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Electromagnetic tensor, the Glossary

In electromagnetism, the electromagnetic tensor or electromagnetic field tensor (sometimes called the field strength tensor, Faraday tensor or Maxwell bivector) is a mathematical object that describes the electromagnetic field in spacetime.^[1]

62 relations: Action (physics), Ampère's circuital law, Cartesian coordinate system, Charge conservation, Charge density, Classical electromagnetism, Classification of electromagnetic fields, Conservative vector field, Continuity equation, Covariant derivative, Covariant formulation of classical electromagnetism, Covariant transformation, Current density, Curvature form, Curved space, Determinant, Differential form, Dirac spinor, Electric field, Electromagnetic field, Electromagnetic four-potential, Electromagnetic stress–energy tensor, Electromagnetism, Electrostatics, Euler–Lagrange equation, Exterior derivative, Faraday's law of induction, Fermionic field, Four-current, Four-gradient, Frame of reference, Gauss's law, Gauss's law for magnetism, Gluon field strength tensor, Gravitation (book), Hamiltonian field theory, Hermann Minkowski, Hodge star operator, Lagrangian (field theory), Levi-Civita symbol, Lorentz scalar, Magnetic field, Magnetostatics, Matrix (mathematics), Maxwell's equations, Maxwell's equations in curved spacetime, Metric signature, Minkowski space, Oxford University Press, Partial derivative, ... Expand index (12 more) »
Minkowski spacetime
Tensor physical quantities
Tensors in general relativity

Action (physics)

In physics, action is a scalar quantity that describes how the balance of kinetic versus potential energy of a physical system changes with trajectory.

See Electromagnetic tensor and Action (physics)

Ampère's circuital law

In classical electromagnetism, Ampère's circuital law (not to be confused with Ampère's force law) relates the circulation of a magnetic field around a closed loop to the electric current passing through the loop. Electromagnetic tensor and Ampère's circuital law are electromagnetism.

See Electromagnetic tensor and Ampère's circuital law

Cartesian coordinate system

In geometry, a Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of real numbers called coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, called coordinate lines, coordinate axes or just axes (plural of axis) of the system.

See Electromagnetic tensor and Cartesian coordinate system

Charge conservation

In physics, charge conservation is the principle that the total electric charge in an isolated system never changes. Electromagnetic tensor and charge conservation are electromagnetism.

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Charge density

In electromagnetism, charge density is the amount of electric charge per unit length, surface area, or volume.

See Electromagnetic tensor and Charge density

Classical electromagnetism

Classical electromagnetism or classical electrodynamics is a branch of theoretical physics that studies the interactions between electric charges and currents using an extension of the classical Newtonian model. Electromagnetic tensor and classical electromagnetism are electromagnetism.

See Electromagnetic tensor and Classical electromagnetism

Classification of electromagnetic fields

In differential geometry and theoretical physics, the classification of electromagnetic fields is a pointwise classification of bivectors at each point of a Lorentzian manifold. Electromagnetic tensor and classification of electromagnetic fields are electromagnetism.

See Electromagnetic tensor and Classification of electromagnetic fields

Conservative vector field

In vector calculus, a conservative vector field is a vector field that is the gradient of some function.

See Electromagnetic tensor and Conservative vector field

Continuity equation

A continuity equation or transport equation is an equation that describes the transport of some quantity.

See Electromagnetic tensor and Continuity equation

Covariant derivative

In mathematics, the covariant derivative is a way of specifying a derivative along tangent vectors of a manifold.

See Electromagnetic tensor and Covariant derivative

Covariant formulation of classical electromagnetism

The covariant formulation of classical electromagnetism refers to ways of writing the laws of classical electromagnetism (in particular, Maxwell's equations and the Lorentz force) in a form that is manifestly invariant under Lorentz transformations, in the formalism of special relativity using rectilinear inertial coordinate systems. Electromagnetic tensor and covariant formulation of classical electromagnetism are electromagnetism.

See Electromagnetic tensor and Covariant formulation of classical electromagnetism

Covariant transformation

In physics, a covariant transformation is a rule that specifies how certain entities, such as vectors or tensors, change under a change of basis.

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Current density

In electromagnetism, current density is the amount of charge per unit time that flows through a unit area of a chosen cross section.

See Electromagnetic tensor and Current density

Curvature form

In differential geometry, the curvature form describes curvature of a connection on a principal bundle.

See Electromagnetic tensor and Curvature form

Curved space

Curved space often refers to a spatial geometry which is not "flat", where a flat space has zero curvature, as described by Euclidean geometry.

See Electromagnetic tensor and Curved space

Determinant

In mathematics, the determinant is a scalar-valued function of the entries of a square matrix.

See Electromagnetic tensor and Determinant

Differential form

In mathematics, differential forms provide a unified approach to define integrands over curves, surfaces, solids, and higher-dimensional manifolds.

See Electromagnetic tensor and Differential form

Dirac spinor

In quantum field theory, the Dirac spinor is the spinor that describes all known fundamental particles that are fermions, with the possible exception of neutrinos.

