Spontaneous symmetry breaking in Quantum Finance

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.

arXiv comment7 pages, published in EPL

References in corpus (4)

• The Quantum Yang Baxter conditions: The fundamental relations behind the Nambu-Goldstone theorem
• The Nambu-Goldstone theorem in non-relativistic systems
• The origin of the mass of the Nambu-Goldstone bosons
• The connection between multiple prices of an Option at a given time with single prices defined at different times: The concept of weak-value in quantum finance

Cited by in corpus (3)

• The probability flow in the Stock market and Spontaneous symmetry breaking in Quantum Finance
• Gauge symmetries and the Higgs mechanism in Quantum Finance
• On the Local equivalence of the Black Scholes and the Merton Garman equations