On Page 138, Quantum Field Theory of Many-body Systems: From the Origin of Sound to an Origin of Light and Electrons by Xiaogang Wen, when he demonstrates the Anderson-Higgs mechanism for the U(1) gauge theory, he starts with the general (real time) Lagrangian
L = i2(φ∗(∂t+iA0)φ−φ(∂t−iA0)φ∗)−12m|(∂i+iAi)φ|2
+μ|φ|2−V02|φ|4+18πe2(E2−B2),
with
c=1.
(I wonder why this is the correct non-relativistic form because in my derivation I always have a term
A20|ϕ|2/2m.)
Then he chooses the gauge such that φ is real (unitarity gauge according to Peskin and Schroeder) and obtains
L = −A0ϕ2−12m(∂iϕ)2−ϕ22mA2i+μϕ2−V02ϕ4
+18πe2(E2−B2).
He claims that if we have ϕ=ϕ0+δϕ and integrate the small fluctuation δϕ, we can get
L = A202V0−ρA2i2m+18πe2(E2−B2).
I am curious what approximations he has done to get here.
Any help is appreciated.
This post imported from StackExchange Physics at 2015-04-15 10:43 (UTC), posted by SE-user L. Su