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Type of physical quantity
In physics and mathematics, a pseudotensor is usually a quantity that transforms like a tensor under an orientation-preserving coordinate transformation
Pseudotensor
Quantity in general relativity
of general relativity, a stress–energy–momentum pseudotensor, such as the Landau–Lifshitz pseudotensor, is an extension of the non-gravitational stress–energy
Stress–energy–momentum pseudotensor
Stress–energy–momentum_pseudotensor
Antisymmetric permutation object acting on tensors
the Levi-Civita symbol is, by definition, a pseudotensor. As the Levi-Civita symbol is a pseudotensor, the result of taking a cross product is a pseudovector
Levi-Civita_symbol
Law of physics and chemistry
typically expressed with the aid of a stress–energy–momentum pseudotensor. However, since pseudotensors are not tensors, they do not transform cleanly between
Conservation_of_energy
Tensor describing energy momentum density in spacetime
pseudotensor. These include the Einstein pseudotensor and the Landau–Lifshitz pseudotensor. The Landau–Lifshitz pseudotensor can be reduced to zero at any event
Stress–energy_tensor
Generalization of tensor fields
vector density. A distinction is made among (authentic) tensor densities, pseudotensor densities, even tensor densities and odd tensor densities. Sometimes
Tensor_density
Type of potential energy
stress–energy tensor to the Landau–Lifshitz pseudotensor results in a combined matter plus gravitational energy pseudotensor that has a vanishing 4-divergence in
Gravitational_energy
Scalar quantity, changing sign in mirrored coordinates
a pseudovector (or axial vector); a similar construction creates the pseudotensor. A pseudoscalar also results from any scalar product between a pseudovector
Pseudoscalar
German-born theoretical physicist (1879–1955)
of coordinates. He maintained that the non-covariant energy momentum pseudotensor was, in fact, the best description of the energy momentum distribution
Albert_Einstein
Topics referred to by the same term
motion of magnetization in a solid Landau–Lifshitz pseudotensor, a stress-energy-momentum pseudotensor The (+1, −1, −1, −1) signature of the metric of the
Landau_and_Lifshitz
Soviet theoretical physicist (1908–1968)
equation Landau–Zener formula Landau–Lifshitz model Landau–Lifshitz pseudotensor Landau–Lifshitz–Gilbert equation Landau–Pomeranchuk–Migdal effect Landau–Yang
Lev_Landau
Soviet physicist (1915–1985)
Landau–Lifshitz model Landau–Lifshitz–Gilbert equation Landau–Lifshitz pseudotensor Landau–Lifshitz aeroacoustic equation Belinski–Khalatnikov–Lifshitz singularity
Evgeny_Lifshitz
Amount of matter present in an object
a given observer, this can be achieved by the stress–energy–momentum pseudotensor. In classical mechanics, the inert mass of a particle appears in the
Mass
Matrix operation which flips a matrix over its diagonal
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Transpose
Theory of interwoven space and time by Albert Einstein
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Special_relativity
Theory of gravitation as curved spacetime
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
General_relativity
Conserved physical quantity; rotational analogue of linear momentum
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Angular_momentum
Algebraic operation on coordinate vectors
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Dot_product
Representation of a tensor in Euclidean space
Contrary to its appearance, the Levi-Civita symbol is not a tensor, but a pseudotensor, the components transform according to: ε ¯ p q r = det ( L ) ε i j k
Cartesian_tensor
Specification of a derivative along a tangent vector of a manifold
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Covariant_derivative
Expression that may be integrated over a region
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Differential_form
Mathematical function, in linear algebra
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Linear_map
Shorthand notation for tensor operations
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Einstein_notation
Array of numbers
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Matrix_(mathematics)
Algebraic object with geometric applications
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Tensor
relativity requires the use of concepts such as vectors, tensors, pseudotensors and curvilinear coordinates. For an introduction based on the example
Introduction to the mathematics of general relativity
Introduction_to_the_mathematics_of_general_relativity
Mathematical operation on vector spaces
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Tensor_product
Rotation composed with a reflection
well as scalars and pseudoscalars, and in general between tensors and pseudotensors), since the latter transform differently under proper and improper rotations
Improper_rotation
Basis used to express spherical tensors
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Spherical_basis
Branch of mathematics
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Differential_geometry
Topological space that locally resembles Euclidean space
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Manifold
Method for specifying point positions
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Coordinate_system
