Abstract
Bosonization in curved spacetime maps massive Thirring model (self-interacting Dirac fermions) to a generalized Sine–Gordon model, both living in 1+1-dimensional curved spacetime. Applying this duality we have shown that the Thirring model fermion, in non-relativistic limit, gets identified with the soliton of non-linear Scrodinger model with Kerr form of non-linearity. We discuss one particular optical soliton in the latter model and relate it with the Thirring model fermion.
Highlights
In a recent paper [3] a novel form of duality has been revealed between a system obeying Dirac equation in (1+1)dimensional curved spacetime and the multiphoton Rabi model
In particular we have shown that a relativistic theory of selfinteracting massive Dirac fermions in curved spacetime can be mapped to a form of non-linear Scroedinger equation supporting Kerr-type of solitons, in the non-relativistic limit
In this paper we have shown that the latter, in non-relativistic limit and for small coupling reduces to Non-linear Schrodinger (NLS) model with Kerr form of non-linearity [30], allowing various types of optical soliton solutions
Summary
In a recent paper [3] a novel form of duality has been revealed between a system obeying Dirac equation in (1+1)dimensional curved spacetime and the multiphoton Rabi model. Enough, experimentally observed (as well as analytically computed in Rabi model framework) nature of the particle trajectory matches with the numerically computed Zitterbewegung motion of the particle in gravitational background. This duality is a result of the algebraic similarity between the two quantum mechanical models where it was sufficient to compare their Hamiltonians. In particular we have shown that a relativistic theory of selfinteracting massive Dirac fermions (massive Thirring model) in curved spacetime can be mapped to a form of non-linear Scroedinger equation supporting Kerr-type of solitons, in the non-relativistic limit. The bosonization technique has been generalized for curved spacetime by Eboli [29] with a non-trivial result that the Sine–Gordon model has a position dependent effective mass
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