See Electromagnetic tensor and Dirac spinor

Electric field

An electric field (sometimes called E-field) is the physical field that surrounds electrically charged particles. Electromagnetic tensor and electric field are electromagnetism.

See Electromagnetic tensor and Electric field

Electromagnetic field

An electromagnetic field (also EM field) is a physical field, mathematical functions of position and time, representing the influences on and due to electric charges. Electromagnetic tensor and electromagnetic field are electromagnetism.

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Electromagnetic four-potential

An electromagnetic four-potential is a relativistic vector function from which the electromagnetic field can be derived. Electromagnetic tensor and electromagnetic four-potential are electromagnetism and theory of relativity.

See Electromagnetic tensor and Electromagnetic four-potential

Electromagnetic stress–energy tensor

In relativistic physics, the electromagnetic stress–energy tensor is the contribution to the stress–energy tensor due to the electromagnetic field. Electromagnetic tensor and electromagnetic stress–energy tensor are electromagnetism and tensor physical quantities.

See Electromagnetic tensor and Electromagnetic stress–energy tensor

Electromagnetism

In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields.

See Electromagnetic tensor and Electromagnetism

Electrostatics

Electrostatics is a branch of physics that studies slow-moving or stationary electric charges. Electromagnetic tensor and Electrostatics are electromagnetism.

See Electromagnetic tensor and Electrostatics

Euler–Lagrange equation

In the calculus of variations and classical mechanics, the Euler–Lagrange equations are a system of second-order ordinary differential equations whose solutions are stationary points of the given action functional.

See Electromagnetic tensor and Euler–Lagrange equation

Exterior derivative

On a differentiable manifold, the exterior derivative extends the concept of the differential of a function to differential forms of higher degree.

See Electromagnetic tensor and Exterior derivative

Faraday's law of induction

Faraday's law of induction (or simply Faraday's law) is a law of electromagnetism predicting how a magnetic field will interact with an electric circuit to produce an electromotive force (emf).

See Electromagnetic tensor and Faraday's law of induction

Fermionic field

In quantum field theory, a fermionic field is a quantum field whose quanta are fermions; that is, they obey Fermi–Dirac statistics.

See Electromagnetic tensor and Fermionic field

Four-current

In special and general relativity, the four-current (technically the four-current density) is the four-dimensional analogue of the current density, with units of charge per unit time per unit area. Electromagnetic tensor and four-current are electromagnetism.

See Electromagnetic tensor and Four-current

Four-gradient

In differential geometry, the four-gradient (or 4-gradient) \boldsymbol is the four-vector analogue of the gradient \vec from vector calculus.

See Electromagnetic tensor and Four-gradient

Frame of reference

In physics and astronomy, a frame of reference (or reference frame) is an abstract coordinate system whose origin, orientation, and scale are specified by a set of reference points―geometric points whose position is identified both mathematically (with numerical coordinate values) and physically (signaled by conventional markers).

See Electromagnetic tensor and Frame of reference

Gauss's law

In physics (specifically electromagnetism), Gauss's law, also known as Gauss's flux theorem (or sometimes Gauss's theorem), is one of Maxwell's equations. Electromagnetic tensor and Gauss's law are electromagnetism.

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Gauss's law for magnetism

In physics, Gauss's law for magnetism is one of the four Maxwell's equations that underlie classical electrodynamics.

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Gluon field strength tensor

In theoretical particle physics, the gluon field strength tensor is a second order tensor field characterizing the gluon interaction between quarks.

See Electromagnetic tensor and Gluon field strength tensor

Gravitation (book)

Gravitation is a widely adopted textbook on Albert Einstein's general theory of relativity, written by Charles W. Misner, Kip S. Thorne, and John Archibald Wheeler.

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Hamiltonian field theory

In theoretical physics, Hamiltonian field theory is the field-theoretic analogue to classical Hamiltonian mechanics.

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Hermann Minkowski

Hermann Minkowski (22 June 1864 – 12 January 1909) was a mathematician and professor at the University of Königsberg, the University of Zürich, and the University of Göttingen, described variously as German, Polish, or Lithuanian-German, or Russian.

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Hodge star operator

In mathematics, the Hodge star operator or Hodge star is a linear map defined on the exterior algebra of a finite-dimensional oriented vector space endowed with a nondegenerate symmetric bilinear form.

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Lagrangian (field theory)

Lagrangian field theory is a formalism in classical field theory.

See Electromagnetic tensor and Lagrangian (field theory)

Levi-Civita symbol

In mathematics, particularly in linear algebra, tensor analysis, and differential geometry, the Levi-Civita symbol or Levi-Civita epsilon represents a collection of numbers; defined from the sign of a permutation of the natural numbers, for some positive integer.

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Lorentz scalar

In a relativistic theory of physics, a Lorentz scalar is a scalar expression whose value is invariant under any Lorentz transformation. Electromagnetic tensor and Lorentz scalar are Minkowski spacetime and theory of relativity.

