Mapping Bosonic and Fermionic Algebras
Author Information
Author(s): Fabio Lingua, Diego Molina Peñafiel, Lucrezia Ravera, Sebastián Salgado, Frank Saueressig
Primary Institution: KTH Royal Institute of Technology
Hypothesis
Can an algebraic method be used to derive the structure of bosonic and fermionic algebras?
Conclusion
The study presents a method for mapping bosonic algebras to fermionic algebras, revealing a deformed Grassmann-type algebra structure.
Supporting Evidence
- Bosons and fermions have different intrinsic properties, particularly their spin and statistics.
- The study introduces a mapping method that preserves or exchanges creation and annihilation operations.
- The algebraic structure obtained corresponds to a graded, deformed Grassmann-type algebra.
Takeaway
This study shows how two types of particles, bosons and fermions, can be related through a special math method, helping us understand their behaviors better.
Methodology
An algebraic approach using identification criteria from Lie algebra expansion methods to derive mappings between bosonic and fermionic operators.
Limitations
The study does not explore the implications of the mappings in non-Abelian gauge theories.
Digital Object Identifier (DOI)
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