Spontaneous symmetry breaking in Quantum Finance
Ivan Arraut, Alan Au, Alan Ching-biu Tse
TL;DR
This paper explores spontaneous symmetry breaking in Quantum Finance, using Hamiltonian formulations of Black-Scholes and Merton-Garman equations, and discusses implications like degenerate states and Nambu-Goldstone bosons.
Contribution
It introduces a novel application of symmetry breaking concepts from physics to financial models, linking martingale states to vacuum states and analyzing broken symmetries.
Findings
Martingale condition as vacuum state
Degeneracy of states indicates symmetry breaking
Potential emergence of Nambu-Goldstone bosons in markets
Abstract
We analyze the phenomena of spontaneous symmetry breaking in Quantum Finance by using as a starting point the Black-Scholes (BS) and the Merton-Garman (MG) equations expressed in the Hamiltonian form. In this scenario the martingale condition (state) corresponds to the vacuum state which becomes degenerate when the symmetry of the system is spontaneously broken. We then analyze the broken symmetries of the system and we interpret from the perspective of Financial markets the possible appearance of the Nambu-Goldstone bosons.
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