Related papers: A modest redirection of quantum field theory solve…
In quantum field theory the path integral is usually formulated in the wave picture, i.e., as a sum over field evolutions. This path integral is difficult to define rigorously because of analytic problems whose resolution may ultimately…
The quantum discrete $\phi ^4$ model at finite temperature is studied in the mean-field approximation. The phase diagrams are obtained for a wide range of the model parameters. The domains of applicability for the classical, quantum, and…
The canonical commutation relations of quantum field theory require all pairs of observables located in spacelike-separated regions to commute. In the theory as it is currently constituted, this implies that the information-carrying…
If the gravitational field is quantized, then a solution of Einstein's field equations is a valid cosmological model only if it corresponds to a classical limit of a quantum cosmology. To determine which solutions are valid requires looking…
Quantization of field theories with gauge symmetry is an extensively discussed and well-established topic. In this short note, we revisit this old problem. While we confirm all details of the existing literature, we highlight a potentially…
I propose to formalize quantum theories as topological quantum field theories in a generalized sense, associating state spaces with boundaries of arbitrary (and possibly finite) regions of space-time. I further propose to obtain such…
We consider the loop quantization of Maxwell theory. A quantization of this type leads to a quantum theory in which the fundamental excitations are loop-like rather than particle-like. Each such loop plays the role of a quantized Faraday's…
Four-dimensional quantum field theories generally require regularization to be well defined. This can be done in various ways, but here we focus on Pauli--Villars (PV) regularization and apply it to nonperturbative calculations of bound…
We develop a reformulation of the functional integral for bosons in terms of bilocal fields. Correlation functions correspond to quantum probabilities instead of probability amplitudes. Discrete and continuous global symmetries can be…
We investigate stochastic quantization as a method to go from a classical PDE (with stochastic time $\lambda$) to a corresponding quantum theory in the limit $\lambda\to\infty$. We test the method for a linear PDE satisfied by the free…
It is generally believed that quantum gravity is necessary to resolve the known tensions between general relativity and the quantum field theories of the standard model. Since perturbatively quantized gravity is non-renormalizable, the…
We discuss Hamiltonian learning in quantum field theories as a protocol for systematically extracting the operator content and coupling constants of effective field theory Hamiltonians from experimental data. Learning the Hamiltonian for…
Quantum mechanics with a generalized uncertainty principle arises through a representation of the commutator $[\hat{x}, \hat{p}] = i f(\hat{p})$. We apply this deformed quantization to free scalar field theory for $f_\pm =1\pm \beta p^2$.…
Covariant, self-interacting scalar quantum field theories admit solutions for low enough spacetime dimensions, but when additional divergences appear in higher dimensions, the traditional approach leads to results, such as triviality, that…
We prove through path integral Monte Carlo computer experiments that the affine quantization of the $\varphi_4^4$ scaled Euclidean covariant relativistic scalar field theory is a valid quantum field theory with a well defined continuum…
The path integral approach to quantum mechanics provides a method of quantization of dynamical systems directly from the Lagrange formalism. In field theory the method presents some advantages over Hamiltonian quantization. The Lagrange…
Quantum field theory offers physicists a tremendously wide range of application; it is both a language with which a vast variety of physical processes can be discussed and also it provides a model for fundamental physics, the so-called…
Quantum field theory can be physically regularized by modularizing it on several levels of aggregation. Since computation is already thoroughly modularized, physical experiments are treated here as quantum relativistic cellular computations…
We give a simple and self-contained construction of of the $P(\Phi)$ Euclidean Quantum Field Theory in the plane and verify the Osterwalder-Schrader axioms: translational and rotational invariance, reflection positivity and regularity. In…
Graph theory is important in information theory. We introduce a quantization process on graphs and apply the quantized graphs in quantum information. The quon language provides a mathematical theory to study such quantized graphs in a…