arXiv subjects

José Luis Alonso

Publications and source records attributed to José Luis Alonso.

4 recordsLinked to original sources

arXiv2024

Geometric flavours of Quantum Field theory on a Cauchy hypersurface. Part I: Gaussian analysis and other Mathematical aspects

In this series of papers we aim to provide a mathematically comprehensive framework to the Hamiltonian pictures of quantum field theory in curved spacetimes. Our final goal is to study the kinematics and the dynamics of the theory from the point of differential geometry in infinite dimensions.In this first part we introduce the tools of Gaussian analysis in infinite dimensional spaces of distributions. These spaces will serve the basis to understand the Schrödinger and Holomorphic pictures, over arbitrary Cauchy hypersurfaces, using tools of Hida-Malliavin calculus. Here the Wiener-Ito decomposition theorem provides the QFT particle interpretation. Special emphasis is done in the applications to quantization of these tools in the second part of this paper. We devote a section to introduce Hida test functions as a notion of second quantized test functions. We also analyze of the ingredients of classical field theory modeled as distributions paving the way for quantization procedures that will be analyzed in the second part of this series.

math-ph↗

arXiv2024

Geometric flavours of Quantum Field theory on a Cauchy hypersurface. Part II: Methods of quantization and evolution

In this series of papers we aim to provide a mathematically comprehensive framework to the Hamiltonian pictures of quantum field theory in curved spacetimes. Our final goal is to study the kinematics and the dynamics of the theory from the point of differential geometry in infinite dimensions. In this second part we use the tools of Gaussian analysis in infinite dimensional spaces introduced in the first part to describe rigorously the procedures of geometric quantization in the space of Cauchy data of a scalar theory. This leads us to discuss and establish relations between different pictures of QFT. We also apply these tools to describe the geometrization of the space of pure states of quantum field theory as a Khäler manifold. We use this to derive an evolution equation that preserves the geometric structure and avoids norm losses in the evolution. This leads us to a modification of the Schrödinger equation via a quantum connection that we discuss and exemplify in a simple case.

math-ph↗

arXiv2023

First glycine isomer detected in the interstellar medium: glycolamide (NH$_2$C(O)CH$_2$OH)

We report the first detection in the interstellar medium of a C$_2$H$_5$O$_2$N isomer: $syn$-glycolamide (NH$_2$C(O)CH$_2$OH). The exquisite sensitivity at sub-mK levels of an ultra-deep spectral survey carried out with the Yebes 40m and IRAM 30m telescopes towards the G+0.693-0.027 molecular cloud have allowed us to unambiguously identify multiple transitions of this species. We derived a column density of (7.4 $\pm$ 0.7)$\times$10$^{12}$ cm$^{-2}$, which implies a molecular abundance with respect to H$_2$ of 5.5$\times$10$^{-11}$. The other C$_2$H$_5$O$_2$N isomers, including the higher-energy $anti$ conformer of glycolamide, and two conformers of glycine, were not detected. The upper limit derived for the abundance of glycine indicates that this amino acid is surely less abundant than its isomer glycolamide in the ISM. The abundances of the C$_2$H$_5$O$_2$N isomers cannot be explained in terms of thermodynamic equilibrium, and thus chemical kinetics need to be invoked. While the low abundance of glycine might not be surprising, based on the relative low abundances of acids in the ISM compared to other compounds (e.g. alcohols, aldehydes or amines), several chemical pathways can favour the formation of its isomer glycolamide. It can be formed through radical-radical reactions on the surface of dust grains. The abundances of these radicals can be significantly boosted in an environment affected by a strong ultraviolet field induced by cosmic rays, such as that expected in G+0.693-0.027. Therefore, as shown by several recent molecular detections towards this molecular cloud, it stands out as the best target to discover new species with carbon, oxygen and nitrogen with increasing chemical complexity.

astro-ph.GA↗

arXiv2011

Exact and efficient calculation of Lagrange multipliers in constrained biological polymers: Proteins and nucleic acids as example cases

In order to accelerate molecular dynamics simulations, it is very common to impose holonomic constraints on their hardest degrees of freedom. In this way, the time step used to integrate the equations of motion can be increased, thus allowing, in principle, to reach longer total simulation times. The imposition of such constraints results in an aditional set of Nc equations (the equations of constraint) and unknowns (their associated Lagrange multipliers), that must be solved in one way or another at each time step of the dynamics. In this work it is shown that, due to the essentially linear structure of typical biological polymers, such as nucleic acids or proteins, the algebraic equations that need to be solved involve a matrix which is banded if the constraints are indexed in a clever way. This allows to obtain the Lagrange multipliers through a non-iterative procedure, which can be considered exact up to machine precision, and which takes O(Nc) operations, instead of the usual O(Nc3) for generic molecular systems. We develop the formalism, and describe the appropriate indexing for a number of model molecules and also for alkanes, proteins and DNA. Finally, we provide a numerical example of the technique in a series of polyalanine peptides of different lengths using the AMBER molecular dynamics package.

physics.bio-ph↗