Duality Between Dirac Fermions in Curved Spacetime and Optical solitons in Non-Linear Schrodinger Model: Magic of $1+1$-Dimensional Bosonization

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.

New reference and related discussion added, some equations corrected, no change in major results, to appear in EPJC

References in corpus (3)

• The Case of the Missing Gates: Complexity of Jackiw-Teitelboim Gravity
• Relativistic Corrections to Nonrelativistic Effective Field Theories
• On the subtelties of nonrelativistic reduction and applications

Cited by in corpus (3)

• Duality family of scalar field
• One-Dimensional Relativistic Self-Gravitating Systems
• Dirac Equation with Space Contributions Embedded in a Quantum-Corrected Gravitational Field