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A Schema for Duality, Illustrated by Bosonization

De Haro, Sebastian and Butterfield, Jeremy (2019) A Schema for Duality, Illustrated by Bosonization. Foundations of Mathematics and Physics one Century after Hilbert.

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Abstract

In this paper we present a schema for describing dualities between physical theories (Sections 2 and 3), and illustrate it in detail with the example of bosonization: a boson-fermion duality in two-dimensional quantum field theory (Sections 4 and 5).

The schema develops proposals in De Haro (2016, 2016a): these proposals include construals of notions related to duality, like representation, model, symmetry and interpretation. The aim of the schema is to give a more precise criterion for duality than has so far been considered.

The bosonization example, or boson-fermion duality, has the feature of being simple, yet rich enough, to illustrate the most relevant aspects of our schema, which also apply to more sophisticated dualities. The richness of the example consists, mainly, in its concern with two non-trivial quantum field theories: including massive Thirring-sine-Gordon duality, and non-abelian bosonization.

This prompts two comparisons with the recent philosophical literature on dualities:---

(a) Unlike the standard cases of duality in quantum field theory and string theory, where only specific simplifying limits of the theories are explicitly known, the boson-fermion duality is known to hold exactly. This exactness can be exhibited explicitly.

(b) The bosonization example illustrates both the cases of isomorphic and non-isomorphic models: which we believe the literature on dualities has not so far discussed.


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Item Type: Published Article or Volume
Creators:
CreatorsEmailORCID
De Haro, Sebastiansd696@cam.ac.uk0000-0002-3000-5967
Butterfield, Jeremyjb56@cam.ac.uk0000-0002-0215-5802
Additional Information: Published in `Foundations of Mathematics and Physics one Century after Hilbert', ed. Joseph Kouneiher: Collection Mathematical Physics, Springer 2018: (a volume dedicated to the centenary of Hilbert's work on the foundations of mathematics and physics).
Keywords: bosonization, conformal field theories, duality, gauge, interpretation of theories, symmetry.
Subjects: General Issues > Scientific Metaphysics
Specific Sciences > Physics > Fields and Particles
Specific Sciences > Physics > Quantum Field Theory
General Issues > Structure of Theories
Specific Sciences > Physics > Symmetries/Invariances
Depositing User: Jeremy Butterfield
Date Deposited: 08 Jun 2019 13:21
Last Modified: 08 Jun 2019 13:21
Item ID: 16096
Journal or Publication Title: Foundations of Mathematics and Physics one Century after Hilbert
Publisher: Springer
Official URL: https://link.springer.com/chapter/10.1007%2F978-3-...
DOI or Unique Handle: https://doi.org/10.1007/978-3-319-64813-2_12 ;
Subjects: General Issues > Scientific Metaphysics
Specific Sciences > Physics > Fields and Particles
Specific Sciences > Physics > Quantum Field Theory
General Issues > Structure of Theories
Specific Sciences > Physics > Symmetries/Invariances
Date: June 2019
URI: http://philsci-archive.pitt.edu/id/eprint/16096

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