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The recently proposed loop representation, used previously to find exact solutions to the quantum constraints of general relativity, is here used to quantize linearized general relativity. The Fock space of graviton states and its…
This paper considers diffeomorphism invariant theories of gravity coupled to matter, with second order equations of motion. This includes Einstein-Maxwell and Einstein-scalar field theory with (after field redefinitions) the most general…
The goal of this work, motivated by the desire to understand causality in classical and quantum gravity, is an in depth investigation of causality in classical field theories with quasilinear equations of motion, of which General Relativity…
It is shown that the introduction of an upper limit to the proper acceleration of a particle can smooth the problem of ultraviolet divergencies in local quantum field theory. For this aim, the classical model of a relativistic particle with…
We define and study the notion of quantum polarity, which is a kind of geometric Fourier transform between sets of positions and sets of momenta. Extending previous work of ours, we show that the orthogonal projections of the covariance…
We introduce two possible ways of defining effective constraints of quantum systems and applied this effective constraint method to models of WDW Quantum Cosmology and Loop Quantum Cosmology. We analyze effective Hamiltonian constraint on…
The leading long-distance quantum correction to the Newtonian potential for heavy spinless particles is computed in quantum gravity. The potential is obtained directly from the sum of all graviton exchange diagrams contributing to lowest…
We show that direct Feynman-parametric loop integration is possible for a large class of planar multi-loop integrals. Much of this follows from the existence of manifestly dual-conformal Feynman-parametric representations of planar loop…
A geometric framework for quantum statistical estimation is used to establish a series of higher order corrections to the Heisenberg uncertainty relations associated with pairs of canonically conjugate variables. These corrections can be…
A scheme for systematically achieving accurate numerical evaluation of multi-loop Feynman diagrams is developed. This shows the feasibility of a project aimed to produce a complete calculation for two-loop predictions in the Standard Model.…
Computing many-body ground state energies and resolving electronic structure calculations are fundamental problems for fields such as quantum chemistry or condensed matter. Several quantum computing algorithms that address these problems…
We show that the computational effort for the numerical solution of fermionic quantum systems, occurring e.g., in quantum chemistry, solid state physics, field theory in principle grows with less than the square of the particle number for…
An algorithm for the systematic analytical approximation of multi-scale Feynman integrals is presented. The algorithm produces algebraic expressions as functions of the kinematical parameters and mass scales appearing in the Feynman…
Solving partial differential equations for extremely large-scale systems within a feasible computation time serves in accelerating engineering developments. Quantum computing algorithms, particularly the Hamiltonian simulations, present a…
We introduce a framework for internal topological symmetries in quantum field theory, including "noninvertible symmetries" and "categorical symmetries". This leads to a calculus of topological defects which takes full advantage of…
In effective models of loop quantum gravity, the onset of quantum effects is controlled by a so-called polymerisation scale. It is sometimes necessary to make this scale phase space dependent in order to obtain sensible physics. A…
The causal representation of multi-loop scattering amplitudes, obtained from the application of the loop-tree duality formalism, comprehensively elucidates, at integrand level, the behaviour of only physical singularities. This…
Since there are quantization ambiguities in constructing the Hamiltonian constraint operator in isotropic loop quantum cosmology, it is crucial to check whether the key features of loop quantum cosmology, such as the quantum bounce and…
A comprehensive study is performed of general massive, tensor, two-loop Feynman diagrams with two and three external legs. Reduction to generalized scalar functions is discussed. Integral representations, supporting the same class of…
Quantum theory is formulated as a probabilistic theory on a flat Minkowski space-time, while general theory of relativity is formulated on a curved manifold as a geometric theory. Bohmian Quantum Gravity approach indicates that one need to…