Related papers: Feynman's clock, a new variational principle, and …
The problem is considered of describing the dynamics of quantum systems generated by a nonlocal in time interaction. It is shown that the use of the Feynman approach to quantum theory in combination with the canonical approach allows one to…
Feynman's laws of quantum dynamics are concisely stated, discussed in comparison with other formulations of quantum mechanics and applied to selected problems in the physical optics of photons and massive particles as well as flavour…
According to relativity, the reading of an ideal clock is interpreted as the elapsed proper time along its classical trajectory through spacetime. In contrast, quantum theory allows the association of many simultaneous trajectories with a…
This article is concerned with the design and analysis of discrete time Feynman-Kac particle integration models with geometric interacting jump processes. We analyze two general types of model, corresponding to whether the reference process…
Quantum simulation using time evolution in phase estimation-based quantum algorithms can yield unbiased solutions of classically intractable models. However, long runtimes open such algorithms to decoherence. We show how measurement-based…
Inspired by the discrete evolution implied by the recent work on loop quantum cosmology, we obtain a discrete time description of usual quantum mechanics viewing it as a constrained system. This description, obtained without any…
We apply the principles discussed in earlier papers to the construction of discrete time quantum field theories. We use the Schwinger action principle to find the discrete time free field commutators for scalar fields, which allows us to…
't Hooft has recently developed a discretisation of (2+1) gravity which has a multiple-valued Hamiltonian and which therefore admits quantum time evolution only in discrete steps. In this paper, we describe several models in the continuum…
Recent progress in the development of quantum technologies has enabled the direct investigation of dynamics of increasingly complex quantum many-body systems. This motivates the study of the complexity of classical algorithms for this…
We develop a rigorous theory of external influences on finite discrete dynamical systems, going beyond the perturbation paradigm, in that the external influence need not be a small contribution. Indeed, the covariance condition can be…
A commonly adopted relational account of time evolution in generally-covariant systems, and more specifically in quantum cosmology, is argued to be unsatisfactory, insofar as it describes evolution relative to observed readings of a clock…
We revisit the issue of time in quantum geometrodynamics and suggest a quantization procedure on the space of true dynamic variables. This procedure separates the issue of quantization from enforcing the constraints caused by the general…
A consistent classical and quantum relativistic mechanics can be constructed if Einstein's covariant time is considered as a dynamical variable. The evolution of a system is then parametrized by a universal invariant identified with…
We describe a quantum mechanical measurement as a variational principle including interaction between the system under measurement and the measurement apparatus. Augmenting the action with a nonlocal term (a double integration over the…
It is shown that discrete-time quantum walks can be used to digitize, i.e., to time discretize fermionic models of continuous-time lattice gauge theory. The resulting discrete-time dynamics is thus not only manifestly unitary, but also…
Feynman's formulation of quantum theory is remarkable in its combination of formal simplicity and computational power. However, as a formulation of the abstract structure of quantum theory, it is incomplete as it does not account for most…
Understanding the electron clock and the role of complex numbers in quantum mechanics is grounded in the geometry of spacetime, and best expressed with Spacetime Algebra (STA). The efficiency of STA is demonstrated with coordinate-free…
The variational principle serves as a fundamental framework for describing equilibrium states of physical systems via the minimization or extremization of an energy-like functional. While quantum algorithms have demonstrated promising…
Advances in isolating, controlling and entangling quantum systems are transforming what was once a curious feature of quantum mechanics into a vehicle for disruptive scientific and technological progress. Pursuing the vision articulated by…
The time-dependent variational principle for many-body trial states is used to discuss the relation between the approaches of different molecular dynamics models to describe indistinguishable fermions. Early attempts to include effects of…