90 relations: Action (physics), Ampère's circuital law, Boson, Boundary (topology), Boundary value problem, Calculus of variations, Christoffel symbols, Classical field theory, Closed and exact differential forms, Compact space, Cosmological constant, Covariant classical field theory, Covariant derivative, Creation and annihilation operators, Degrees of freedom (physics and chemistry), Dependent and independent variables, Derivative, Differential form, Dirac adjoint, Dirac spinor, Einstein field equations, Einstein–Hilbert action, Einstein–Maxwell–Dirac equations, Electromagnetic four-potential, Electromagnetic tensor, Equations of motion, Equivalence principle, Euler–Lagrange equation, Fermion, Fermionic field, Feynman diagram, Feynman slash notation, Four-gradient, Four-vector, Functional (mathematics), Functional derivative, Functional integration, Gauge covariant derivative, Gauss's law, Gauss's law for gravity, Generalized coordinates, Glossary of tensor theory, Gluon field strength tensor, Gravitational constant, Hamiltonian field theory, Hamiltonian mechanics, Hodge star operator, Integral, Integration by parts, Isomorphism, ..., Jacobian matrix and determinant, Kaluza–Klein theory, Kinetic term, Kronecker delta, Lagrangian and Eulerian specification of the flow field, Lagrangian mechanics, Lagrangian point, Lagrangian system, Levi-Civita symbol, Manifold, Metric tensor, Minkowski space, Natural units, Noether's theorem, On shell and off shell, Onsager–Machlup function, Particle physics, Principle of least action, Quantum chromodynamics, Quantum electrodynamics, Quantum field theory, Real number, Reissner–Nordström metric, Ricci curvature, Riemann curvature tensor, Scalar curvature, Scalar field, Scalar field theory, Set (mathematics), Smoothness, Spacetime, Spinor field, Stress–energy tensor, Subspace topology, Tangent bundle, Tensor density, Tensor field, Tidal force, Vector field, Volume integral. Expand index (40 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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Ampère's circuital law
In classical electromagnetism, Ampère's circuital law (not to be confused with Ampère's force law that André-Marie Ampère discovered in 1823) relates the integrated magnetic field around a closed loop to the electric current passing through the loop.
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Boson
In quantum mechanics, a boson is a particle that follows Bose–Einstein statistics.
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Boundary (topology)
In topology and mathematics in general, the boundary of a subset S of a topological space X is the set of points which can be approached both from S and from the outside of S. More precisely, it is the set of points in the closure of S not belonging to the interior of S. An element of the boundary of S is called a boundary point of S. The term boundary operation refers to finding or taking the boundary of a set.
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Boundary value problem
In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions.
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Calculus of variations
Calculus of variations is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to the real numbers.
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Christoffel symbols
In mathematics and physics, the Christoffel symbols are an array of numbers describing a metric connection.
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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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Closed and exact differential forms
In mathematics, especially vector calculus and differential topology, a closed form is a differential form α whose exterior derivative is zero (dα.
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Compact space
In mathematics, and more specifically in general topology, compactness is a property that generalizes the notion of a subset of Euclidean space being closed (that is, containing all its limit points) and bounded (that is, having all its points lie within some fixed distance of each other).
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Cosmological constant
In cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: Λ) is the value of the energy density of the vacuum of space.
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Covariant classical field theory
In mathematical physics, covariant classical field theory represents classical fields by sections of fiber bundles, and their dynamics is phrased in the context of a finite-dimensional space of fields.
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Covariant derivative
In mathematics, the covariant derivative is a way of specifying a derivative along tangent vectors of a manifold.
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Creation and annihilation operators
Creation and annihilation operators are mathematical operators that have widespread applications in quantum mechanics, notably in the study of quantum harmonic oscillators and many-particle systems.
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Degrees of freedom (physics and chemistry)
In physics, a degree of freedom is an independent physical parameter in the formal description of the state of a physical system.
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Dependent and independent variables
In mathematical modeling, statistical modeling and experimental sciences, the values of dependent variables depend on the values of independent variables.
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Derivative
The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).
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Differential form
In the mathematical fields of differential geometry and tensor calculus, differential forms are an approach to multivariable calculus that is independent of coordinates.
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Dirac adjoint
In quantum field theory, the Dirac adjoint defines the dual operation of a Dirac spinor.
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Dirac spinor
In quantum field theory, the Dirac spinor is the bispinor in the plane-wave solution of the free Dirac equation, where (in the units \scriptstyle c \,.
