Related papers: Area expectation values in quantum area Regge calc…
Quantum theory (QT) provides statistical predictions for various physical phenomena. The outcomes of these measurements are in general some numerical time series registered by some macroscopic instruments. The various empirical probability…
The local limit of a quantum field theory on the loop space is studied. It is proved that the invariance of the theory with respect to the group of diffeomorphisms leads to Feynman diagrams convergence in the local limit.
In quantum mechanics the time dimension is treated as a parameter, while the three space dimensions are treated as observables. This assumption is both untested and inconsistent with relativity. From dimensional analysis, we expect quantum…
Quantum transition amplitudes are formulated for a model system with local internal time, using path integrals. The amplitudes are shown to be more regular near a turning point of internal time than could be expected based on existing…
The path integral formalism gives a very illustrative and intuitive understanding of quantum mechanics but due to its difficult sum over phases one usually prefers Schr\"odinger's approach. We will show that it is possible to calculate…
We develop simple rules for performing integrals over products of distributions in coordinate space. Such products occur in perturbation expansions of path integrals in curvilinear coordinates, where the interactions contain terms of the…
A continuously measured quantum system may be described by restricted path integrals (RPI) or equivalently by non-Hermitian Hamiltonians. The measured system is then considered as an open system, the influence of the environment being taken…
A quantum mechanical theory is proposed which abandons an external parameter ``time'' in favor of a self-adjoint operator on a Hilbert space whose elements represent measurement events rather than system states. The standard quantum…
We describe a general method of obtaining the constraints between area variables in one approach to area Regge calculus, and illustrate it with a simple example. The simplicial complex is the simplest tessellation of the 4-sphere. The…
In perturbative calculations of quantum mechanical path integrals in curvilinear coordinates, Feynman diagrams involve multiple temporal integrals over products of distributions, which are mathematically undefined. We derive simple rules…
The formulation of a consistent measurement theory for relativistic quantum fields has become a problem of growing foundational and practical significance. Standard non-relativistic measurement models fail to incorporate the essential…
Quantum gauge theories with finite-dimensional representation spaces are constructed that can have canonical gauge field theories as singular limits. They describe nature as a recursive quantum assembly by iterating Fermi-Dirac…
We investigate pinched geometries in a two-dimensional Lorentzian model of quantum Regge calculus (QRC) using the tensor renormalization group (TRG) method. A pinched geometry refers to a configuration with an infinitely long temporal…
As argued previously, amplitudes of quantum field theories on noncommutative space and time cannot be computed using naive path integral Feynman rules. One of the proposals is to use the Gell-Mann--Low formula with time-ordering applied…
We describe a theory of quantum gravity which is based on the assumption that the spacetime structure at small distances is given by a piecewise linear (PL) 4-manifold corresponding to a triangulation of a smooth 4-manifold. The fundamental…
We study quantum gravity in the path-integral formulation using the Regge calculus. In spite of the unbounded gravitational action the existence of an entropy-dominated phase is confirmed. The influence of various types of measures on this…
The equations of time-dependent density functional theory are derived, via the expression for the quantum weak value, from ring polymer quantum theory using a symmetry between time and imaginary time. The imaginary time path integral…
Tensor universality often implies that multi-partite quantum-state processing is determined by what happens in totally disentangled cases. In independent systems relative time direction for the parts is arbitrary. This hints that time may…
In this work we continue and extend our recent work on the correlation energy of the quantized electron gas of uniform density at temperature $T=0$. As before we utilize the methods, properties, and results obtained by means of classical…
We formulate continuous time quantum walks (CTQW) in a discrete quantum mechanical phase space. We define and calculate the Wigner function (WF) and its marginal distributions for CTQWs on circles of arbitrary length $N$. The WF of the CTQW…