Everything about Tensor field
Assignment of a tensor continuously varying across a region of space
In mathematics and physics, a tensor field is a function assigning a tensor to each point of a region of a mathematical space or of a physical space, in which case the field quantity acquires a unit of measurement. Tensor fields are used in differential geometry, algebraic geometry, general relativity, in the analysis of stress and strain in material object, and in numerous applications in the physical sciences. As a tensor is a generalization of a scalar and a vector, a tensor field is a generalization of a scalar field and a vector field that assigns, respectively, a scalar or vector to each point of space. If a tensor A is defined on a vector fields set X(M) over a module M, we call A a tensor field on M. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Tensor fieldA 5-minute orientation
- Skim a recent paper: Tensor lattice field theory for renormalization and quantum computingInfluential work since 2022
- Pick up a classic book: Quantum groups, quantum categories, and quantum field theoryThe most-reprinted book on the subject
- Read the landmark paper: Electric-Field Gradient Tensor in Ferrous CompoundsCited 687 times
- Go sideways: Vector fieldA closely related topic
- Go sideways: Metric tensorA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
Electric-Field Gradient Tensor in Ferrous Compounds
Tensor Scattering Matrix for the Electromagnetic Field
Phases of antisymmetric tensor field theories
Energy-momentum tensor in quantum field theory
A Renormalizable 4-Dimensional Tensor Field Theory
Energy-momentum tensor for the gravitational field
Highly improved lattice field-strength tensor
The geomagnetic field gradient tensor
🆕 Influential since 2022
Tensor lattice field theory for renormalization and quantum computing
The effective field theory of vector-tensor theories
Notes on tensor models and tensor field theories
Simple single-field inflation models with arbitrarily small tensor/scalar ratio
Past-directed scalar field gradients and scalar-tensor thermodynamics
📚 Books worth reading
Quantum groups, quantum categories, and quantum field theoryJürg Fröhlich, Jürg Fröhlich · 1992- 📕Elements of tensor calculusA. Lichnerowicz · 1962
Visualization of fields and applications in engineeringStephen Tou · 2011
Tensorial Methods and Renormalization in Group Field TheoriesSylvain Carrozza · 2014- 📕Introduction to tensors, spinors, and relativistic wave-equations (relation structure)E. M. Corson · 1953
- 📕Tensor-Valued Random Fields for Continuum PhysicsAnatoliy Malyarenko, Martin Ostoja-Starzewski · 2018
- 📕Tensor Categories and Endomorphisms of Von Neumann AlgebrasMarcel Bischoff, Yasuyuki Kawahigashi · 2015
- 📕Differential Geometry and Kinematics of ContinuaJohn D. Clayton · 2014
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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