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Modelling the market dynamics of the exchange rate through Maxwell electrodynamic system

Authors

  • Jennifer López-Chacon Facultad de Biología, Universidad Michoacana de San Nicolás de Hidalgo. Francisco J. Mújica s/n, Col. Felicitas del Río. CP 58040, Morelia, Michoacán, México, https://orcid.org/0000-0001-5317-2496 https://orcid.org/0000-0001-5317-2496
  • Martha Beatriz Flores-Romero Facultad de Contabilidad y Ciencias Administrativas,Universidad Michoacana de San Nicolás de Hidalgo. Francisco J. Mújica s/n, Col. Felicitas del Río. CP 58040, Morelia, Michoacán, México, https://orcid.org/0000-0003-4567-5485 https://orcid.org/0000-0003-4567-5485
  • Alfredo Raya Facultad de Ingeniería Eléctrica, Universidad Michoacana de San Nicolás de Hidalgo. Francisco J. Mújica s/n, Col. Felicitas del Río. CP 58040, Morelia, Michoacán, México. Centro de Ciencias Exactas - Universidad del Bío-Bío. Avda. Andrés Bello 720, Casilla 447, Chillán, Chile. https://orcid.org/0000-0002-5394-8634 https://orcid.org/0000-0002-5394-8634
  • José Álvarez-García Departamento de Economía Financiera y Contabilidad, Instituto Universitario de Investigación para el Desarrollo Territorial Sostenible (INTERRA), Universidad de Extremadura, Cáceres, Spain, https://orcid.org/0000-0002-0056-5488 https://orcid.org/0000-0002-0056-5488

DOI:

https://doi.org/10.21919/remef.v21i2.1384

Keywords:

Econophysics, Gauge Theory, Currency Arbitrage, FOREX.

Abstract

This study explores the application of gauge theory in the description of the foreign exchange market (FOREX), a global platform for currency trading. By modelling market dynamics through a one-dimensional electrodynamic system, the research examines arbitrage behaviour from the perspective of gauge symmetry. This approach offers an alternative perspective to traditional econometric models. The article discusses the connections between physics, mathematics, and economics, focusing on how gauge theory contributes to financial modelling. It is based on the theoretical framework developed by Igor Ilinsky, in which asset prices are influenced by “gauge connections”, and develops a simplified model of an electrodynamic system. This model captures the interactions between traders and external economic factors within the FOREX market, known for its liquidity and high daily trading volumes. Using an idealised model, the study analyses currency exchanges involving the euro, the US dollar, and the Mexican peso, focusing on the relationship between profits and market dynamics. The findings indicate that, although the model is an approximation, it captures behaviours observed in financial markets out of equilibrium. 

Author Biographies

Jennifer López-Chacon, Facultad de Biología, Universidad Michoacana de San Nicolás de Hidalgo. Francisco J. Mújica s/n, Col. Felicitas del Río. CP 58040, Morelia, Michoacán, México, https://orcid.org/0000-0001-5317-2496

Facultad de Biología, Universidad Michoacana de San Nicolás de Hidalgo. Francisco J. Mújica s/n, Col. Felicitas del Río. CP 58040, Morelia, Michoacán, México, https://orcid.org/0000-0001-5317-2496

Martha Beatriz Flores-Romero, Facultad de Contabilidad y Ciencias Administrativas,Universidad Michoacana de San Nicolás de Hidalgo. Francisco J. Mújica s/n, Col. Felicitas del Río. CP 58040, Morelia, Michoacán, México, https://orcid.org/0000-0003-4567-5485

Facultad de Contabilidad y Ciencias Administrativas,Universidad Michoacana de San Nicolás de Hidalgo. Francisco J. Mújica s/n, Col. Felicitas del Río. CP 58040, Morelia, Michoacán, México, https://orcid.org/0000-0003-4567-5485

Alfredo Raya, Facultad de Ingeniería Eléctrica, Universidad Michoacana de San Nicolás de Hidalgo. Francisco J. Mújica s/n, Col. Felicitas del Río. CP 58040, Morelia, Michoacán, México. Centro de Ciencias Exactas - Universidad del Bío-Bío. Avda. Andrés Bello 720, Casilla 447, Chillán, Chile. https://orcid.org/0000-0002-5394-8634

Facultad de Ingeniería Eléctrica, Universidad Michoacana de San Nicolás de Hidalgo. Francisco J. Mújica s/n, Col. Felicitas del Río. CP 58040, Morelia, Michoacán, México. Centro de Ciencias Exactas - Universidad del Bío-Bío. Avda. Andrés Bello 720, Casilla 447, Chillán, Chile.  https://orcid.org/0000-0002-5394-8634   

José Álvarez-García, Departamento de Economía Financiera y Contabilidad, Instituto Universitario de Investigación para el Desarrollo Territorial Sostenible (INTERRA), Universidad de Extremadura, Cáceres, Spain, https://orcid.org/0000-0002-0056-5488

Departamento de Economía Financiera y Contabilidad, Instituto Universitario de Investigación para el Desarrollo Territorial Sostenible (INTERRA), Universidad de Extremadura, Cáceres, Spain, https://orcid.org/0000-0002-0056-5488

 

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2026-03-12 — Updated on 2026-03-16

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Vol. 21 No. 2: April - June 2026

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