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Classical field theory

Index Classical field theory

A classical field theory is a physical theory that predicts how one or more physical fields interact with matter through field equations. [1]

101 relations: Action (physics), Affine connection, Albert Einstein, Arthur Eddington, Biot–Savart law, Cauchy stress tensor, Charge density, Classical field theory, Classical physics, Classical unified field theories, Conservation law, Conservative vector field, Coulomb's law, Current density, Curvature form, Density, Determinant, Divergence theorem, Einstein field equations, Einstein tensor, Einstein–Hilbert action, Electric field, Electricity, Electromagnetic field, Electromagnetic four-potential, Electromagnetic tensor, Electromagnetism, Equivalence principle, Fiber bundle, Field (physics), Flow velocity, Four-current, Fundamental interaction, Gauge fixing, Gauge theory, Gauss's law, Gauss's law for gravity, General relativity, Gradient, Gravitational constant, Gravitational field, Gravitational potential, Gravity, Gustav Mie, Hamiltonian field theory, Hermann Weyl, Higgs field (classical), Inverse-square law, James Clerk Maxwell, James MacCullagh, ..., Kaluza–Klein theory, Lagrangian (field theory), Laplace's equation, Line of force, Lorentz covariance, Lorenz gauge condition, Magnetic field, Magnetic monopole, Magnetic potential, Magnetism, Mass, Maxwell's equations, Metric tensor (general relativity), Michael Faraday, Multipole expansion, Navier–Stokes equations, Newton's law of universal gravitation, Nuclear force, Orbit, Partial derivative, Physical quantity, Poisson's equation, Potential theory, Prussian Academy of Sciences, Quantum field theory, Reflection (physics), Refraction, Relativistic wave equations, Retarded potential, Ricci curvature, Royal Irish Academy, Scalar curvature, Scalar potential, Space, Spacetime, Special relativity, Spherical harmonics, Tensor, Tensor calculus, Tensor field, Test particle, Theodor Kaluza, Theoretical physics, Theory of relativity, Time, Tullio Levi-Civita, Unit vector, Vacuum solution, Variational methods in general relativity, Vector field, Weak interaction. Expand index (51 more) »

Action (physics)

In physics, action is an attribute of the dynamics of a physical system from which the equations of motion of the system can be derived.

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Affine connection

In the branch of mathematics called differential geometry, an affine connection is a geometric object on a smooth manifold which connects nearby tangent spaces, so it permits tangent vector fields to be differentiated as if they were functions on the manifold with values in a fixed vector space.

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Albert Einstein

Albert Einstein (14 March 1879 – 18 April 1955) was a German-born theoretical physicist who developed the theory of relativity, one of the two pillars of modern physics (alongside quantum mechanics).

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Arthur Eddington

Sir Arthur Stanley Eddington (28 December 1882 – 22 November 1944) was an English astronomer, physicist, and mathematician of the early 20th century who did his greatest work in astrophysics.

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Biot–Savart law

In physics, specifically electromagnetism, the Biot–Savart law is an equation describing the magnetic field generated by a stationary electric current.

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Cauchy stress tensor

In continuum mechanics, the Cauchy stress tensor \boldsymbol\sigma, true stress tensor, or simply called the stress tensor is a second order tensor named after Augustin-Louis Cauchy.

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Charge density

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

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Classical field theory

A classical field theory is a physical theory that predicts how one or more physical fields interact with matter through field equations.

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Classical physics

Classical physics refers to theories of physics that predate modern, more complete, or more widely applicable theories.

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Classical unified field theories

Since the 19th century, some physicists, notably Albert Einstein, have attempted to develop a single theoretical framework that can account for all the fundamental forces of nature – a unified field theory.

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Conservation law

In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves over time.

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Conservative vector field

In vector calculus, a conservative vector field is a vector field that is the gradient of some function, known in this context as a scalar potential.

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Coulomb's law

Coulomb's law, or Coulomb's inverse-square law, is a law of physics for quantifying the amount of force with which stationary electrically charged particles repel or attract each other.

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Current density

In electromagnetism, current density is the electric current per unit area of cross section.

