Related papers: Reparametrization invariant statistical inference …
Causal inference requires evaluating models on balanced distributions between treatment and control groups, while training data often exhibits imbalance due to historical decision-making policies. Most conventional statistical methods…
We study four-dimensional quantum gravity using non-perturbative renormalization group methods. We solve the corresponding equations for the fully momentum-dependent propagator, Newton's coupling and the cosmological constant. For the first…
An approach to quantization of fields and gravity based on the De Donder-Weyl covariant Hamiltonian formalism is outlined. It leads to a hypercomplex extension of quantum mechanics in which the algebra of complex numbers is replaced by the…
Reparametrization invariance being treated as a gauge symmetry shows some specific peculiarities. We study these peculiarities both from a general point of view and on concrete examples. We consider the canonical treatment of…
We consider two-dimensional quantum gravity coupled to matter in the temporal gauge, using the Polyakov path integral. We show that the integration over the metric can be explicitly performed under some plausible assumptions. We also…
We show that, in four-dimensional spacetimes with an arbitrary Einstein metric, with and without a cosmological constant, perturbative dynamical degrees of freedom in generic quadratic-curvature gravity can be decoupled into massless and…
We argue that a conformally invariant extension of general relativity coupled to the Standard Model is the fundamental theory that needs to be quantized. We show that it can be treated by loop quantum gravity techniques. Through a gauge…
General Teleparallel theories assume that curvature is vanishing in which case gravity can be solely represented by torsion and/or nonmetricity. Using differential form language, we express the Riemannian Gauss-Bonnet invariant concisely in…
A crucial property of Weyl gravity is its conformal invariance. It is shown how this gauge symmetry is exactly reflected by the two constraints in the Hamiltonian framework. Since the spatial 3-metric is one of the configuration variables,…
The construction of a consistent theory of quantum gravity is a problem in theoretical physics that has so far defied all attempts at resolution. One ansatz to try to obtain a non-trivial quantum theory proceeds via a discretization of…
We summarize our renormalization group approach for the vector model as well as the matrix model which are the discretized quantum gravity in one- and two-dimensional spacetime. A difference equation is obtained which relates free energies…
The reparametrization-invariant generating functional for the unitary and causal perturbation theory in general relativity in a finite space-time is obtained. The region of validity of the Faddeev-Popov-DeWitt functional is studied. It is…
We prove that Riemannian metrics in General Relativity in the \emph{`normal-coordinates'} gauge are in one-to-one correspondence with curvature 2-forms. We discuss how this can be used as a change of variables in the operator formalism to…
A gauge invariant quantization in a closed integral form is developed over a linear phase space endowed with an inhomogeneous Faraday electromagnetic tensor. An analog of the Groenewold product formula (corresponding to Weyl ordering) is…
The quantization of General Relativity invariant with respect to time-reparametrizations is considered. We construct the Faddeev-Popov generating functional for the unitary perturbation theory in terms of invariants of the kinemetric group…
Using a new Bayesian method for solving inverse quantum problems, potentials of quantum systems are reconstructed from coordinate measurements in non-stationary states. The approach is based on two basic inputs: 1. a likelihood model,…
Transition to a nonrelativistic Pauli equation in Riemann space of constant positive curvature for a Dirac particle in presence of the Coulomb field is performed in the system of radial equations, exact solutions are constructed in terms of…
In this article, the axioms presented in the first one are reformulated according to the special theory of relativity. Using these axioms, quantum mechanic's relativistic equations are obtained in the presence of electromagnetic fields for…
A two dimensional matter coupled model of quantum gravity is studied in the Dirac approach to constrained dynamics in the presence of a cosmological constant. It is shown that after partial fixing to the conformal gauge the requirement of a…
We show how the quantum potential arises in various ways and trace its connection to quantum fluctuations and Fisher information along with its realization in terms of Weyl curvature. It is a quantization factor for certain classical…