Related papers: A path-integral approach to the problem of time
Normally we quantize along the space dimensions but treat time classically. But from relativity we expect a high level of symmetry between time and space. What happens if we quantize time using the same rules we use to quantize space? To do…
Path integrals appear to offer natural and intuitively appealing methods for defining quantum-mechanical amplitudes for questions involving spacetime regions. For example, the amplitude for entering a spatial region during a given time…
This paper is a generalization of previous work on the use of classical canonical transformations to evaluate Hamiltonian path integrals for quantum mechanical systems. Relevant aspects of the Hamiltonian path integral and its measure are…
Three simple examples illustrate properties of path integral amplitudes in fixed background spacetimes with closed timelike curves: non-relativistic potential scattering in the Born approximation is non-unitary, but both an example with…
We consider the backreaction of a quantum system $q$ on an effectively classical degree of freedom $C$ that is interacting with it. The backreaction equation based on the standard path integral formalism gives the so-called `in-out'…
In these short notes, we compute non-perturbatively the time-dependent quantum gravity amplitudes for a four-dimensional spherically symmetric space-time with space-like and time-like boundaries. We solve the 4D classical and quantum…
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…
A specific class of explicitly time-dependent potentials is studied by means of path integrals. For this purpose a general formalism to treat explicitly time-dependent space-time transformations in path integrals is sketched. An explicit…
A method is presented which restricts the space of paths entering the path integral of quantum mechanics to subspaces of $C^\alpha$, by only allowing paths which possess at least $\alpha$ derivatives. The method introduces two external…
Time in relativity theory has a status different from that adopted by standard quantum mechanics, where time is considered as a parameter measured with reference to an external absolute Newtonian frame. This status strongly restricts its…
This paper presents an analytical treatment of the path integral formalism for time-dependent quantum systems within the framework of Wigner-Dunkl mechanics, emphasizing systems with varying masses and time-dependent potentials. By…
Feynman path integrals are now a standard tool in quantum physics and their use in differential geometry leads to new mathematical insights. A logical treatment of quantum phenomena seems to require a sustained mathematical analysis of path…
We consider a number of aspects of the problem of defining time observables in quantum theory. Time observables are interesting quantities in quantum theory because they often cannot be associated with self-adjoint operators. Their…
For description of the quantum dynamics on a curved group manifold the path integrals in a space of the group parameters is offered. The formalism is illustrated by the $H$-atom problem.
We give a consistent quantum description of time, based on Page and Wootters' conditional probabilities mechanism, that overcomes the criticisms that were raised against similar previous proposals. In particular we show how the model allows…
The action functional of the anisotropic Kantowski--Sachs cosmological model is turned into that of an ordinary gauge system. Then a global phase time is identified for the model by imposing canonical gauge conditions, and the quantum…
The question of how long a particle takes to pass through a potential barrier is still a controversial topic in quantum mechanics. Arguably, the main theoretical problem in obtaining estimates for measurable times is the fact that…
For a general quantum theory that is describable by a path integral formalism, we construct a mathematical model of the universe as a sample point of an accumulative stochastic process. The model give predictions that are nearly identical…
A fundamentally different approach to path integral quantum mechanics in curved space-time is presented, as compared to the standard approaches currently available in the literature. Within the context of scalar particle propagation in a…
We revisit the path integral description of quantum tunneling and lay the groundwork for its generalization to excites states through real-time path integral techniques. For clarity, we focus on the simple toy model of a point particle in a…