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Curvature form

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

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Density

The density, or more precisely, the volumetric mass density, of a substance is its mass per unit volume.

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Determinant

In linear algebra, the determinant is a value that can be computed from the elements of a square matrix.

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Divergence theorem

In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, reprinted in is a result that relates the flow (that is, flux) of a vector field through a surface to the behavior of the vector field inside the surface.

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Einstein field equations

The Einstein field equations (EFE; also known as Einstein's equations) comprise the set of 10 equations in Albert Einstein's general theory of relativity that describe the fundamental interaction of gravitation as a result of spacetime being curved by mass and energy.

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Einstein tensor

In differential geometry, the Einstein tensor (named after Albert Einstein; also known as the trace-reversed Ricci tensor) is used to express the curvature of a pseudo-Riemannian manifold.

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Einstein–Hilbert action

The Einstein–Hilbert action (also referred to as Hilbert action) in general relativity is the action that yields the Einstein field equations through the principle of least action.

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Electric field

An electric field is a vector field surrounding an electric charge that exerts force on other charges, attracting or repelling them.

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Electricity

Electricity is the set of physical phenomena associated with the presence and motion of electric charge.

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Electromagnetic field

An electromagnetic field (also EMF or EM field) is a physical field produced by electrically charged objects.

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Electromagnetic four-potential

An electromagnetic four-potential is a relativistic vector function from which the electromagnetic field can be derived.

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Electromagnetic tensor

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.

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Electromagnetism

Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles.

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Equivalence principle

In the theory of general relativity, the equivalence principle is any of several related concepts dealing with the equivalence of gravitational and inertial mass, and to Albert Einstein's observation that the gravitational "force" as experienced locally while standing on a massive body (such as the Earth) is the same as the pseudo-force experienced by an observer in a non-inertial (accelerated) frame of reference.

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Fiber bundle

In mathematics, and particularly topology, a fiber bundle (or, in British English, fibre bundle) is a space that is locally a product space, but globally may have a different topological structure.

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Field (physics)

In physics, a field is a physical quantity, represented by a number or tensor, that has a value for each point in space and time.

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Flow velocity

In continuum mechanics the macroscopic velocity, also flow velocity in fluid dynamics or drift velocity in electromagnetism, is a vector field used to mathematically describe the motion of a continuum.

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Four-current

In special and general relativity, the four-current (technically the four-current density) is the four-dimensional analogue of the electric current density.

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Fundamental interaction

In physics, the fundamental interactions, also known as fundamental forces, are the interactions that do not appear to be reducible to more basic interactions.

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Gauge fixing

In the physics of gauge theories, gauge fixing (also called choosing a gauge) denotes a mathematical procedure for coping with redundant degrees of freedom in field variables.

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Gauge theory

In physics, a gauge theory is a type of field theory in which the Lagrangian is invariant under certain Lie groups of local transformations.

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Gauss's law

In physics, Gauss's law, also known as Gauss's flux theorem, is a law relating the distribution of electric charge to the resulting electric field.

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Gauss's law for gravity

In physics, Gauss's law for gravity, also known as Gauss's flux theorem for gravity, is a law of physics that is essentially equivalent to Newton's law of universal gravitation.

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General relativity

General relativity (GR, also known as the general theory of relativity or GTR) is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics.

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Gradient

In mathematics, the gradient is a multi-variable generalization of the derivative.

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Gravitational constant

The gravitational constant (also known as the "universal gravitational constant", the "Newtonian constant of gravitation", or the "Cavendish gravitational constant"), denoted by the letter, is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton's law of universal gravitation and in Albert Einstein's general theory of relativity.

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Gravitational field

In physics, a gravitational field is a model used to explain the influence that a massive body extends into the space around itself, producing a force on another massive body.

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Gravitational potential

In classical mechanics, the gravitational potential at a location is equal to the work (energy transferred) per unit mass that would be needed to move the object from a fixed reference location to the location of the object.

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Gravity

Gravity, or gravitation, is a natural phenomenon by which all things with mass or energy—including planets, stars, galaxies, and even light—are brought toward (or gravitate toward) one another.

