Gauge Theory of Economics

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A gauge theory of economics is the application of differential geometric methods to economic problems.

Example

Gauge theory is all you need to break out of the economics flatland. The following is an equation that Eric Weinstein talked about. We are going to break it down together and picture the meaning of each part in a geometrical and intuitive way. The results of this work will be interesting for the present economics community.

[math]\displaystyle{ q = \frac{ {p_0}\cdot{q} }{ {p_0}\cdot{q_0} } q_0 + (q - \frac{ {p_0}\cdot{q} }{ {p_0}\cdot{q_0} } q_0) }[/math]

where we label the first term as Reference Basket and the second one as Barter.

Suppose that we live in a world where there are only 3 different types of items for sale: apples, berries and cherries (A, B and C respectively.) Say today we pick up our basket and go to the market. At the market, the price of each item is posted up as a number on the wall where we can see. So, we represent the prices by a $${1}\times{3}$$ row vector $$p$$. On the other hand, we buy different quantities of each item and so a $${3}\times{1}$$ column vector $$q$$ denotes the list of 3 quantities for items A, B and C.

The next day, we go back to the market and now we are interested in measuring price changes.

Reference Materials

Papers

• The Index Number Problem: A Differential Geometric Approach by Pia Malaney.
• Time and symmetry in models of economic markets by Lee Smolin.

Books

• The Physics of Wall Street by James Weatherall.

Lectures

Lectures, presentations, and panels by Pia Malaney and Eric Weinstein on the topic.

• Stanford University: Systems Architecture, Kabuki Capitalism, and the Economic Manhattan Project (YouTube)
• Gauge Theory and Inflation: Enlarging the Wu-Yang Dictionary (YouTube)
• Towards a Mathematics of New Economic Thinking for Reflexive Markets: A Natural Economic Connection on Preference Bundles over the Taste-Time Continuum (The Fields Institute)
• A Science Less Dismal: Welcome to the Economic Manhattan Project
  • Video

Interviews

• Eric talking about this on Quora