What is it about?
Gauge theory is a mathematical structure which underpins quantum physics, but classical theories such as mechanics and electromagnetism are lacking such a unifying framework. This paper defines a generalization of gauge theory which accommodates all fundamental classical physical models, expressing them in a way which is geometric and consistent, while making it straightforward to see the limits under which each previous theory may be obtained from the more precise one.
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Why is it important?
Expressing classical theories in terms of a geometric framework which already underpins the standard model may point to new directions in trying to reconcile general relativity and quantum physics.
Perspectives
The practical side of physics is about being able to systematically describe and predict the world around us; but the more philosophical side is about asking what the fundamental objects of this world “really are.” Today’s theories describe reality in terms of abstract notions such as group representations, transformation properties, and spaces of complex functions. This paper is part of an effort to find a new description in terms of more concrete geometric notions such as manifolds, tangent vectors, and parallel transport.
Adam Marsh
Read the Original
This page is a summary of: Defining geometric gauge theory to accommodate particles, continua, and fields, Journal of Mathematical Physics, September 2024, American Institute of Physics,
DOI: 10.1063/5.0230212.
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