, or experiential reason suggests otherwise in a given class of cases or the promisee can achieve virtual specific performance by acquiring goods or services in the market that are equivalent to the contracted-for goods or services. Under this principle specific performance should be liberally but not routinely granted.

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35

Baulieu, Laurent, John Iliopoulos, and Roland Sénéor. General Relativity: A Field Theory of Gravitation. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198788393.003.0004.

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General relativity. The equivalence principle and the derivation of the Einstein–Hilbert equations. The geometrical notions of curvature and affine connection are introduced. Geodesics and the bending of light by a gravitational field. General relativity as a gauge invariant classical field theory.

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36

Mashhoon, Bahram. Toward Nonlocal Gravitation. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198803805.003.0004.

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Is gravity nonlocal? Einstein interpreted the principle of equivalence of inertial and gravitational masses to mean that there exists a profound relationship between inertia and gravitation. Based on Einstein’s fundamental insight, it would seem natural to extend history dependence to the gravitational domain. However, it is not clear how to develop a nonlocal extension of Einstein’s local principle of equivalence. To go forward, we therefore choose an indirect approach based on a certain analogy with electromagnetism. In a material medium, the electromagnetic constitutive relations are nonlocal and this fact leads to the nonlocal electrodynamics of media. It turns out that general relativity can be formulated in a form that resembles the electrodynamics of media. Making the corresponding gravitational constitutive relations nonlocal would then lead to nonlocal GR. This indirect approach is adopted in the rest of this book.

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37

Gilbert, Margaret. Problems with Moral Principle Accounts. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198813767.003.0008.

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In offering accounts of the obligation accrued by a promisor on the basis of his promise some theorists invoke a social convention or practice of promising and some do not. Promise theorists of both types generally assume that the primary obligation of a promisor is a moral requirement derived from a moral principle. Taking Thomas Scanlon’s prominent practice-independent account as its focus, this chapter argues that moral principle approaches cannot account for the inevitability of a promisor’s obligation. Nor can they account for its directedness. They cannot therefore account for a promisee’s demand-right which is equivalent to the directed obligation of his promisor. The demand-right problem for promises, therefore, remains unsolved.

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38

Ewan, McKendrick. Ch.7 Non-performance, s.4: Damages, Art.7.4.7. Oxford University Press, 2015. http://dx.doi.org/10.1093/law/9780198702627.003.0156.

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This commentary analyses Article 7.4.7 of the UNIDROIT Principles of International Commercial Contracts (PICC) concerning harm due in part to the aggrieved party. Art 7.4.7 deals with the case in which the harm suffered by the aggrieved party stems in part from its own act or omission or to an event for which it bears the risk. In such a case, the amount of damages shall be reduced to the extent that these factors have contributed to the harm, having regard to the conduct of each of the parties. The principle enshrined in Art 7.4.7 is equivalent in English law to the principle of contributory negligence. The burden of proof is upon the non-performing party to establish that the harm was due in part to an act or omission of the aggrieved party or to another event as to which the aggrieved party bears the risk.

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39

Galileo Galilei (GG) Flight Experiment on the equivalence principle with field emission electric propulsion (FEEP), pre-phase A report, September 1996. 1996.

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40

D, Bingcheng Zhao Ph. Look at the Mechanism Behind the Postulate of the Equivalence Principle: The Mechanism Behind This Extremely Important Postulate Has Been Revealed. Independently Published, 2019.

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41

Arthur, Richard T. W. Motion, Relativity, and Force. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198812869.003.0006.

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This chapter traces the development of Leibniz’s thought on form as the principle of activity of bodies, from his earliest thoughts on motion as interrupted by rests, through his neo-Hobbesian theory of endeavour as the foundation of continuity, to his rejection of this and a return to a variant occasionalist account, “transcreation”, and finally to his introduction of force as the foundation of continuity. It is explained in the chapter how the Principle of Equipollence functions as Leibniz’s Ariadnean thread leading him to his philosophy of force, and how the identification of causes breaks the equivalence of hypotheses regarding motion.

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42

Tenney, James. Meta ⌿ Hodos. Edited by Larry Polansky, Lauren Pratt, Robert Wannamaker, and Michael Winter. University of Illinois Press, 2017. http://dx.doi.org/10.5406/illinois/9780252038723.003.0002.

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In this essay, James Tenney discusses a phenomenology of twentieth-century musical materials and an approach to the study of form. Before describing the musical materials, Tenney examines the factors that account for the increased aural complexity of much of the music of the twentieth century and of some of its effects in our perception of music. He analyzes the gradual use of more and more complex sound-units in place of single tones, one manifestation of which can be seen in the expansion of the very concept of “melodic line” by way of various kinds of doublings. He also talks about the notion of equivalence in Arnold Schoenberg's arguments about consonance/dissonance and compares it with his own principle of equivalence. Tenney goes on to explore the gestalt-factors of cohesion and segregation by referring to the ideas of Max Wertheimer and concludes with an assessment of formal factors in the clang and sequence.

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43

The Hardship Approach In The Unidroit Principles Of International Commercial Contracts And Its Equivalent In German Law Of Obligations A Comparison. Grin Verlag, 2007.

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44

Martinez-Conde, Susana, and Stephen L. Macknik. Vasarely’s Nested Squares and the Alternating Brightness Star Illusion. Oxford University Press, 2017. http://dx.doi.org/10.1093/acprof:oso/9780199794607.003.0054.