Straight path on a curved surface or a Riemannian manifold
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Geodesic
Property of a mathematical space
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Dimension
Branch of physics which studies the behavior of materials modeled as continuous media
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Continuum_mechanics
Minimum energy to remove a system from a gravitationally bound state
M_{x}}{R-738.313\,M_{x}}}} Stress–energy tensor Stress–energy–momentum pseudotensor Nordtvedt effect "Spot the cluster". www.eso.org. Retrieved 31 July 2017
Gravitational_binding_energy
Section of a certain line bundle
orientation bundle of M and the n-th exterior product bundle of T∗M (see pseudotensor). In general, there does not exist a natural concept of a "volume" for
Density_on_a_manifold
Structure defining distance on a manifold
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Metric_tensor
Force in which the work done in moving an object depends only on its displacement
needed] However, general relativity does conserve a stress–energy–momentum pseudotensor. Conservative vector field Conservative system HyperPhysics - Conservative
Conservative_force
Vector behavior under coordinate changes
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Covariance and contravariance of vectors
Covariance_and_contravariance_of_vectors
Scalar measure of the rotational inertia with respect to a fixed axis of rotation
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Moment_of_inertia
Tensor in differential geometry
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Ricci_curvature
Mathematical function of two variables; outputs 1 if they are equal, 0 otherwise
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Kronecker_delta
Algebra associated to any vector space
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Exterior_algebra
Statement relating differentiable symmetries to conserved quantities
(non-gravitational stress–energy) and the Landau–Lifshitz stress–energy–momentum pseudotensor (gravitational stress–energy). The local conservation of non-gravitational
Noether's_theorem
Spinning motion in theoretical physics
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Spin_tensor
Continuous surjection satisfying a local triviality condition
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Fiber_bundle
Differential form of degree one or section of a cotangent bundle
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
One-form
Set of vectors used to define coordinates
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Basis_(linear_algebra)
Non-tensorial representation of the spin group
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Spinor
Isomorphism between the tangent and cotangent bundles of a manifold
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Musical_isomorphism
Array of numbers describing a metric connection
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Christoffel_symbols
Exterior algebraic map taking tensors from p forms to n-p forms
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Hodge_star_operator
Theory of fundamental physics
gravitational field alone has no well-defined stress–energy tensor, only the pseudotensor one. Therefore, the property (2) cannot be completely justified in a
Superfluid_vacuum_theory
Mathematical Concept
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Voigt_notation
Tensor field in Riemannian geometry
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Riemann_curvature_tensor
Coordinate-free definition of a tensor
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Tensor_(intrinsic_definition)
Operation that pairs a left and a right R-module into an abelian group
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Tensor_product_of_modules
Facet of general relativity
relativity is the use of pseudotensors such as the Landau–Lifshitz pseudotensor.(Landau and Lifshitz, 1962). Pseudotensors are not gauge invariant –
Mass_in_general_relativity
Mapping from p forms to p-1 forms
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Interior_product
Affine connection on the tangent bundle of a manifold
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Levi-Civita_connection
Operation in mathematics
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Tensor_contraction
gravity Kähler–Einstein metric Wiener–Khinchin–Einstein theorem Einstein pseudotensor Stark–Einstein law Stokes–Einstein equation (translational diffusion)
List of things named after Albert Einstein
List_of_things_named_after_Albert_Einstein
Tensor invariant under permutations of vectors it acts on
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Symmetric_tensor
Measure of the curvature of a pseudo-Riemannian manifold
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Weyl_tensor
Israeli-American physicist (1909–1995)
improve on general relativity by removing singularities and replacing pseudotensors with tensors to eliminate nonlocality. The effort eventually failed
Nathan_Rosen
Representation of mechanical stress at every point within a deformed 3D object
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Cauchy_stress_tensor
Ternary operation on vectors
contraction of vectors with a rank-3 tensor equivalent to the form (or a pseudotensor equivalent to the volume pseudoform); see below. The vector triple product
