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  • Arraut, I., Segovia, C., & Rosado, W. (2023). The Hawking Radiation in Massive Gravity: Path Integral and the Bogoliubov Method. Universe, 9(5), 228. https://doi.org/10.3390/universe9050228

    We prove the consistency of the different approaches for deriving the black hole radiation for the spherically symmetric case inside the theory of Massive Gravity. By comparing the results obtained by using the Bogoliubov transformations with those obtained by using the Path Integral formulation, we find that in both cases, the presence of the extra-degrees of freedom creates the effect of extra-particles creation due to the distortions on the definitions of time defined by the different observers at large scales. This, however, does not mean extra-particle creation at the horizon level. Instead, the apparent additional particles perceived at large scales emerge from how distant observers define their time coordinate, which is distorted due to the existence of extra-degrees of freedom.

  • Arraut, I., & Lei, K.-I. (2023). The Role of the Volatility in the Option Market. AppliedMath, 3(4), 882–908. https://doi.org/10.3390/appliedmath3040047

    We review some general aspects about the Black–Scholes equation, which is used for predicting the fair price of an option inside the stock market. Our analysis includes the symmetry properties of the equation and its solutions. We use the Hamiltonian formulation for this purpose. Taking into account that the volatility inside the Black–Scholes equation is a parameter, we then introduce the Merton–Garman equation, where the volatility is stochastic, and then it can be perceived as a field. We then show how the Black–Scholes equation and the Merton–Garman one are locally equivalent by imposing a gauge symmetry under changes in the prices over the Black–Scholes equation. This demonstrates that the stochastic volatility emerges naturally from symmetry arguments. Finally, we analyze the role of the volatility on the decisions taken by the holders of the options when they use the solution of the Black–Scholes equation as a tool for making investment decisions.

  • Arraut, I. (2023). Gauge symmetries and the Higgs mechanism in Quantum Finance (No. arXiv:2306.03237). arXiv. https://doi.org/https://doi.org/10.48550/arXiv.2306.03237

    By using the Hamiltonian formulation, we demonstrate that the Merton-Garman equation emerges naturally from the Black-Scholes equation after imposing invariance (symmetry) under local (gauge) transformations over changes in the stock price. This is the case because imposing gauge symmetry implies the appearance of an additional field, which corresponds to the stochastic volatility. The gauge symmetry then imposes some constraints over the free-parameters of the Merton-Garman Hamiltonian. Finally, we analyze how the stochastic volatility gets massive dynamically via Higgs mechanism.

  • Arraut, I. (2023). Gauge symmetries and the Higgs mechanism in Quantum Finance. Europhysics Letters, 143(4), 42001. https://doi.org/10.1209/0295-5075/acedce

    By using the Hamiltonian formulation, we demonstrate that the Merton-Garman equation emerges naturally from the Black-Scholes equation after imposing invariance (symmetry) under local (gauge) transformations over changes in the stock price. This is the case because imposing gauge symmetry implies the appearance of an additional field, which corresponds to the stochastic volatility. The gauge symmetry then imposes some constraints over the free parameters of the Merton-Garman Hamiltonian. Finally, we analyze how the stochastic volatility gets massive dynamically via Higgs mechanism.

  • Arraut, I. (2023). The solution to the Hardy’s paradox (No. arXiv:2106.06397). arXiv. https://doi.org/10.48550/arXiv.2106.06397

    By using both, the weak-value formulation as well as the standard probabilistic approach, we analyze the Hardy's experiment introducing a complex and dimensionless parameter ($\epsilon$) which eliminates the assumption of complete annihilation when both, the electron and the positron departing from a common origin, cross the intersection point $P$. We then find that the paradox does not exist for all the possible values taken by the parameter. The apparent paradox only appears when $\epsilon=1$; however, even in this case we can interpret this result as a natural consequence of the fact that the particles can cross the point $P$, but at different times due to a natural consequence of the energy-time uncertainty principle.

  • Arraut, I. (2023). The Tully-Fisher law and dark matter effects derived via modified symmetries. Europhysics Letters, 144(2), 29003. https://doi.org/10.1209/0295-5075/ad05f7

    In any physical system, when we move from short to large scales, new spacetime symmetries emerge which help us to simplify the dynamics of the system. In this letter we demonstrate that certain variations on the symmetries of general relativity at large scales generate the effects equivalent to dark matter ones. In particular, we reproduce the Tully-Fisher law, consistent with the predictions proposed by MOND. Additionally, we demonstrate that the dark matter effects derived in this way are consistent with the predictions suggested by MOND, without modifying gravity.

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Last update from database: 5/23/24, 9:28 PM (UTC)

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