History state formalism for Dirac's theory

We propose a history state formalism for a Dirac particle. By introducing a reference quantum clock system it is first shown that Dirac's equation can be derived by enforcing a timeless Wheeler-DeWitt-like equation for a global state. The Hilbert space of the whole system constitutes a unitary representation of the Lorentz group with respect to a properly defined invariant product, and the proper normalization of global states directly ensures standard Dirac's norm. Moreover, by introducing a second quantum clock, the previous invariant product emerges naturally from a generalized continuity equation. The invariant parameter $\tau$ associated with this second clock labels history states for different particles, yielding an observable evolution in the case of an hypothetical superposition of different masses. Analytical expressions for both space-time density and electron-time entanglement are provided for two particular families of electron's states, the former including Pryce localized particles.Comment: 9 pages, 2 figures, final versio

Prostaglandin E2-EP1 and EP2 receptor signaling promotes apical junctional complex disassembly of Caco-2 human colorectal cancer cells

<p>Abstract</p> <p>Background</p> <p>The apical junctional complex (AJC) is a dynamic structure responsible to maintain epithelial cell-cell adhesions and it plays important functions such as, polarity, mechanical integrity, and cell signaling. Alteration of this complex during pathological events leads to an impaired epithelial barrier by perturbation of the cell-cell adhesion system. Although clinical and experimental data indicate that prostaglandin E₂(PGE₂) plays a critical function in promoting cell motility and cancer progression, little is known concerning its role in AJC disassembly, an event that takes place at the beginning of colorectal tumorigenesis. Using Caco-2 cells, a cell line derived from human colorectal cancer, we investigated the effects of prostaglandin E₂(PGE₂) treatment on AJC assembly and function.</p> <p>Results</p> <p>Exposition of Caco-2 cells to PGE₂promoted differential alteration of AJC protein distribution, as evidenced by immunofluorescence and immunoblotting analysis and impairs the barrier function, as seen by a decrease in the transepithelial electric resistance and an increase in the permeability to ruthenium red marker. We demonstrated the involvement of EP1 and EP2 prostaglandin E₂receptor subtypes in the modulation of the AJC disassembly caused by prostanoid. Furthermore, pharmacological inhibition of protein kinase-C, but not PKA and p38MAPK significantly prevented the PGE₂effects on the AJC disassembly.</p> <p>Conclusion</p> <p>Our findings strongly suggest a central role of Prostaglandin E2-EP1 and EP2 receptor signaling to mediate AJC disassembly through a mechanism that involves PKC and claudin-1 as important target for the TJ-related effects in human colorectal cancer cells (Caco-2).</p

One More Step Towards Well-Composedness of Cell Complexes over nD Pictures

An nD pure regular cell complex K is weakly well-composed (wWC) if, for each vertex v of K, the set of n-cells incident to v is face-connected. In previous work we proved that if an nD picture I is digitally well composed (DWC) then the cubical complex Q(I) associated to I is wWC. If I is not DWC, we proposed a combinatorial algorithm to “locally repair” Q(I) obtaining an nD pure simplicial complex PS(I) homotopy equivalent to Q(I) which is always wWC. In this paper we give a combinatorial procedure to compute a simplicial complex PS(¯I) which decomposes the complement space of |PS(I)| and prove that PS(¯I) is also wWC. This paper means one more step on the way to our ultimate goal: to prove that the nD repaired complex is continuously well-composed (CWC), that is, the boundary of its continuous analog is an (n − 1)- manifold.Ministerio de Economía y Competitividad MTM2015-67072-

Path Integrals from Spacetime Quantum Actions

We present a spacetime Hilbert space formulation of Feynman path integrals (PIs). It relies on a tensor product structure in time which provides extended representations of dynamical quantum observables through a spacetime quantum action operator. As a consequence, the ``sum over paths'' of the different PI formulations naturally arise within the same Hilbert space, with each one associated with a different quantum trajectory basis. New insights on PI-based results naturally follow, including exact discretizations and a non-trivial approach to the continuum limit.Comment: 8 pages, 1 figur

