nLab
vacuum

Context

Physics

physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes


theory (physics), model (physics)

experiment, measurement, computable physics

under construction

Contents

Idea

In quantum field theory

In the perturbation theory of a quantum field theory defined by an action functional S:ConfS : Conf \to \mathbb{R}, a vacuum of the theory is a classical solution: a configuration ϕ 0Conf\phi_0 \in Conf that solves the Euler-Lagrange equations of SS.

Because in the perturbative quantum dynamics around ϕ 0\phi_0 quanta are small deviations from a classical solution. Hence the absence of any quanta, hence the “vacuum”, is the solution ϕ 0\phi_0 itself.

(…)

In string theory

In string theory the vacua of the effective background QFT are at the same time identified with certain 2-dimensional CFTs – namely the string sigma-models which have the given effective QFT as their second quantization.

Perturbative string theory is defined as the string perturbation series of these sigma-models about these vacua.

The moduli space of these vacua – which is hardly understood – has come to be called the landscape of string theory vacua .

Revised on May 10, 2014 08:06:42 by Urs Schreiber (31.55.40.250)