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Noether identities

Context

Physics

physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes


theory (physics), model (physics)

experiment, measurement, computable physics

Contents

Definition

For S:C𝔸 1S : C \to \mathbb{A}^1 an action functional, the 𝒪(C)\mathcal{O}(C)-module of its Noether identities is the kernel N SDer(𝒪(C))N_S \hookrightarrow Der(\mathcal{O}(C)) of the canonical morphism

ι dS:Der(𝒪(S))𝒪(S). \iota_{d S} : Der(\mathcal{O}(S)) \to \mathcal{O}(S) \,.

See BRST-BV complex for background and details.

Examples

Assume that CC is sufficiently well behaved and of finite dimension such that the module of derivations has (locally) a basis { i} i\{\partial_i\}_i. Then the Noether identities are (locally) tuples of functions {v i}\{v^i\} such that

iv i iS=0. \sum_i v^i \partial_i S = 0 \,.
Created on March 8, 2011 14:13:44 by Urs Schreiber (131.211.232.88)