Spacetime quantum and classical mechanics with dynamical foliation

The conventional phase space of classical physics treats space and time differently, and this difference carries over to field theories and quantum mechanics (QM). In this paper, the phase space is enhanced through two main extensions. Firstly, we promote the time choice of the Legendre transform to a dynamical variable. Secondly, we extend the Poisson brackets of matter fields to a spacetime symmetric form. The ensuing "spacetime phase space" is employed to obtain an explicitly covariant version of Hamilton equations for relativistic field theories. A canonical-like quantization of the formalism is then presented in which the fields satisfy spacetime commutation relations and the foliation is quantum. In this approach, the classical action is also promoted to an operator and retains explicit covariance through its non-separability in the matter-foliation partition. The problem of establishing a correspondence between the new noncausal framework (where fields at different times are independent) and conventional QM is solved through a generalization of spacelike correlators to spacetime. In this generalization, the Hamiltonian is replaced by the action, and conventional particles by off-shell particles. When the foliation is quantized, the previous map is recovered by conditioning on foliation eigenstates, in analogy with the Page and Wootters mechanism. We also provide an interpretation of the correspondence in which the causal structure of a given theory emerges from the quantum correlations between the system and an environment. This idea holds for general quantum systems and allows one to generalize the density matrix to an operator containing the information of correlators both in space and time.Comment: 25 pages, 4 figure

Spacetime Quantum Actions

We propose a formulation of quantum mechanics in an extended Fock space in which a tensor product structure is applied to time. Subspaces of histories consistent with the dynamics of a particular theory are defined by a direct quantum generalization of the corresponding classical action. The diagonalization of such quantum actions enables us to recover the predictions of conventional quantum mechanics and reveals an extended unitary equivalence between all physical theories. Quantum correlations and coherent effects across time and between distinct theories acquire a rigorous meaning, which is encoded in the rich temporal structure of physical states. Connections with modern relativistic schemes and the path integral formulation also emerge.Comment: 16 pages, 3 figures, accepted for publication in Phys. Rev.

Renormalization Group and Grand Unification with 331 Models

By making a renormalization group analysis we explore the possibility of having a 331 model as the only intermediate gauge group between the standard model and the scale of unification of the three coupling constants. We shall assume that there is no necessarily a group of grand unification at the scale of convergence of the couplings. With this scenario, different 331 models and their corresponding supersymmetric versions are considered, and we find the versions that allow the symmetry breaking described above. Besides, the allowed interval for the 331 symmetry breaking scale, and the behavior of the running coupling constants are obtained. It worths saying that some of the supersymmetric scenarios could be natural frameworks for split supersymmetry. Finally, we look for possible 331 models with a simple group at the grand unification scale, that could fit the symmetry breaking scheme described above.Comment: 18 pages. 3 figures. Some results reinterpreted, a new section and references added. Version to appear in International Journal of Modern Physics

Optical detection of the radio supernova SN 2000ft in the circumnuclear region of the luminous infrared galaxy NGC 7469

SN 2000ft is detected in two independent Planetary Camera images (F547W and F814W) taken May 13, 2000, about two months before the predicted date of the explosion (July 19, 2000), based on the analysis of its radio light evolution by Alberdi and collaborators. The apparent optical magnitudes and red color of SN 2000ft indicate that it is observed through an extinction of at least A$_V$= 3.0 magnitudes. The extinction corrected lower limit to the absolute visual magnitude (M$_V$ $\leq -$ 18.0), identifies SN 2000ft as a luminous supernova in the optical, as other luminous radio supernovae before. SN 2000ft exploded in a region located at only 0.1 arcsec (i.e. 34 +/- 3 pc) west of a faint cluster (C24). No parent cluster is identified within the detection limits of the HST short exposures. The unambiguous detection of SN 2000ft in the visual shows that multi-epoch sub-arcsecond (FWHM less than 0.1 arcsec) optical imaging is also a valid tool that should be explored further to detect supernovae in the dusty (circum)nuclear regions of (U)LIRGs

Giant and Broadband THz and IR Emission in Drift-biased Graphene-Based Hyperbolic Nanostructures

We demonstrate that Cherenkov radiation can be manipulated in terms of operation frequency, bandwidth, and efficiency by simultaneously controlling the properties of drifting electrons and the photonic states supported by their surrounding media. We analytically show that the radiation rate strongly depends on the momentum of the excited photonic state, in terms of magnitude, frequency dispersion, and its variation versus the properties of the drifting carriers. This approach is applied to design and realize miniaturized, broadband, tunable, and efficient terahertz and far-infrared sources by manipulating and boosting the coupling between drifting electrons and engineered hyperbolic modes in graphene-based nanostructures. The broadband, dispersive, and confined nature of hyperbolic modes relax momentum matching issues, avoid using electron beams, and drastically enhance the radiation rate - allowing that over 90% of drifting electrons emit photons. Our findings open a new paradigm for the development of solid-state terahertz and infrared sources.Comment: 4 figure