A general procedure to describe the coupling $U_A (1) times U_B (1)$ between antisymmetric gauge fields is proposed. For vector gauge theories the inclusion of magnetic mixing in the hidden sector induces millicharges -- in principle -- observable. W
e extend the analysis to antisymmetric fields and the extension to higher order monopoles is discussed. A modification of the model discussed in cite{Ibarra} with massless antisymmetric fields as dark matter is also considered and the total cross section ratio are found and discussed.
An approach to study a generalization of the classical-quantum transition for general systems is proposed. In order to develop the idea, a deformation of the ladder operators algebra is proposed that contains a realization of the quantum group $SU(2)
_q$ as a particular case. In this deformation Plancks constant becomes an operator whose eigenvalues approach $hbar $ for small values of $n$ (the eigenvalue of the number operator), and zero for large values of $n$ (the system is classicalized).
The dynamics of an anapole seen as dark matter at low energies is studied by solving the Schrodinger-Pauli equation in a potential involving Dirac-delta and its derivatives in three-dimensions. This is an interesting mathematical problem that, as far
as we know, has not been previously discussed. We show how bound states emerge in this approach and the scattering problem is formulated (and solved) directly. The total cross section is in full agreement with independent calculations in the standard model.
The Landau problem for inhomogeneous magnetic fields is examined in a very general context and several interesting analogies with the Nielsen-Olesen vortices are established. Firstly we show that the Landau problem with non-homogeneous magnetic field
s exhibits Meissner effect that is unstable unless two-body interactions are added and vortices emerge. Using the scaling freedom we can write the Schrodinger equation in terms of the scales ratio $kappa ={ E}/{ m }propto 1- T/T_c $ where the last identification is realised simply by using the Gizburg-Landau theory. We find our equations are valid in the superconducting regime, and it is not possible for the Cooper pairs amplitude to reach to a constant, non-zero value, and therefore the theory is unstable. The supersymmetric quantum mechanics version, by completeness, is also considered.
We propose a bicosmology model which is the classical analog of noncommutative quantum mechanics. From this point of view the sources of the modified FRW equations are dark energy ones governed by a Chapligyns equation state. The parameters of noncom
mutativity $theta$ and $B$ are interpreted in terms of the Planck area and a like-magnetic field, presumably the magnetic seed of magnetogenesis.
The twin paradox, which evokes from the the idea that two twins may age differently because of their relative motion, has been studied and explained ever since it was first described in 1906, the year after special relativity was invented. The questi
on can be asked: Is there anything more to say? It seems evident that acceleration has a role to play, however this role has largely been brushed aside since it is not required in calculating, in a preferred reference frame, the relative age difference of the twins. Indeed, if one tries to calculate the age difference from the point of the view of the twin that undergoes the acceleration, then the role of the acceleration is crucial and cannot be dismissed. In the resolution of the twin paradox, the role of the acceleration has been denigrated to the extent that it has been treated as a red-herring. This is a mistake and shows a clear misunderstanding of the twin paradox.
In the framework of a bimetric model, we discuss a relation between the (modified) Friedmann equations and a mechanical system similar to the quantum Hall effect problem. Firstly, we show how these modified Friedmann equations are mapped to an anisot
ropic two-dimensional charged harmonic oscillator in the presence of a constant magnetic field, with the frequencies of the oscillator playing the role of the cosmological constants. This problem has two energy scales leading to the identification of two different regimes, namely, one dominated by the cosmological constants, with exponential expansions for the scale factors, and the other dominated by a magnetic seed, which would be responsible for both a component of dark energy and a primordial magnetic field. The latter regime would be described by a (nonperturbative) mapping between the cosmological evolution and the quantum Hall effect.
The interaction between two initially causally disconnected regions of the universe is studied using analogies of non-commutative quantum mechanics and deformation of Poisson manifolds. These causally disconnect regions are governed by two independen
t Friedmann-Lema^{i}tre-Robertson-Walker (FLRW) metrics with scale factors $a$ and $b$ and cosmological constants $Lambda_a$ and $Lambda_b$, respectively. The causality is turned on by positing a non-trivial Poisson bracket $[ {cal P}_{alpha}, {cal P}_{beta} ] =epsilon_{alpha beta}frac{kappa}{G}$, where $G$ is Newtons gravitational constant and $kappa $ is a dimensionless parameter. The posited deformed Poisson bracket has an interpretation in terms of 3-cocycles, anomalies and Poissonian manifolds. The modified FLRW equations acquire an energy-momentum tensor from which we explicitly obtain the equation of state parameter. The modified FLRW equations are solved numerically and the solutions are inflationary or oscillating depending on the values of $kappa$. In this model the accelerating and decelerating regime may be periodic. The analysis of the equation of state clearly shows the presence of dark energy. By completeness, the perturbative solution for $kappa ll1 $ is also studied.
A kinetic mixing term, which generalizes the duality symmetry of Dirac, is studied in a theory with two photons (visible and hidden). This theory can be either CP conserving or CP violating depending on the transformation of fields in the hidden sect
or. However if CP is violated, it necessarily occurs in the hidden sector. This opens up an interesting possibility of new sources of CP violation.
We suggest that dark matter may be partially constituted by a dilute t Hooft-Polyakov monopoles gas. We reach this conclusion by using the Georgi-Glashow model coupled to a dual kinetic mixing term $ F{tilde {cal G}}$ where $F$ is the electromagnetic
field and ${cal G}$ the t Hooft tensor. We show that these monopoles carry both (Maxwell) electric and (Georgi-Glashow) magnetic charges and the electric charge quantization condition is modified in terms of a dimensionless real parameter. This parameter could be determined from milli-charged particle experiments.
