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Renormalization group methods: Which kind of explanation?

Elena Castellani1, Emilia Margoni2

  • 1Università degli Studi di Firenze, Italy.

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Renormalization Group (RG) methods offer powerful explanations in physics. This paper argues RG explanations arise from a non-trivial intersection of mathematical and physical features, not solely from mathematics.

Keywords:
Critical phenomenaEffective theoriesMathematical explanationNon-causal explanationRenormalization group

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Area of Science:

  • Theoretical Physics
  • Philosophy of Science
  • Mathematical Physics

Background:

  • Renormalization and Renormalization Group (RG) are crucial tools in modern physics, impacting the conceptualization of physical theories.
  • Existing philosophical accounts, such as Morrison's, characterize RG explanations as mathematical, non-reductive, and non-causal.

Purpose of the Study:

  • To investigate the philosophical underpinnings of explanations provided by Renormalization Group (RG) methods.
  • To critically examine the claim that RG explanations are exclusively mathematical.

Main Methods:

  • Historical overview of Renormalization Group (RG) in physics.
  • Scrutiny of recent philosophical debates on RG explanations.
  • Focused analysis of Morrison's account of RG explanation.

Main Results:

  • RG explanations are not solely derived from their mathematical character.
  • A non-trivial interplay between mathematical and physical aspects is essential for RG's explanatory power.
  • RG theory's explanatory role is a synthesis of mathematical structure and physical interpretation.

Conclusions:

  • The explanatory capacity of Renormalization Group (RG) methods transcends purely mathematical descriptions.
  • Effective RG explanations necessitate an integrated understanding of both mathematical formalisms and their physical significance.
  • Future philosophical analyses of RG should acknowledge this crucial intersection of mathematical and physical elements.