Editing Vector calculus (section)

== Basic objects ==

=== Scalar fields ===
{{Main|Scalar field}}
A [[scalar field]] associates a [[scalar (mathematics)|scalar]] value to every point in a space. The scalar is a mathematical number representing a [[scalar (physics)|physical quantity]]. Examples of scalar fields in applications include the [[temperature]] distribution throughout space, the [[pressure]] distribution in a fluid, and spin-zero quantum fields (known as [[Scalar boson|scalar bosons]]), such as the [[Higgs field]]. These fields are the subject of [[scalar field theory]].

=== Vector fields ===
{{Main|Vector field}}

A [[vector field]] is an assignment of a [[vector (geometry)|vector]] to each point in a [[Space (mathematics)|space]].<ref name="Galbis-2012-p12">{{cite book|author1=Galbis, Antonio |author2=Maestre, Manuel |title=Vector Analysis Versus Vector Calculus|publisher=Springer|year=2012|isbn=978-1-4614-2199-3|page=12|url=https://books.google.com/books?id=tdF8uTn2cnMC&pg=PA12}}</ref> A vector field in the plane, for instance, can be visualized as a collection of arrows with a given [[Magnitude_(mathematics)#Vector_spaces|magnitude]] and direction each attached to a point in the plane. Vector fields are often used to model, for example, the speed and direction of a moving fluid throughout space, or the strength and direction of some [[force]], such as the [[magnetic field|magnetic]] or [[gravity|gravitational]] force, as it changes from point to point. This can be used, for example, to calculate [[Work (physics)|work]] done over a line.

=== Vectors and pseudovectors ===
In more advanced treatments, one further distinguishes [[pseudovector]] fields and [[pseudoscalar]] fields, which are identical to vector fields and scalar fields, except that they change sign under an orientation-reversing map: for example, the [[Curl (mathematics)|curl]] of a vector field is a pseudovector field, and if one reflects a vector field, the curl points in the opposite direction. This distinction is clarified and elaborated in [[geometric algebra]], as described below.