论文标题
关于马丁纳尔条件的多样性：量子融资中的自发对称性破坏
On the multiplicity of the martingale condition: Spontaneous symmetry breaking in Quantum Finance
论文作者
论文摘要
我们证明，当我们以汉密尔顿形式表达金融方程时，股票市场中的马丁格条件可以被解释为真空状况。然后，我们表明价格变化下的对称性通常会自发损坏，而在波动性变化下的对称性（对于Merton-Garman（mg）方程式）也被自发损坏。这重现了系统的真空变性。通过这种方式，我们发现了可以将Martingale条件视为非分类真空的条件。这使我们在自发对称性破坏与通过金融系统边界的信息流之间存在令人惊讶的联系。随后，我们发现了MG方程的延长的MARNINGALE条件，这不仅取决于价格，而且还取决于波动性，最后，我们展示了如果在黑色Scholes和MG方程式上包括其他非衍生术语，那么会发生什么，然后破坏该系统的其他一些对称性。
We demonstrate that the martingale condition in the stock market can be interpreted as a vacuum condition when we express the financial equations in the Hamiltonian form. We then show that the symmetry under the changes of the prices is spontaneously broken in general and the symmetry under changes in the volatility, for the case of the Merton-Garman (MG) equation, is also spontaneously broken. This reproduces a vacuum degeneracy for the system. In this way, we find the conditions under which, the martingale condition can be considered to be a non-degenerate vacuum. This gives us a surprising connection between spontaneous symmetry breaking and the flow of information through the boundaries for the financial systems. Subsequently, we find an extended martingale condition for the MG equation, depending not only prices but also on the volatility and finally, we show what happens if we include additional non-derivative terms on the Black Scholes and on the MG equations, breaking then some other symmetries of the system spontaneously.
