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We present a new approach to quantum general relativity based on the idea of Feynman to treat the graviton in Einstein's theory as a point particle field subject to quantum fluctuations just as any such field is in the well-known Standard…
The recently available high-intensity quantum light pulses provide novel tools for controlling light-matter interactions. However, the rigor of the theoretical frameworks currently used to describe the interaction of strong quantum light…
Response functions are a fundamental aspect of physics; they represent the link between experimental observations and the underlying quantum many-body state. However, this link is often under-appreciated, as the Lehmann formalism for…
Using the path-integral formalism, we show that photons possess a nontrivial quantum metric in momentum space. We derive the semiclassical action and equations of motion by taking into account the quantum metric. In media with a spatially…
Proposals for nonlinear extenstions of quantum mechanics are discussed. Two different concepts of "mixed state" for any nonlinear version of quantum theory are introduced: (i) >genuine mixture< corresponds to operational "mixing" of…
This paper gives a rigorous interpretation of a Feynman path integral on a Riemannian manifold M with non-positive sectional curvature. A $L^2$ Riemannian metric $G_P$ is given on the space of piecewise geodesic paths $H_P(M)$ adapted to…
We present a rigorous derivation and numerical validation of a universal projection-law factorization for quartic nonlinear coupling rates across physically distinct platforms. The central result is that observable Kerr-type interactions --…
Physical systems, characterized by an ensemble of interacting elementary constituents, can be represented and studied by different algebras of observables or operators. For example, a fully polarized electronic system can be investigated by…
Coherent quantum optics, where the interaction of a photon with an emitter does not scramble phase coherence, lies at the heart of many quantum optical effects and emerging technologies. Solid-state emitters coupled to nanophotonic…
A geometrical way to calculate N-point Feynman diagrams is reviewed. As an example, the dimensionally-regulated three-point function is considered, including all orders of its epsilon-expansion. Analytical continuation to other regions of…
Quantum physics allows an object to be detected even in the absence of photon absorption by the use of so-called interaction-free measurements. We provide a formulation of this protocol using a three-level system, where the object to be…
A new method of approximation scheme with potential application to a general interacting quantum system is presented. The method is non-perturbative, self- consistent, systematically improvable and uniformly applicable for arbitrary…
In a recent paper we showed that the correlators of free scalar field theory in four dimensions can be constructed from a two dimensional topological field theory based on so(4,2) equivariant maps (intertwiners). The free field result,…
A pedagogical and self-contained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity. Topics covered include the Weyl-Wigner…
We completely generalize previous results related to the counting of connected Feynman diagrams. We use a generating function approach, which encodes the Wick contraction combinatorics of the respective connected diagrams. Exact solutions…
Quantum geometry, i.e., the quantum theory of intrinsic and extrinsic spatial geometry, is a cornerstone of loop quantum gravity. Recently, there have been many new ideas in this field, and I will review some of them. In particular, after a…
The geometric formulation of quantum mechanics is a very interesting field of research which has many applications in the emerging field of quantum computation and quantum information, such as schemes for optimal quantum computers. In this…
Noncommutative geometry governs the physics of quantum Hall (QH) effects. We introduce the Weyl ordering of the second quantized density operator to explore the dynamics of electrons in the lowest Landau level. We analyze QH systems made of…
Applications of decision diagrams in quantum circuit analysis have been an active research area. Our work introduces FeynmanDD, a new method utilizing standard and multi-terminal decision diagrams for quantum circuit simulation and…
Starting from square-integrable wave functions on a Lie group, we build an invertible Fourier transform mapping them on wave functions on the dual of the Lie algebra. This is a group-theoretic version of the map from position space to…