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Gustav Mie

Gustav Adolf Feodor Wilhelm Ludwig Mie (29 September 1868 – 13 February 1957) was a German physicist.

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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 Weyl

Hermann Klaus Hugo Weyl, (9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist and philosopher.

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Higgs field (classical)

Spontaneous symmetry breaking, a vacuum Higgs field, and its associated fundamental particle the Higgs boson are quantum phenomena.

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Inverse-square law

The inverse-square law, in physics, is any physical law stating that a specified physical quantity or intensity is inversely proportional to the square of the distance from the source of that physical quantity.

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James Clerk Maxwell

James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish scientist in the field of mathematical physics.

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James MacCullagh

James MacCullagh (1809 – 24 October 1847) was an Irish mathematician.

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Kaluza–Klein theory

In physics, Kaluza–Klein theory (KK theory) is a classical unified field theory of gravitation and electromagnetism built around the idea of a fifth dimension beyond the usual four of space and time and considered an important precursor to string theory.

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Lagrangian (field theory)

Lagrangian field theory is a formalism in classical field theory.

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Laplace's equation

In mathematics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace who first studied its properties.

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Line of force

A line of force in Faraday's extended sense is synonymous with Maxwell's line of induction.

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Lorentz covariance

In relativistic physics, Lorentz symmetry, named for Hendrik Lorentz, is an equivalence of observation or observational symmetry due to special relativity implying that the laws of physics stay the same for all observers that are moving with respect to one another within an inertial frame.

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Lorenz gauge condition

In electromagnetism, the Lorenz gauge condition or Lorenz gauge is a partial gauge fixing of the electromagnetic vector potential.

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Magnetic field

A magnetic field is a vector field that describes the magnetic influence of electrical currents and magnetized materials.

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Magnetic monopole

A magnetic monopole is a hypothetical elementary particle in particle physics that is an isolated magnet with only one magnetic pole (a north pole without a south pole or vice versa).

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Magnetic potential

The term magnetic potential can be used for either of two quantities in classical electromagnetism: the magnetic vector potential, or simply vector potential, A; and the magnetic scalar potential ψ. Both quantities can be used in certain circumstances to calculate the magnetic field B. The more frequently used magnetic vector potential is defined so that its curl is equal to the magnetic field: curl A.

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Magnetism

Magnetism is a class of physical phenomena that are mediated by magnetic fields.

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Mass

Mass is both a property of a physical body and a measure of its resistance to acceleration (a change in its state of motion) when a net force is applied.

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Maxwell's equations

Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits.

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Metric tensor (general relativity)

In general relativity, the metric tensor (in this context often abbreviated to simply the metric) is the fundamental object of study.

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Michael Faraday

Michael Faraday FRS (22 September 1791 – 25 August 1867) was an English scientist who contributed to the study of electromagnetism and electrochemistry.

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Multipole expansion

A multipole expansion is a mathematical series representing a function that depends on angles—usually the two angles on a sphere.

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Navier–Stokes equations

In physics, the Navier–Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of viscous fluid substances.

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Newton's law of universal gravitation

Newton's law of universal gravitation states that a particle attracts every other particle in the universe with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

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Nuclear force

The nuclear force (or nucleon–nucleon interaction or residual strong force) is a force that acts between the protons and neutrons of atoms.

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Orbit

In physics, an orbit is the gravitationally curved trajectory of an object, such as the trajectory of a planet around a star or a natural satellite around a planet.

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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).

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Physical quantity

A physical quantity is a physical property of a phenomenon, body, or substance, that can be quantified by measurement.or we can say that quantities which we come across during our scientific studies are called as the physical quantities...

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Poisson's equation

In mathematics, Poisson's equation is a partial differential equation of elliptic type with broad utility in mechanical engineering and theoretical physics.

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Potential theory

In mathematics and mathematical physics, potential theory is the study of harmonic functions.

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Prussian Academy of Sciences

The Royal Prussian Academy of Sciences (Königlich-Preußische Akademie der Wissenschaften) was an academy established in Berlin, Germany on 11 July 1700, four years after the Akademie der Künste, or "Arts Academy," to which "Berlin Academy" may also refer.

