The Probability Flow in the Stock Market and Spontaneous Symmetry Breaking in Quantum Finance

Ivan Arraut, João Alexandre Lobo Marques and Sergio Gomes
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Ivan Arraut: Lee Shau Kee School of Business and Administration, The Open University of Hong Kong, 30 Good Shepherd Street, Homantin, Kowloon, Hong Kong, China
João Alexandre Lobo Marques: FBL, University of Saint Joseph Estrada Marginal da Ilha Verde, 14-17, Macao, China
Sergio Gomes: FBL, University of Saint Joseph Estrada Marginal da Ilha Verde, 14-17, Macao, China

Mathematics, 2021, vol. 9, issue 21, 1-18

Abstract: The spontaneous symmetry breaking phenomena applied to Quantum Finance considers that the martingale state in the stock market corresponds to a ground (vacuum) state if we express the financial equations in the Hamiltonian form. The original analysis for this phenomena completely ignores the kinetic terms in the neighborhood of the minimal of the potential terms. This is correct in most of the cases. However, when we deal with the martingale condition, it comes out that the kinetic terms can also behave as potential terms and then reproduce a shift on the effective location of the vacuum (martingale). In this paper, we analyze the effective symmetry breaking patterns and the connected vacuum degeneracy for these special circumstances. Within the same scenario, we analyze the connection between the flow of information and the multiplicity of martingale states, providing in this way powerful tools for analyzing the dynamic of the stock markets.

Keywords: martingale condition; vacuum condition; spontaneous symmetry breaking; degenerate vacuum; flow of information; Hermiticity; random fluctuations; conservation of the information (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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