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Eduardo J. S. Villaseñor

Publications and source records attributed to Eduardo J. S. Villaseñor.

67 records · Page 4Linked to original sources
arXiv2004

Particles and vacuum for perturbative and non-perturbative Einstein-Rosen gravity

We discuss the connection between the Fock space introduced by Ashtekar and Pierri for Einstein-Rosen waves and its perturbative counterpart based on the concept of particle that arises in linearized gravity with a de Donder gauge. We show that the gauge adopted by Ashtekar and Pierri is a generalization of the de Donder gauge to full (i.e. non-linearized) cylindrical gravity. This fact allows us to relate the two descriptions of the Einstein-Rosen waves analyzed here by means of a simple field redefinition. Employing this redefinition, we find the highly non-linear relation that exists between the annihilation and creation-like variables of the two approaches. We next represent the particle-like variables of the perturbative approach as regularized operators, introducing a cut-off. These can be expanded in powers of the annihilation and creation operators of the Ashtekar and Pierri quantization, each additional power being multiplied by an extra square-root of the three-dimensional gravitational constant, $\sqrt{G}$. In principle, the perturbative vacuum may be reached as the limit of a state annihilated by these regularized operators when the cut-off is removed. This state can be written as the vacuum of the Ashtekar and Pierri quantization corrected by a perturbative series in $\sqrt{G}$ with no contributions from particles with energies above the cut-off. We show that the first-order correction is in fact a state of infinite norm. This result is interpreted as indicating that the Fock quantizations in the two approaches are unitarily inequivalent and, in any case, proves that the perturbative vacuum is not analytic in the interaction constant. Therefore a standard perturbative quantum analysis fails.

gr-qc↗
arXiv2004

Asymptotic Analysis of Field Commutators for Einstein-Rosen Gravitational Waves

We give a detailed study of the asymptotic behavior of field commutators for linearly polarized, cylindrically symmetric gravitational waves in different physically relevant regimes. We also discuss the necessary mathematical tools to carry out our analysis. Field commutators are used here to analyze microcausality, in particular the smearing of light cones owing to quantum effects. We discuss in detail several issues related to the semiclassical limit of quantum gravity, in the simplified setting of the cylindrical symmetry reduction considered here. We show, for example, that the small G behavior is not uniform in the sense that its functional form depends on the causal relationship between spacetime points. We consider several physical issues relevant for this type of models such as the emergence of large gravitational effects.

gr-qc↗
arXiv2004

Quantum Cylindrical Waves and Sigma Models

We analyze cylindrical gravitational waves in vacuo with general polarization and develop a viewpoint complementary to that presented recently by Niedermaier showing that the auxiliary sigma model associated with this family of waves is not renormalizable in the standard perturbative sense.

gr-qc↗
arXiv2004

Time Uncertainty in Quantum Gravitational Systems

It is generally argued that the combined effect of Heisenberg principle and general relativity leads to a minimum time uncertainty. Most of the analyses supporting this conclusion are based on a perturbative approach to quantization. We consider a simple family of gravitational models, including the Einstein-Rosen waves, in which the (non-linearized) inclusion of gravity changes the normalization of time translations by a monotonic energy-dependent factor. In these circumstances, it is shown that a maximum time resolution emerges non-perturbatively only if the total energy is bounded. Perturbatively, however, there always exists a minimum uncertainty in the physical time.

gr-qc↗
arXiv2003

Lorentz Violations and Euclidean Signature Metrics

We show that the families of effective actions considered by Jacobson et al. to study Lorentz invariance violations contain a class of models that represent pure General Relativity with Euclidean signature. We also point out that some members of this family of actions preserve Lorentz invariance in a generalized sense.

gr-qc↗
arXiv2003

Microcausality and Quantum Cylindrical Gravitational Waves

We study several issues related to the different choices of time available for the classical and quantum treatment of linearly polarized cylindrical gravitational waves. We pay especial attention to the time evolution of creation and annihilation operators and the definition of Fock spaces for the different choices of time involved. We discuss also the issue of microcausality and the use of field commutators to extract information about the causal properties of quantum spacetime.

gr-qc↗
arXiv2002

Higher Derivative Fermionic Field Theories

We carry out the extension of the covariant Ostrogradski method to fermionic field theories. Higher-derivative Lagrangians reduce to second order differential ones with one explicit independent field for each degree of freedom.

hep-th↗
arXiv2002

Kinetic Terms for 2-Forms in Four Dimensions

We study the general form of the possible kinetic terms for 2-form fields in four dimensions, under the restriction that they have a semibounded energy density. This is done by using covariant symplectic techniques and generalizes previous partial results in this direction.

hep-th↗
arXiv2002

Diff-invariant Kinetic Terms in Arbitrary Dimensions

We study the physical content of quadratic diff-invariant Lagrangians in arbitrary dimensions by using covariant symplectic techniques. This paper extends previous results in dimension four. We discuss the difference between the even and odd dimensional cases.

hep-th↗
arXiv2001

Higher-Derivative Boson Field Theories and Constrained Second-Order Theories

As an alternative to the covariant Ostrogradski method, we show that higher-derivative relativistic Lagrangian field theories can be reduced to second differential-order by writing them directly as covariant two-derivative theories involving Lagrange multipliers and new fields. Despite the intrinsic non-covariance of the Dirac's procedure used to deal with the constraints, the explicit Lorentz invariance is recovered at the end. We develop this new setting on the grounds of a simple scalar model and then its applications to generalized electrodynamics and higher-derivative gravity are worked out. For a wide class of field theories this method is better suited than Ostrogradski's for a generalization to 2n-derivative theories

hep-th↗
arXiv2001

BF Actions for the Husain-Kuchar Model

We show that the Husain-Kuchar model can be described in the framework of BF theories. This is a first step towards its quantization by standard perturbative QFT techniques or the spin-foam formalism introduced in the space-time description of General Relativity and other diff-invariant theories. The actions that we will consider are similar to the ones describing the BF-Yang-Mills model and some mass generating mechanisms for gauge fields. We will also discuss the role of diffeomorphisms in the new formulations that we propose.

gr-qc↗
arXiv2000

Quadratic s-Form Field Actions with Semi-bounded Energy

We give in this paper a partial classification of the consistent quadratic gauge actions that can be written in terms of s-form fields. This provides a starting point to study the uniqueness of the Yang-Mills action as a deformation of Maxwell-like theories. We also show that it is impossible to write kinetic 1-form terms that can be consistently added to other 1-form actions such as tetrad gravity in four space-time dimensions even in the presence of a Minkowskian metric background.

hep-th↗