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Quantum field theory

In theoretical physics, quantum field theory (QFT) is the theoretical framework for constructing quantum mechanical models of subatomic particles in particle physics and quasiparticles in condensed matter physics.

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Reflection (physics)

Reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated.

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Refraction

Refraction is the change in direction of wave propagation due to a change in its transmission medium.

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Relativistic wave equations

In physics, specifically relativistic quantum mechanics (RQM) and its applications to particle physics, relativistic wave equations predict the behavior of particles at high energies and velocities comparable to the speed of light.

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Retarded potential

In electrodynamics, the retarded potentials are the electromagnetic potentials for the electromagnetic field generated by time-varying electric current or charge distributions in the past.

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Ricci curvature

In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, represents the amount by which the volume of a small wedge of a geodesic ball in a curved Riemannian manifold deviates from that of the standard ball in Euclidean space.

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Royal Irish Academy

The Royal Irish Academy (RIA) (Acadamh Ríoga na hÉireann), based in Dublin, is an all-Ireland independent academic body that promotes study and excellence in the sciences, and humanities and social sciences.

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Scalar curvature

In Riemannian geometry, the scalar curvature (or the Ricci scalar) is the simplest curvature invariant of a Riemannian manifold.

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Scalar potential

Scalar potential, simply stated, describes the situation where the difference in the potential energies of an object in two different positions depends only on the positions, not upon the path taken by the object in traveling from one position to the other.

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Space

Space is the boundless three-dimensional extent in which objects and events have relative position and direction.

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Spacetime

In physics, spacetime is any mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum.

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Special relativity

In physics, special relativity (SR, also known as the special theory of relativity or STR) is the generally accepted and experimentally well-confirmed physical theory regarding the relationship between space and time.

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Spherical harmonics

In mathematics and physical science, spherical harmonics are special functions defined on the surface of a sphere.

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Tensor

In mathematics, tensors are geometric objects that describe linear relations between geometric vectors, scalars, and other tensors.

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Tensor calculus

In mathematics, tensor calculus or tensor analysis is an extension of vector calculus to tensor fields (tensors that may vary over a manifold, e.g. in spacetime).

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Tensor field

In mathematics and physics, a tensor field assigns a tensor to each point of a mathematical space (typically a Euclidean space or manifold).

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Test particle

In physical theories, a test particle is an idealized model of an object whose physical properties (usually mass, charge, or size) are assumed to be negligible except for the property being studied, which is considered to be insufficient to alter the behavior of the rest of the system.

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Theodor Kaluza

Theodor Franz Eduard Kaluza (9 November 1885, Wilhelmsthal, Silesia, German Empire, today part of Opole in Poland – 19 January 1954, Göttingen) was a German mathematician and physicist known for the Kaluza–Klein theory involving field equations in five-dimensional space.

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Theoretical physics

Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena.

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Theory of relativity

The theory of relativity usually encompasses two interrelated theories by Albert Einstein: special relativity and general relativity.

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Time

Time is the indefinite continued progress of existence and events that occur in apparently irreversible succession from the past through the present to the future.

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Tullio Levi-Civita

Tullio Levi-Civita, FRS (29 March 1873 – 29 December 1941) was an Italian mathematician, most famous for his work on absolute differential calculus (tensor calculus) and its applications to the theory of relativity, but who also made significant contributions in other areas.

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Unit vector

In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1.

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Vacuum solution

A vacuum solution is a solution of a field equation in which the sources of the field are taken to be identically zero.

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Variational methods in general relativity

Variational methods in general relativity refers to various mathematical techniques that employ the use of variational calculus in Einstein's theory of general relativity.

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Vector field

In vector calculus and physics, a vector field is an assignment of a vector to each point in a subset of space.

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Weak interaction

In particle physics, the weak interaction (the weak force or weak nuclear force) is the mechanism of interaction between sub-atomic particles that causes radioactive decay and thus plays an essential role in nuclear fission.

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References

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

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