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The arts sometimes precede the sciences in the discovery of fundamental visual principles. Victor Vasarely’s “Nested Squares” show an illusory effect in which corners look brighter and more salient than straight edges, despite having equivalent luminance. This chapter summarizes recent research, originally based on Victor Vasarely’s Nested Squares illusion, to discover the related perceptual and underlying physiological principles. The results offer significant insights into how corners, angles, curves, and line endings affect the appearance of brightness, shape, salience, depth, and color in our brains. Concepts covered include the alternating brightness star illusion, center-surround simulations, brain activation, corner perception, and the redundancy-reducing hypothesis.

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45

Lee, Richard. Pulse oximetry and capnography in the ICU. Oxford University Press, 2016. http://dx.doi.org/10.1093/med/9780199600830.003.0073.

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The estimation of arterial oxygen saturation by pulse oximetry and arterial carbon dioxide tension by capnography are vital monitoring techniques in critical care medicine, particularly during intubation, ventilation and transport. Equivalent continuous information is not otherwise available. It is important to understand the principles of measurement and limitations, for safe use and error detection. PETCO2 and oxygen saturation should be regularly checked against PaCO2 and co-oximeter SO2 obtained from the blood gas machine. The PECO2 trace informs endotracheal tube placement, ventilation, and blood flow to the lungs. It is essential their principles of estimation, the information gained and the traps in interpretation are understood.

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46

Deruelle, Nathalie, and Jean-Philippe Uzan. The Nordström theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0028.

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This chapter turns to the description of the interaction of a scalar field with particles which ‘feel’—that is, ‘charged’ particles. If the field is massless, and therefore long-range, and if the particle charge corresponds to its inertial mass, we have what is known as Nordström theory, a coherent theory of gravity which, however, disagrees with experiment. Nordström theory describes gravity by means of a massless scalar field φ‎. According to the ‘weak equivalence principle’, gravitational masses are equal to inertial masses, m = mg. When velocities are small, the gravitational field created is also weak.

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47

Mercati, Flavio. Barbour–Bertotti Best Matching. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198789475.003.0004.

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Barbour and Bertotti’s Mach–Poincaré Principle can be realized in classical mechanics with a mathematical procedure which was beyond the grasp of Leibniz or Newton, and turns out to be equivalent to modern gauge theory. This is the formulation of a variational principle based on ‘best matching’: one transforms subsequent configurations of the system with the Euclidean group, and by minimizing a certain functional a notion of ‘equilocality’ is established: now it makes sense to say that a particle comes back to the same point at different times.

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48

Calvert, Gemma A., Charles Spence, and Barry E. Stein, eds. The Handbook of Multisensory Processes. The MIT Press, 2004. http://dx.doi.org/10.7551/mitpress/3422.001.0001.

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A reference work for the emerging field of multisensory integration, covering multidisciplinary research that goes beyond the traditional "sense-by-sense" approach and recognizes that perception is fundamentally a multisensory experience. This landmark reference work brings together for the first time in one volume the most recent research from different areas of the emerging field of multisensory integration. After many years of using a modality-specific "sense-by-sense" approach, researchers across different disciplines in neuroscience and psychology now recognize that perception is fundamentally a multisensory experience. To understand how the brain synthesizes information from the different senses, we must study not only how information from each sensory modality is decoded but also how this information interacts with the sensory processing taking place within other sensory channels. The findings cited in The Handbook of Multisensory Processes suggest that there are broad underlying principles that govern this interaction, regardless of the specific senses involved. The book is organized thematically into eight sections; each of the 55 chapters presents a state-of-the-art review of its topic by leading researchers in the field. The key themes addressed include multisensory contributions to perception in humans; whether the sensory integration involved in speech perception is fundamentally different from other kinds of multisensory integration; multisensory processing in the midbrain and cortex in model species, including rat, cat, and monkey; behavioral consequences of multisensory integration; modern neuroimaging techniques, including EEG, PET, and fMRI, now being used to reveal the many sites of multisensory processing in the brain; multisensory processes that require postnatal sensory experience to emerge, with examples from multiple species; brain specialization and possible equivalence of brain regions; and clinical studies of such breakdowns of normal sensory integration as brain damage and synesthesia. Bradford Books imprint

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49

McDuff, Dusa, and Dietmar Salamon. Constructing symplectic manifolds. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198794899.003.0008.

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This chapter examines various ways to construct symplectic manifolds and submanifolds. It begins by studying blowing up and down in both the complex and the symplectic contexts. The next section is devoted to a discussion of fibre connected sums and describes Gompf’s construction of symplectic four-manifolds with arbitrary fundamental group. The chapter also contains an exposition of Gromov’s telescope construction, which shows that for open manifolds the h-principle rules and the inclusion of the space of symplectic forms into the space of nondegenerate 2-forms is a homotopy equivalence. The final section outlines Donaldson’s construction of codimension two symplectic submanifolds and explains the associated decompositions of the ambient manifold.

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50

Mercati, Flavio. Best Matching: Technical Details. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198789475.003.0005.

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The best matching procedure described in Chapter 4 is equivalent to the introduction of a principal fibre bundle in configuration space. Essentially one introduces a one-dimensional gauge connection on the time axis, which is a representation of the Euclidean group of rotations and translations (or, possibly, the similarity group which includes dilatations). To accommodate temporal relationalism, the variational principle needs to be invariant under reparametrizations. The simplest way to realize this in point–particle mechanics is to use Jacobi’s reformulation of Mapertuis’ principle. The chapter concludes with the relational reformulation of the Newtonian N-body problem (and its scale-invariant variant).

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