TL;DR
This paper presents a new concise quantum operator formula for bosonization that naturally incorporates Lie group structures, simplifying fermion-boson transformations in two-dimensional quantum field theories.
Contribution
It introduces a novel formula linking fermions and bosons through Lie group elements, enhancing understanding of bosonization in quantum field theory.
Findings
Lie group structure appears naturally in bosonization
Exact connection between fermions and bosons via Lie group parameters
Simplifies the equation of motion for fermion fields in 2D
Abstract
We introduce a concise quantum operator formula for bosonization in which the Lie group structure appears in a natural way. The connection between fermions and bosons is found to be exactly the connection between Lie group elements and the group parameters. Bosonization is an extraordinary way of expressing the equation of motion of a complex fermion field in terms of a real scalar boson in two dimensions. All the properties of the fermion field theory are known to be preserved under this remarkable transformation with substantial simplification and elucidation of the original theory, much like Lie groups can be studied by their Lie algebras.
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