Related papers: Path-Integral Measures in Higher-Derivative Gravit…
We consider minisuperspace gravity system described by piecewise flat metric discontinuous on three-dimensional faces (tetrahedra). There are infinite terms in the Einstein action. However, starting from proper regularization, these terms…
In the conformal-gauge two-dimensional quantum gravity, the solution obtained by the perturbative or path-integral approach is compared with the one obtained by the operator-formalism approach. Treatments of the anomaly problem in both…
Damped mechanical systems with various forms of damping are quantized using the path integral formalism. In particular, we obtain the path integral kernel for the linearly damped harmonic oscillator and a particle in a uniform gravitational…
Our main aim in this paper is to promote the coframe variational method as a unified approach to derive field equations for any given gravitational action containing the algebraic functions of the scalars constructed from the Riemann…
A method based on the path integral approach is engaged to consider the gravitational emission from a quantum mechanical bound system in a locally inertial frame. In such a frame, interaction between the electromagnetic (bound potential)…
The action $A$ of Quadratic Gravity in FLRW metric is invariant under the group of diffeomorphisms of the time coordinate and can be written in terms of the only dynamical variable $g(\tau)\,.$ We construct perturbation theory for…
The method of the factorization of the path integral measure, based on a nonlinear filtering equation, is extended to the case of a nonfree isometric action of the compact semisimple unimodular Lie group on a smooth compact Riemannian…
Properties of the space $\Ab$ of generalized connections in the Ashtekar framework are investigated. First a construction method for new connections is given. The new parallel transports differ from the original ones only along paths that…
We to define a Path Integral in Lorentzian time by restricting the relevant domain of integration on $C([0,1],M)$ over a Riemannian configuration manifold $(M,g)$ and considering the dynamics of a particle evolving between to fixed…
A new analysis of the gauge invariances and their unity with diffeomorphism invariances in second order metric gravity is presented which strictly follows Dirac's constrained Hamiltonian approach.
We discuss an elementary derivation of variational symmetries and corresponding integrals of motion for the Lagrangian systems depending on acceleration. Providing several examples, we make the manuscript accessible to a wide range of…
The notion of a measure on the space of connections modulo gauge transformations that is invariant under diffeomorphisms of the base manifold is important in a variety of contexts in mathematical physics and topology. At the formal level,…
For massive gravity in a de Sitter background one encounters problems of stability when the curvature is larger than the graviton mass. I analyze this situation from the path integral point of view and show that it is related to the…
We briefly present two-dimensional dilaton gravity from the point of view of integrable systems.
We consider straight line flows on a translation surface that are minimal but not uniquely ergodic. We give bounds for the number of generic invariant probability measures.
Interpretability methods for deep neural networks mainly focus on the sensitivity of the class score with respect to the original or perturbed input, usually measured using actual or modified gradients. Some methods also use a…
A path-integral quantization on a homogeneous space G/H is proposed based on the guiding principle `first lift to G and then project to G/H'. It is then shown that this principle gives a simple procedure to obtain the inequivalent…
This work is devoted to the study of two-scale gradient Young measures naturally arising in nonlinear elasticity homogenization problems. Precisely, a characterization of this class of measures is derived and an integral representation…
A new method for approximating fractional derivatives of the Gaussian function and Dawson's integral are presented. Unlike previous approaches, which are dominantly based on some discretization of Riemann-Liouville integral using polynomial…
A simplified model of tachyon matter in classical and quantum mechanics is constructed. p-Adic path integral quantization of the model is considered. Recent results in using p-adic analysis, as well as perspectives of an adelic…