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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–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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Einstein–Maxwell–Dirac equations
The Einstein–Maxwell–Dirac equations (EMD) are a classical field theory defined in the setting of general relativity.
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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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Equations of motion
In physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time.
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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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Euler–Lagrange equation
In the calculus of variations, the Euler–Lagrange equation, Euler's equation, or Lagrange's equation (although the latter name is ambiguous—see disambiguation page), is a second-order partial differential equation whose solutions are the functions for which a given functional is stationary.
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Fermion
In particle physics, a fermion is a particle that follows Fermi–Dirac statistics.
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Fermionic field
In quantum field theory, a fermionic field is a quantum field whose quanta are fermions; that is, they obey Fermi–Dirac statistics.
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Feynman diagram
In theoretical physics, Feynman diagrams are pictorial representations of the mathematical expressions describing the behavior of subatomic particles.
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Feynman slash notation
In the study of Dirac fields in quantum field theory, Richard Feynman invented the convenient Feynman slash notation (less commonly known as the Dirac slash notation).
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Four-gradient
In differential geometry, the four-gradient (or 4-gradient) \mathbf is the four-vector analogue of the gradient \vec from Gibbs–Heaviside vector calculus.
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Four-vector
In special relativity, a four-vector (also known as a 4-vector) is an object with four components, which transform in a specific way under Lorentz transformation.
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Functional (mathematics)
In mathematics, the term functional (as a noun) has at least two meanings.
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Functional derivative
In the calculus of variations, a field of mathematical analysis, the functional derivative (or variational derivative) relates a change in a functional to a change in a function on which the functional depends.
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Functional integration
Functional integration is a collection of results in mathematics and physics where the domain of an integral is no longer a region of space, but a space of functions.
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Gauge covariant derivative
The gauge covariant derivative is a variation of the covariant derivative used in general relativity.
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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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Generalized coordinates
In analytical mechanics, specifically the study of the rigid body dynamics of multibody systems, the term generalized coordinates refers to the parameters that describe the configuration of the system relative to some reference configuration.
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Glossary of tensor theory
This is a glossary of tensor theory.
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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.
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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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Hamiltonian field theory
In theoretical physics, Hamiltonian field theory is the field-theoretic analogue to classical Hamiltonian mechanics.
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Hamiltonian mechanics
Hamiltonian mechanics is a theory developed as a reformulation of classical mechanics and predicts the same outcomes as non-Hamiltonian classical mechanics.
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Hodge star operator
In mathematics, the Hodge isomorphism or Hodge star operator is an important linear map introduced in general by W. V. D. Hodge.
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Integral
In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.
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Integration by parts
In calculus, and more generally in mathematical analysis, integration by parts or partial integration is a process that finds the integral of a product of functions in terms of the integral of their derivative and antiderivative.
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Isomorphism
In mathematics, an isomorphism (from the Ancient Greek: ἴσος isos "equal", and μορφή morphe "form" or "shape") is a homomorphism or morphism (i.e. a mathematical mapping) that can be reversed by an inverse morphism.
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Jacobian matrix and determinant
In vector calculus, the Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function.
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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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Kinetic term
In physics, a kinetic term is the part of the Lagrangian that is bilinear in the fields (and for nonlinear sigma models, they are not even bilinear), and usually contains two derivatives with respect to time (or space); in the case of fermions, the kinetic term usually has one derivative only.
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Kronecker delta
In mathematics, the Kronecker delta (named after Leopold Kronecker) is a function of two variables, usually just non-negative integers.
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Lagrangian and Eulerian specification of the flow field
In classical field theory the Lagrangian specification of the field is a way of looking at fluid motion where the observer follows an individual fluid parcel as it moves through space and time.
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Lagrangian mechanics
Lagrangian mechanics is a reformulation of classical mechanics, introduced by the Italian-French mathematician and astronomer Joseph-Louis Lagrange in 1788.
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Lagrangian point
In celestial mechanics, the Lagrangian points (also Lagrange points, L-points, or libration points) are positions in an orbital configuration of two large bodies, wherein a small object, affected only by the gravitational forces from the two larger objects, will maintain its position relative to them.
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Lagrangian system
In mathematics, a Lagrangian system is a pair, consisting of a smooth fiber bundle and a Lagrangian density, which yields the Euler–Lagrange differential operator acting on sections of.
