12.7. Equivalence of the SineGordon and Thirring models Consider the SineGordon model of a scalar bosonic field
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12.7. Equivalence of the Sine–Gordon and Thirring models Consider the Sine–Gordon model of a scalar bosonic field ϕ, whose Lagrangian is L = 1 2
(∂ϕ)2 + m2
β2 (cosβϕ −1).
Use the bosonization formulae, prove that this Lagrangian can be transformed in the Lagrangian of the Thirring model L = i ¯ γμ ∂μ −M ¯ − 1 2
g ( ¯ γμ)( ¯ γμ)
where is a complex fermionic field, with the coupling constants related as
β2 4π
= 1 1+ g
π
.
Note that β2 = 4π is equivalent to g = 0, i.e. a free fermionic model!
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Related Book For
Statistical Field Theory An Introduction To Exactly Solved Models In Statistical Physics
ISBN: 9780198788102
2nd Edition
Authors: Giuseppe Mussardo
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