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Secrets in the Fields...

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Published on Dec 28, 2008

To understand the presence of objects in string theory that are not strings, but higher dimensional objects, or even points, it helps to know the formulation of Maxwell's equations in the language of differential forms, because this is what tells us that the sources of charge in the Maxwell equations are zero-dimensional objects. Gauge field strengths that are p+2-forms turn out to have sources that are p-dimensional objects. We call these p-branes.
In the regular maxwell equations in d=4 spacetime dimension, the electric and magentic fields are packed together into the field strength F, which satisfies the equation F=dA, d is the exterior derivative, and A is the vector potential, a one-form. The two-form *F is the dual of F relative to the spacetime volume four-form v. (The subscripts on F, etc, below are just to indicate the degree of the differential form.

Electromagnetism is the physics of the electromagnetic field: a field which exerts a force on particles that possess the property of electric charge, and is in turn affected by the presence and motion of those particles.

A changing magnetic field produces an electric field (this is the phenomenon of electromagnetic induction, the basis of operation for electrical generators, induction motors, and transformers). Similarly, a changing electric field generates a magnetic field. Because of this interdependence of the electric and magnetic fields, it makes sense to consider them as a single coherent entity - the electromagnetic field.

The magnetic field is produced by the motion of electric charges, i.e., electric current. The magnetic field causes the magnetic force associated with magnets.The theoretical implications of electromagnetism led to the development of special relativity by Albert Einstein in 1905.

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