![]() ![]() 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. Gauge symmetry was generalized mathematically in 1954 by Chen Ning Yang and Robert Mills in an attempt to describe the strong nuclear forces. 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. : 5, 12 Although Weyl's choice of the gauge was incorrect, the name "gauge" stuck to the approach. ![]() Later Hermann Weyl, inspired by success in Einstein's general relativity, conjectured (incorrectly, as it turned out) in 1919 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 electromagnetism. Similarly unnoticed, Hilbert had derived Einstein's equations of general relativity by postulating a symmetry under any change of coordinates, just as Einstein was completing his work. The importance of this symmetry remained unnoticed in the earliest formulations. 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 culmination of these efforts is the Standard Model, a quantum field theory that accurately predicts all of the fundamental interactions except gravity. The nature of these particles is determined by the nature of the gauge transformations. Perturbative quantum field theory (usually employed for scattering theory) describes forces in terms of force-mediating particles called gauge bosons. 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. 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. 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. Under a gauge transformation in which a constant is added to V, no observable change occurs in E or B. Generally, any theory that has the property of gauge invariance is considered a gauge theory.įor example, in electromagnetism the electric field E and the magnetic field B are observable, while the potentials V ("voltage") and A (the vector potential) are not. Since any kind of invariance under a field transformation is considered a symmetry, gauge invariance is sometimes called gauge symmetry. ![]() For example, if you could measure the color of lead balls and discover that when you change the color, you still fit the same number of balls in a pound, the property of "color" would show gauge invariance. ![]() A transformation from one such field configuration to another is called a gauge transformation the lack of change in the measurable quantities, despite the field being transformed, is a property called gauge invariance. In field theories, different configurations of the unobservable fields can result in identical observable quantities. Using the number of balls, the density of lead, and the formula for calculating the volume of a sphere from its diameter, one could indirectly determine the diameter of a single lead ball. For example, say you cannot measure the diameter of a lead ball, but you can determine how many lead balls, which are equal in every way, are required to make a pound. 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. 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. The word gauge means a measurement, a thickness, an in-between distance (as in railroad tracks), or a resulting number of units per certain parameter (a number of loops in an inch of fabric or a number of lead balls in a pound of ammunition). A gauge theory is a type of theory in physics. ![]()
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