arXiv subjects
Publications and source records attributed to Ivan Arraut.
We demonstrate that the number of Nambu-Goldstone bosons is always equal to the number of conserved currents inside the scenario of non-Hermitian field theories with spontaneous symmetry breaking. This eliminates the redundancies which normally appears in Hermitian field theories, specifically when the Lagrangian under analysis violates explicitly the Lorentz symmetry.
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.
We analyze the loss of information and the loss of learning capability inside an arrangement of neural networks. Our method is new and based on the formulation of non-unitary Bogoliubov transformations in order to connect the information between different points of the arrangement. This can be done after expanding the activation function in a Fourier series and then assuming that its information is stored inside a Quantum scalar field.
It is known that the probability is not a conserved quantity in the stock market, given the fact that it corresponds to an open system. In this paper we analyze the flow of probability in this system by expressing the ideal Black-Scholes equation in the Hamiltonian form. We then analyze how the non-conservation of probability affects the stability of the prices of the Stocks. Finally, we find the conditions under which the probability might be conserved in the market, challenging in this way the non-Hermitian nature of the Black-Scholes Hamiltonian.
We compare the standard Higgs mechanism corresponding to the scalar field, with the dynamical origin of the graviton mass inside the scenario of the dRGT theory of massive gravity. We demonstrate that the effective mass perceived locally by different observers, depends on the way how they define the local time with respect to the preferred notion of time defined by the Stückelberg function $T_0(r,t)$.
We demonstrate that when there is spontaneous symmetry breaking in any system, relativistic or non-relativistic, the dynamic of the Nambu-Goldstone bosons is governed by the Quantum Yang-Baxter equations. These equations describe the triangular dynamical relations between pairs of Nambu-Goldstone bosons and the degenerate vacuum. We then formulate a theorem and a corollary showing that these relations guarantee the appropriate dispersion relation and the appropriate counting for the Nambu-Goldstone bosons.
We introduce a new tool for predicting the evolution of an option for the cases where at some specific time, there is a high-degree of uncertainty for identifying its price. We work over the special case where we can predict the evolution of the system by joining a single price for the Option, defined at some specific time with a pair of prices defined at another instant. This is achieved by describing the evolution of the system through a financial Hamiltonian. The extension to the case of multiple prices at a given instant is straightforward. We also explain how to apply these results in real situations.
We study the black-hole evaporation from the perspective of neural networks. We then analyze the evolution of the Hamiltonian, finding in this way the conditions under which the synapse connecting the neurons changes from gravitatory to inhibitory during the evaporation process.
We explain the origin of the mass for the Nambu-Goldstone bosons when there is a chemical potential in the action which breaks explicitly the symmetry. The method is based on the number of independent histories for the interaction of the pair of Nambu-Goldstone bosons with the degenerate vacuum (triangle relations). The analysis suggests that under some circumstances, pairs of massive Nambu-Goldstone bosons can become a single degree of freedom with an effective mass defined by the superposition of the individual masses of each boson. Possible mass oscillations for the Nambu-Goldstone bosons are discussed.
We apply the Bogoliubov transformations in order to connect two different vacuums, one~located at past infinity and another located at future infinity around a black hole inside the scenario of the nonlinear theory of massive gravity. The presence of the extra degrees of freedom changes the behavior of the logarithmic singularity and, as a consequence, the relation between the two Bogoliubov coefficients. This has an effect on the number of particles, or equivalently, on the black hole temperature perceived by observers defining the time arbitrarily.
An approach for $q$-deformed Bogoliubov transformations is presented. Assuming a left-right module action together with an *-operation and deformed commutation relations, we construct a q-deformation of the nonlinear Bogoliubov transformation. Moreover we give a general result which can be applied in Quantum Field Theory. Finally, we introduce a Hopf structure when q is a root of unity.
If we apply the path integral formulation in order to analyze the particle creation process of black-holes inside the non-linear formulation of massive gravity, it is possible to demonstrate that the effect of the extra-degrees of freedom is to deform the periodicity of the poles of the propagator in the complex $t$-plane. This might create the effect of extra-particle creation process at scales where the extra-degrees of freedom become relevant. For stationary solutions, depending on the values taken by the free parameters of the theory, the periodicity structure of the propagator reveal two effects. The first one is a shift on the positions of the pole of the propagator with respect to the GR case, affecting then the instant at which the particles are detected. The second one is the existence of branch points, affecting then the perception of particles. The branch point can be finite (including the zero order case) or infinite depending on the free-parameters of the theory.
In non-relativistic systems, when there is spontaneous symmetry breaking, the number of Nambu-Goldstone bosons ($n_{NG}$) are not necessarily equal to the number of broken generators ($n_{BG}$). Here we use the method of operators for analyzing the necessary conditions in order to obtain the correct dispersion relation for the Nambu-Goldstone bosons.
The presence of Nambu-Goldstone bosons introduce a natural degeneracy inside the vacuum solutions of the non-linear formulations of massive gravity in the same spirit of the $σ$-models. When the gravitational effects are taken into account, and the observers are located at any distance with respect to the source, this degeneracy corresponds to a multiplicity (flow) of the fundamental scales of the theory. The different values of the fundamental scales are connected each other through the broken generators of the theory.
We calculate explicitly the black-hole temperature for the Schwarzschild de-Sitter solution inside massive gravity by defining the Killing-vector in the direction of the Stückelberg function. We then consider the conditions which an observer in massive gravity has to obey in order to agree with the standard results of General Relativity.
We formulate the Nambu-Goldstone theorem as a triangular relation between pairs of Goldstone bosons with the degenerate vacuum. The vacuum degeneracy is then a natural consequence of this relation. Inside the scenario of String Theory, we then find that there is a correspondence between the way how the $D$-branes interact and the properties of the Goldstone bosons.
We show the direct analogy between the ghost-free non-linear formulation of massive gravity and the standard $σ$-models well understood in the literature. This issue explains why there are two non-trivial family of solutions for the spherically symmetric case inside the non-linear massive gravity formulations with two free-parameters $α$ and $β$. In general, the case $β<α^2$ has a single physical vacuum state. On the other hand, the case $β=α^2$ contains a natural vacuum degeneracy. This is in perfect analogy with the $σ$-model for scalar fields where depending on the values taken by the parameters of the theory the vacuum can be single or degenerate.
The Higgs mechanism at the graviton level formulated as a Vainshtein mechanism in time domains implies that the extra-degrees of freedom become relevant depending on the direction of time (frame of reference) with respect to the preferred time direction (preferred frame) defined by the Stückelberg function $T_0(r,t)$ which contains the information of the extra-degrees of freedom of the theory. In this manuscript, I make the general definition of the Higgs mechanism by analyzing the gauge symmetries of the action and the general form of the vacuum solutions for the graviton field. In general, the symmetry generators depending explicitly on the Stückelberg fields are broken at the vacuum level. These broken generators, define the number of Nambu-Goldstone bosons which will be eating up by the dynamical metric in order to become massive.