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A generalized Noether's theorem and the operational determination of a physical geometry in quantum physics are used to motivate a quantum geometry consisting of relations between quantum states that are defined by a universal group. Making…
We present a new approximation technique for quantum field theory. The standard one-loop result is used as a seed for a recursive formula that gives a sequence of improved Gaussian approximations for the generating functional. In a…
Mechanical quantum systems, such as resonators and levitated particles, offer unique opportunities for quantum metrology. Particularly, their significant mass and quantum-level control enable applications in measuring gravitational effects.…
Exploiting novel aspects of the quantum geometry of charged particles in a magnetic field via gauge-invariant variables, we provide tangible connections between the response of quantum Hall fluids to non-uniform electric fields and the…
In this article we propose a consistent scheme of doing computations directly in four dimensions using conventional quantum field theory methods. This work is continuation of a stochastic quantization program reported earlier.
We show how to construct a compact quantum metric space from a proper continuous length function on an \'etale groupoid with compact unit space, where the unit space additionally has the structure of a compact metric space. Using compactly…
We focus on the interaction of a plane gravitational wave with electromagnetic fields and we describe this interaction in the proper detector frame where, thanks to the introduction of Fermi coordinates, it is possible to refer to directly…
The formulation of Geometric Quantization contains several axioms and assumptions. We show that for real polarizations we can generalize the standard geometric quantization procedure by introducing an arbitrary connection on the…
Within the effective average action approach to quantum gravity, we recover the low energy effective action as derived in the effective field theory framework, by studying the flow of possibly non-local form factors that appear in the…
We propose a quantum imaging-inspired setup for measuring gravitational fields using an atom that emits a photon at one of two possible locations. The atom acquires a gravitationally induced quantum phase that it shares with the photon. By…
Mathematical modeling of gravitating configurations of physical fields is one of the priority directions of the modern theory of gravity. Most of the exact solutions constructed within the framework of the general relativity are static or…
Recent progress in quantum field theory and quantum gravity relies on mixed boundary conditions involving both normal and tangential derivatives of the quantized field. In particular, the occurrence of tangential derivatives in the boundary…
Quantum field theory provides the framework for the most fundamental physical theories to be confirmed experimentally and has enabled predictions of unprecedented precision. However, calculations of physical observables often require great…
We discuss new approaches to fundamental problems of mathematics and mathematical physics such as mathematical foundation of quantum field theory, the Riemann hypothesis, and construction of noncommutative algebraic geometry.
Geometric Algebra and Calculus are mathematical languages encoding fundamental geometric relations that theories of physics seem to respect. We propose criteria given which statistics of expressions in geometric algebra are computable in…
It is shown that the recently geometric formulation of quantum mechanics implies the use of Weyl geometry. It is discussed that the natural framework for both gravity and quantum is Weyl geometry. At the end a Weyl invariant theory is…
The quantum-reduced loop-gravity technique has been introduced for dealing with cosmological models. We show that it can be applied rather generically: anytime the spatial metric can be gauge-fixed to a diagonal form. The technique selects…
The geometro-stochastic method of quantization provides a framework for quantum general relativity, in which the principal frame bundles of local Lorentz frames that underlie the fibre-theoretical approach to classical general relativity…
A non-perturbative and background-independent quantum formulation of quadratic gravity is provided. A canonical quantization procedure introduced in previous works, named after Dirac and Pauli, is here applied to quadratic gravity to…
There is debate as to whether quantum field theory is, at bottom, a quantum theory of fields or particles. One can take a field approach to the theory, using wave functionals over field configurations, or a particle approach, using wave…