The probability flow in the Stock market and Spontaneous symmetry breaking in Quantum Finance

TL;DR

This paper explores how spontaneous symmetry breaking in quantum finance affects the martingale condition in stock markets, revealing the influence of kinetic terms on vacuum states and linking information flow to market dynamics.

Contribution

It introduces a novel analysis of symmetry breaking patterns considering kinetic terms as potential, connecting vacuum degeneracy with information flow in financial markets.

Findings

Kinetic terms can shift the effective vacuum in quantum finance models.

Vacuum degeneracy relates to multiple martingale states in stock markets.

Information flow influences the symmetry breaking patterns.

Abstract

The Spontaneous Symmetry breaking in Quantum Finance considers the martingale condition in the stock market as a vacuum state if we express the financial equations in the Hamiltonian form. The original analysis for this phenomena ignores completely 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 market.