Bosonization and the lattice: the $d=2$ Gross-Neveu model
Matteo Beccaria
TL;DR
This paper explores the lattice formulation of bosonized quantum field theories using the two-dimensional Gross-Neveu model as a case study, demonstrating that the lattice approach accurately reproduces continuum physics without fermionic doubling issues.
Contribution
It introduces a lattice formulation for bosonized quantum field theories and shows its effectiveness using the 2D Gross-Neveu model, avoiding fermion doubling problems.
Findings
Lattice model reproduces continuum physics accurately
No need for anticommuting fields in the lattice formulation
Numerical simulations support analytical results
Abstract
We consider the lattice formulation of bosonized quantum field theories. As a non trivial example, we study the two dimensional Gross-Neveu model. Analytical investigations and direct numerical simulation strongly suggest that the lattice model reproduces the continuum physics. Anticommuting fields are not required and there are not related doubling problems. (3 PostScript figures available from the author)
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Taxonomy
TopicsNoncommutative and Quantum Gravity Theories · Advanced Operator Algebra Research · Black Holes and Theoretical Physics