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Levi-Civita symbol
In mathematics, particularly in linear algebra, tensor analysis, and differential geometry, the Levi-Civita symbol represents a collection of numbers; defined from the sign of a permutation of the natural numbers, for some positive integer.
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Manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.
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Metric tensor
In the mathematical field of differential geometry, a metric tensor is a type of function which takes as input a pair of tangent vectors and at a point of a surface (or higher dimensional differentiable manifold) and produces a real number scalar in a way that generalizes many of the familiar properties of the dot product of vectors in Euclidean space.
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Minkowski space
In mathematical physics, Minkowski space (or Minkowski spacetime) is a combining of three-dimensional Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two events is independent of the inertial frame of reference in which they are recorded.
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Natural units
In physics, natural units are physical units of measurement based only on universal physical constants.
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Noether's theorem
Noether's (first) theorem states that every differentiable symmetry of the action of a physical system has a corresponding conservation law.
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On shell and off shell
In physics, particularly in quantum field theory, configurations of a physical system that satisfy classical equations of motion are called on shell, and those that do not are called off shell.
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Onsager–Machlup function
The Onsager–Machlup function is a function that summarizes the dynamics of a continuous stochastic process.
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Particle physics
Particle physics (also high energy physics) is the branch of physics that studies the nature of the particles that constitute matter and radiation.
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Principle of least action
The principle of least action – or, more accurately, the principle of stationary action – is a variational principle that, when applied to the action of a mechanical system, can be used to obtain the equations of motion for that system.
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Quantum chromodynamics
In theoretical physics, quantum chromodynamics (QCD) is the theory of the strong interaction between quarks and gluons, the fundamental particles that make up composite hadrons such as the proton, neutron and pion.
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Quantum electrodynamics
In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics.
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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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Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
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Reissner–Nordström metric
In physics and astronomy, the Reissner–Nordström metric is a static solution to the Einstein-Maxwell field equations, which corresponds to the gravitational field of a charged, non-rotating, spherically symmetric body of mass M. The metric was discovered by Hans Reissner, Hermann Weyl, Gunnar Nordström and G. B. Jeffery.
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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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Riemann curvature tensor
In the mathematical field of differential geometry, the Riemann curvature tensor or Riemann–Christoffel tensor (after Bernhard Riemann and Elwin Bruno Christoffel) is the most common method used to express the curvature of Riemannian manifolds.
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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 field
In mathematics and physics, a scalar field associates a scalar value to every point in a space – possibly physical space.
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Scalar field theory
In theoretical physics, scalar field theory can refer to a relativistically invariant classical or quantum theory of scalar fields.
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Set (mathematics)
In mathematics, a set is a collection of distinct objects, considered as an object in its own right.
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Smoothness
In mathematical analysis, the smoothness of a function is a property measured by the number of derivatives it has that are continuous.
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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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Spinor field
In differential geometry, given a spin structure on an n-dimensional orientable Riemannian manifold (M, g), a section of the spinor bundle S is called a spinor field.
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Stress–energy tensor
The stress–energy tensor (sometimes stress–energy–momentum tensor or energy–momentum tensor) is a tensor quantity in physics that describes the density and flux of energy and momentum in spacetime, generalizing the stress tensor of Newtonian physics.
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Subspace topology
In topology and related areas of mathematics, a subspace of a topological space X is a subset S of X which is equipped with a topology induced from that of X called the subspace topology (or the relative topology, or the induced topology, or the trace topology).
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Tangent bundle
In differential geometry, the tangent bundle of a differentiable manifold M is a manifold TM which assembles all the tangent vectors in M. As a set, it is given by the disjoint unionThe disjoint union ensures that for any two points x1 and x2 of manifold M the tangent spaces T1 and T2 have no common vector.
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Tensor density
In differential geometry, a tensor density or relative tensor is a generalization of the tensor field concept.
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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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Tidal force
The tidal force is an apparent force that stretches a body towards the center of mass of another body due to a gradient (difference in strength) in gravitational field from the other body; it is responsible for the diverse phenomena, including tides, tidal locking, breaking apart of celestial bodies and formation of ring systems within Roche limit, and in extreme cases, spaghettification of objects.
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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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Volume integral
In mathematics—in particular, in multivariable calculus—a volume integral refers to an integral over a 3-dimensional domain, that is, it is a special case of multiple integrals.
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Redirects here:
Interaction Lagrangian, Lagrangian density, Lagrangian field theory.
References
[1] https://en.wikipedia.org/wiki/Lagrangian_(field_theory)