nLab
interaction

Contents

Context

Physics

physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes


theory (physics), model (physics)

experiment, measurement, computable physics

Contents

Idea

Given a local Lagrangian density LL defining the action functional of a local field theory, typically it splits as a sum

L=L free+L int L = L_{free} + L_{int}

of a term L freeL_{free} that defines a free field theory (kinetic energy) and a remainder L intL_{int} defining the interactions of a corresponding interacting field theory. That remainder then describes the interactions that the otherwise free fields undergo.

The interaction picture of quantum physics serves to decompose the quantization of local field theories such that the interaction is seen as a perturbation of the quantization of the free field theory. This underlies most constructions of perturbative quantum field theory, including the mathematically rigorous formulation via causal perturbation theory.

Examples

action functionalkinetic actioninteractionpath integral measure
exp(S(ϕ))μ=\exp(-S(\phi)) \cdot \mu = exp((ϕ,Qϕ))\exp(-(\phi, Q \phi)) \cdotexp(I(ϕ))\exp(I(\phi)) \cdotμ\mu
BV differentialelliptic complex +antibracket with interaction +BV-Laplacian
d q=d_q =QQ +{I,}\{I,-\} +Δ\hbar \Delta

Last revised on February 20, 2018 at 00:49:55. See the history of this page for a list of all contributions to it.