Noether's theorem in nLab
This is of interest notably in view of Noether's theorem, which says ... Equation in Classical Field Theory, Commun.Math.Phys. 243 ...
geometry of physics -- perturbative quantum field theory in nLab
ϕ * ω = ϕ * ( ω i d x i ) ≔ ( ϕ * ω ) i ∂ ϕ i ∂ x ˜ j d x ˜ j = ( ω i ∘ ϕ ) ⋅ ∂ ϕ i ∂ x ˜ j d x ˜ j .
Topological symmetry and Noether's Theorem in Physics
Symmetry in the context of Noether's theorem means the existence of an invariant function for a certain dynamical system (X,T).
Hamiltonian n-vector field in nLab
holds. The following is the higher/local analog of the symplectic Noether theorem. For ( X , ω ) (X,\omega) a pre-n-plectic manifold ...
chiral perturbation theory in nLab
Additionally, the application of noether's theorem? to the classical global symmetry of the lagrangian density in the chiral limit yields 2 ...
A first idea of quantum field theory -- Interacting quantum fields in nLab
... theory, thus generalizing the Schwinger-Dyson equation to interacting field theory (example 1.76 below). Applied to Noether's theorem it ...
for the moment see at geometry of physics – A first idea of quantum field theory this prop. Last revised on December 13, 2017 at 21:49:41. See the history ...
multisymplectic geometry in nLab
in the multisymplectic extended phase space of an n n -dimensional field theory a state is not just a point, but an n n -dimensional subspace.
A first idea of quantum field theory -- Lagrangians in nLab
For many field theories of interest, their differential equation of motion is not a random partial differential equations, but is of the special ...
John Baez, Jordan algebras, Section 4 of: Getting to the Bottom of Noether's Theorem [arXiv:2006.14741]. See also: Wikipedia, Jordan algebra.
In perturbative quantum gravity, the soft graviton theorem (Weinberg 65) re-formulates scattering amplitudes of a set of finite energy external ...
geometry of physics -- fundamental super p-branes in nLab
But the Quillen model of rational homotopy theory effectively says that for X X a rational topological space then its loop space ∞-group Ω X \ ...
Hilbert's basis theorem in nLab
Emmy Noether wrote a short paper in 1920 that sidestepped the use of the HBT to construct a basis for, and so implying the finite generation of, ...
we conclude that the Euler-Lagrange equations of L ( ϕ ) L(\phi) are satisfied on solutions of P ( ϕ ) = 0 P(\phi)=0 , since EL ( ϕ ) δ ϕ = P ( ...
Noether's theorem · conserved current, charge · symmetry. Derived differential geometric version. BV-BRST complex · D-module · Edit this sidebar ...
The construction in van Nieuwenhuizen 82 in turn was motivated by the Sullivan algebras in rational homotopy theory (Sullivan 77). Indeed, their ...
may be read as encoding the differential equation v ( f ) x = α v(f)_x = \alpha (at one point) whose solutions f ∈ A X f \in A^X are the ...
A first idea of quantum field theory -- Phase space in nLab
1.1 below). By the Hamiltonian Noether theorem (prop. ) the presymplectic current induces infinitesimal symmetries acting on field histories and ...
in classical mechanics and classical field theory – by the action principle or principle of least action – the extrema of the action functional ...
Euler-Lagrange equation in nLab
This originates from and is mainly used in physics, specifically in Lagrangian field theory, where the functional in question is the action ...
Noether's theorem
Noether's theorem states that every continuous symmetry of the action of a physical system with conservative forces has a corresponding conservation law. This is the first of two theorems published by mathematician Emmy Noether in 1918.
Emmy Noether
MathematicianWard–Takahashi identity
In quantum field theory, a Ward–Takahashi identity is an identity between correlation functions that follows from the global or gauge symmetries of the theory, and which remains valid after renormalization.
Variational bicomplex
In mathematics, the Lagrangian theory on fiber bundles is globally formulated in algebraic terms of the variational bicomplex, without appealing to the calculus of variations. For instance, this is the case of classical field theory on fiber bundles.