Related papers: Spacetime Paths as a Whole
We investigate quantum correlations in time in different approaches. We assume that temporal correlations should be treated in an even-handed manner with spatial correlations. We compare the pseudo-density matrix formalism with several…
If we use the path integral approach, we can write quantum electrodynamics (QED) in a way that is manifestly relativistic. However the path integrals are confined to paths that are on mass-shell. What happens if we extend QED by computing…
Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…
The description of the universe evolving in time according to general relativity is given in comparison with the quantum description of the same universe in terms of semiclassical wave functions. The spacetime geometry is determined by the…
Feynman path integrals provide an elegant, classically inspired representation for the quantum propagator and the quantum dynamics, through summing over a huge manifold of all possible paths. From computational and simulational…
A natural mapping of paths in a curved space onto the paths in the corresponding (tangent) flat space may be used to reduce the curved-space-time path integral to the flat-space-time path integral. The dynamics of the particle in a curved…
We have developed a proper path integral formalism consistent with the deformed version of the quantum mechanics which contains a maximum observable length scale at the order of the Cosmological particle horizon, existing in cosmology.…
Using the 3+1 formalism of general relativity we obtain the equations governing the dynamics of spherically symmetric spacetimes with arbitrary sources. We then specialize for the case of perfect fluids accompanied by a flow of interacting…
We propose a general theoretical approach to quantum measurements based on the path (histories) summation technique. For a given dynamical variable A, the Schr\"odinger state of a system in a Hilbert space of arbitrary dimensionality is…
Spacetime, understood as a globally hyperbolic manifold, may be characterized by spectral data using a 3+1 splitting into space and time, a description of space by spectral triples and by employing causal relationships, as proposed earlier.…
The path integral formulation in quantum mechanics corresponds to the first quantization since it is just to rewrite the quantum mechanical amplitude into many dimensional integrations over discretized coordinates $x_n$. However, the path…
Many interesting physical theories have analytic classical actions. We show how Feynman's path integral may be defined non-perturbatively, for such theories, without a Wick rotation to imaginary time. We start by introducing a class of…
Input-output theory is a well-known tool in quantum optics and ubiquitous in the description of quantum systems probed by light. Owing to the generality of the setup it describes, the theory finds application in a wide variety of…
We show that the emergence of time evolution in an otherwise timeless nonrelativistic closed quantum system -- viewed as a poor man's model of generally covariant quantum theory -- can be understood from the perspective of the path integral…
There is a formal analogy between the evolution of the universe, when this is seen as a trajectory in the minisuperspace, and the worldline followed by a test particle in a curved spacetime. The analogy can be extended to the quantum realm,…
Feynman's Lagrangian path integral was an outgrowth of Dirac's vague surmise that Lagrangians have a role in quantum mechanics. Lagrangians implicitly incorporate Hamilton's first equation of motion, so their use contravenes the uncertainty…
While our natural intuition suggests us that we live in 3D space evolving in time, modern physics presents fundamentally different picture: 4D spacetime, Einstein's block universe, in which we travel in thermodynamically emphasized…
We introduce configuration space path integrals for quantum fields interacting with classical fields. We show that this can be done consistently by proving that the dynamics are completely positive directly, without resorting to master…
An analysis of classical mechanics in a complex extension of phase space shows that a particle in such a space can behave in a way redolant of quantum mechanics; additional degrees of freedom permit 'tunnelling' without recourse to…
Given an arbitrary Lagrangian function on \RR^d and a choice of classical path, one can try to define Feynman's path integral supported near the classical path as a formal power series parameterized by "Feynman diagrams," although these…