Triple_product
Object in differential geometry
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Torsion_tensor
Supergravity in eleven dimensions
additionally invariant under parity, with the gauge field transforming as a pseudotensor A → − A {\displaystyle A\rightarrow -A} . The equations of motion for
Eleven-dimensional supergravity
Eleven-dimensional_supergravity
Physical quantity that changes sign with improper rotation
The label "pseudo-" can be further generalized to pseudoscalars and pseudotensors, both of which gain an extra sign-flip under improper rotations compared
Pseudovector
Thought experiment in physics
attended and gave a talk in which he computed the Einstein pseudotensor and Landau–Lifshitz pseudotensor (two alternative, non-covariant, descriptions of the
Sticky_bead_argument
Decomposition in multilinear algebra
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Tensor_rank_decomposition
Second order tensor in vector algebra
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Dyadics
Electromagnetism in general relativity
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Maxwell's equations in curved spacetime
Maxwell's_equations_in_curved_spacetime
Type of derivative in differential geometry
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Lie_derivative
Assignment of a tensor continuously varying across a region of space
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Tensor_field
Tensor that describes the 4D geometry of spacetime
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Metric tensor (general relativity)
Metric_tensor_(general_relativity)
Tensor used in general relativity
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Einstein_tensor
Operation on differential forms
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Exterior_derivative
Mathematical object that describes the electromagnetic field in spacetime
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Electromagnetic_tensor
Universal construction in multilinear algebra
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Tensor_algebra
Branch of mathematics
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Multilinear_algebra
Equations describing elastic deformation
stress functions. ε {\displaystyle \varepsilon } is the Levi-Civita pseudotensor, with all values equal to zero except those in which the indices are
Stress_functions
Tensor index notation for tensor-based calculations
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Ricci_calculus
Study of curves from a differential point of view
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Differentiable_curve
Differential form
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Volume_form
System of moving vectors in differential geometry
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Parallel_transport
Concept in differential geometry
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Exterior_covariant_derivative
Tensor operator generalizes the notion of operators which are scalars and vectors
be shown by using the Baker Hausdorff lemma. As the symbol εijk is a pseudotensor, pseudovector operators are invariant up to a sign: +1 for proper rotations
Tensor_operator
Ways of writing certain laws of physics
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Covariant formulation of classical electromagnetism
Covariant_formulation_of_classical_electromagnetism
turbulence Landau–Levich problem Landau–Lifshitz model Landau-Lifshitz pseudotensor Landau–Lifshitz–Gilbert equation Landau–Lifshitz aeroacoustic equation
List of things named after Lev Landau
List_of_things_named_after_Lev_Landau
Mathematics of smooth surfaces
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Differential geometry of surfaces
Differential_geometry_of_surfaces
Function that is invariant under all permutations of its variables
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Symmetric_function
Construct in differenital geometry
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Metric_connection
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Symmetrization
Construct allowing differentiation of tangent vector fields of manifolds
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Affine_connection
Graphical notation for multilinear algebra calculations
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Penrose_graphical_notation
Math/physics concept
Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker delta
Connection_form
Operator in quantum field theory
Pseudovector – Physical quantity that changes sign with improper rotation Pseudotensor – Type of physical quantity Induced representation – Process of extending
Pauli–Lubanski_pseudovector
PSEUDOTENSOR
PSEUDOTENSOR
PSEUDOTENSOR
PSEUDOTENSOR
Girl/Female
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Mythological, Sanskrit
Name of Arjun's Wife
Boy/Male
Biblical
Viol, honeycomb.
Boy/Male
Irish
War; strife.
Boy/Male
German
Elm.
Girl/Female
Basque
Place in France where Virgin Mary reportedly appeared to a young girl and miracles of healing...
Girl/Female
Norse
Church farm. Church village.
Boy/Male
Indian
Facilitation
Girl/Female
Indian, Punjabi, Sikh
Desire; Wish
Girl/Female
Muslim
Wild horse, Born with feet first (1)
Biblical
given or offered
PSEUDOTENSOR
PSEUDOTENSOR
PSEUDOTENSOR
PSEUDOTENSOR
PSEUDOTENSOR