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A gauge theory is a type of theory in physics. Modern theories describe physical forces in terms of fields, e.g., the electromagnetic field, the gravitational field, and fields that describe forces between the elementary particles. A general feature of these field theories is that the fundamental fields cannot be directly measured; however, some associated quantities can be measured, such as charges, energies, and velocities. In field theories, different configurations of the unobservable fields can result in identical observable quantities. A transformation from one such field configuration to another is called a gauge transformation;〔Donald H. Perkins (1982) ''Introduction to High-Energy Physics''. Addison-Wesley: 22.〕〔Roger Penrose (2004) ''The Road to Reality'', p. 451. For an alternative formulation in terms of symmetries of the Lagrangian density, see p. 489. Also see J. D. Jackson (1975) ''Classical Electrodynamics'', 2nd ed. Wiley and Sons: 176.〕 the lack of change in the measurable quantities, despite the field being transformed, is a property called gauge invariance. Since any kind of invariance under a field transformation is considered a symmetry, gauge invariance is sometimes called gauge symmetry. Generally, any theory that has the property of gauge invariance is considered a gauge theory. For example, in electromagnetism the electric and magnetic fields, E and B, are observable, while the potentials ''V'' ("voltage") and A (the vector potential) are not.〔For an argument that ''V'' and A are more fundamental, see Feynman, Leighton, and Sands, The Feynman Lectures, Addison Wesley Longman, 1970, II-15-7,8,12, but this is partly a matter of personal preference.〕 Under a gauge transformation in which a constant is added to ''V'', no observable change occurs in E or B. With the advent of quantum mechanics in the 1920s, and with successive advances in quantum field theory, the importance of gauge transformations has steadily grown. Gauge theories constrain the laws of physics, because all the changes induced by a gauge transformation have to cancel each other out when written in terms of observable quantities. Over the course of the 20th century, physicists gradually realized that all forces (fundamental interactions) arise from the constraints imposed by ''local'' gauge symmetries, in which case the transformations vary from point to point in space and time. Perturbative quantum field theory (usually employed for scattering theory) describes forces in terms of force-mediating particles called gauge bosons. The nature of these particles is determined by the nature of the gauge transformations. The culmination of these efforts is the Standard Model, a quantum field theory that accurately predicts all of the fundamental interactions except gravity. ==History and importance== The earliest field theory having a gauge symmetry was Maxwell's formulation, in 1864–65, of electrodynamics ("A Dynamical Theory of the Electromagnetic Field"). The importance of this symmetry remained unnoticed in the earliest formulations. Similarly unnoticed, Hilbert had derived Einstein's equations of general relativity by postulating a symmetry under any change of coordinates. Later Hermann Weyl, in an attempt to unify general relativity and electromagnetism, conjectured (incorrectly, as it turned out) that invariance under the change of scale or "gauge" (a term inspired by the various track gauges of railroads) might also be a local symmetry of general relativity. Although Weyl's choice of the gauge was incorrect, the name "gauge" stuck to the approach. After the development of quantum mechanics, Weyl, Fock and London modified their gauge choice by replacing the scale factor with a change of wave phase, and applying it successfully to electromagnetism. Gauge symmetry was generalized mathematically in 1954 by Chen Ning Yang and Robert Mills in an attempt to describe the strong nuclear forces. This idea, dubbed Yang–Mills theory, later found application in the quantum field theory of the weak force, and its unification with electromagnetism in the electroweak theory. The importance of gauge theories for physics stems from their tremendous success in providing a unified framework to describe the quantum-mechanical behavior of electromagnetism, the weak force and the strong force. This gauge theory, known as the Standard Model, accurately describes experimental predictions regarding three of the four fundamental forces of nature. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Introduction to gauge theory」の詳細全文を読む スポンサード リンク
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