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Dirac`s Equation and the Sea of Negative Energy, Music of the
Dirac`s Equation and the Sea of Negative Energy, Music of the

... test of the soundness of a theory, as the general trend of successful science is from disorder and complexity toward order and simplicity. Before the advent of modern chemistry, although matter was thought to consist of the four “elements” earth, air, fire, and water, these could combine in unlimite ...
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... – 1820, Oersted and Ampère established the relation between the electric currents and the generation of a magnetic field. – Ampère define the fundamental theory of the electrodinamics, relation between current and forces created by the magnetic fields. – 1831, Faraday shows the autoinduction phenome ...
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... Earth’s magnetosphere at times attained negative potentials of several kilovolts. A record potential of - 19 kV was observed on ATS-6 (Olsen and Purvis 1981). The largest potentials were observed during times of magnetic activity as these synchronousorbit spacecraft entered the Earth’s shadow. In qu ...
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Introduction to gauge theory

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; 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. 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.
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