See Electromagnetic tensor and Lorentz scalar

Magnetic field

A magnetic field (sometimes called B-field) is a physical field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials.

See Electromagnetic tensor and Magnetic field

Magnetostatics

Magnetostatics is the study of magnetic fields in systems where the currents are steady (not changing with time).

See Electromagnetic tensor and Magnetostatics

Matrix (mathematics)

In mathematics, a matrix (matrices) is a rectangular array or table of numbers, symbols, or expressions, with elements or entries arranged in rows and columns, which is used to represent a mathematical object or property of such an object.

See Electromagnetic tensor and Matrix (mathematics)

Maxwell's equations

Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, electric and magnetic circuits. Electromagnetic tensor and Maxwell's equations are electromagnetism.

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Maxwell's equations in curved spacetime

In physics, Maxwell's equations in curved spacetime govern the dynamics of the electromagnetic field in curved spacetime (where the metric may not be the Minkowski metric) or where one uses an arbitrary (not necessarily Cartesian) coordinate system.

See Electromagnetic tensor and Maxwell's equations in curved spacetime

Metric signature

In mathematics, the signature of a metric tensor g (or equivalently, a real quadratic form thought of as a real symmetric bilinear form on a finite-dimensional vector space) is the number (counted with multiplicity) of positive, negative and zero eigenvalues of the real symmetric matrix of the metric tensor with respect to a basis.

See Electromagnetic tensor and Metric signature

Minkowski space

In physics, Minkowski space (or Minkowski spacetime) is the main mathematical description of spacetime in the absence of gravitation. Electromagnetic tensor and Minkowski space are Minkowski spacetime.

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Oxford University Press

Oxford University Press (OUP) is the publishing house of the University of Oxford.

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Partial derivative

In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary).

See Electromagnetic tensor and Partial derivative

Pseudoscalar

In linear algebra, a pseudoscalar is a quantity that behaves like a scalar, except that it changes sign under a parity inversion while a true scalar does not.

See Electromagnetic tensor and Pseudoscalar

Quantization of the electromagnetic field

The quantization of the electromagnetic field is a procedure in physics turning Maxwell's classical electromagnetic waves into particles called photons.

See Electromagnetic tensor and Quantization of the electromagnetic field

Quantum electrodynamics

In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. Electromagnetic tensor and quantum electrodynamics are electromagnetism.

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Quantum field theory

In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics.

See Electromagnetic tensor and Quantum field theory

Ricci calculus

In mathematics, Ricci calculus constitutes the rules of index notation and manipulation for tensors and tensor fields on a differentiable manifold, with or without a metric tensor or connection.

See Electromagnetic tensor and Ricci calculus

Riemann–Silberstein vector

In mathematical physics, in particular electromagnetism, the Riemann–Silberstein vector or Weber vector named after Bernhard Riemann, Heinrich Martin Weber and Ludwik Silberstein, (or sometimes ambiguously called the "electromagnetic field") is a complex vector that combines the electric field E and the magnetic field B. Electromagnetic tensor and Riemann–Silberstein vector are electromagnetism.

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Skew-symmetric matrix

In mathematics, particularly in linear algebra, a skew-symmetric (or antisymmetric or antimetric) matrix is a square matrix whose transpose equals its negative.

See Electromagnetic tensor and Skew-symmetric matrix

Solenoidal vector field

In vector calculus a solenoidal vector field (also known as an incompressible vector field, a divergence-free vector field, or a '''transverse vector field''') is a vector field v with divergence zero at all points in the field: \nabla \cdot \mathbf.

See Electromagnetic tensor and Solenoidal vector field

Special relativity

In physics, the special theory of relativity, or special relativity for short, is a scientific theory of the relationship between space and time. Electromagnetic tensor and special relativity are theory of relativity.

See Electromagnetic tensor and Special relativity

Tensor

In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space.

See Electromagnetic tensor and Tensor

Trace (linear algebra)

In linear algebra, the trace of a square matrix, denoted, is defined to be the sum of elements on the main diagonal (from the upper left to the lower right) of.

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Wiley (publisher)

John Wiley & Sons, Inc., commonly known as Wiley, is an American multinational publishing company that focuses on academic publishing and instructional materials.

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References

[1] https://en.wikipedia.org/wiki/Electromagnetic_tensor

Also known as Dual electromagnetic field tensor, EM field tensor, EM tensor, Electromagnetic Field Tensor, Electromagnetic field strength, Faraday tensor, Faraday's tensor, Field strength tensor, Maxwell bivector.

, Pseudoscalar, Quantization of the electromagnetic field, Quantum electrodynamics, Quantum field theory, Ricci calculus, Riemann–Silberstein vector, Skew-symmetric matrix, Solenoidal vector field, Special relativity, Tensor, Trace (linear algebra), Wiley (publisher).

Electromagnetic tensor, the Glossary

Table of Contents

See also

Minkowski spacetime

Tensor physical quantities

Tensors in general relativity

References