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  Anderson-Higgs mechanism for the (non-relativistic) U(1) gauge theory under the unitarity gauge

+ 2 like - 0 dislike
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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)φφ(tiA0)φ)12m|(i+iAi)φ|2

+μ|φ|2V02|φ|4+18πe2(E2B2),
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 = A0ϕ212m(iϕ)2ϕ22mA2i+μϕ2V02ϕ4

+18πe2(E2B2).

He claims that if we have ϕ=ϕ0+δϕ and integrate the small fluctuation δϕ, we can get

L = A202V0ρA2i2m+18πe2(E2B2).

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
asked Apr 10, 2015 in Theoretical Physics by DarKnightS (125 points) [ no revision ]
retagged Apr 15, 2015

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