Related papers: Time Evolution in Quantum Mechanics with a Minimal…
Ever since Schrodinger, Time in quantum theory is postulated Newtonian for every reference frame. With the help of certain known mathematical results, we show that the concept of the so-called Local Time allows avoiding the postulate. In…
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 study the complexity of both time-optimal and time sub-optimal quantum Hamiltonian evolutions connecting arbitrary source and a target states on the Bloch sphere equipped with the Fubini-Study metric. This investigation is performed in a…
The wave-function in quantum gravity is supposed to obey the Wheeler-DeWitt (WDW) equation, however there is neither a satisfactory probability interpretation nor a successful solution to the problem of time in the WDW framework. To gain…
The equations governing the evolution of non-minimally coupled scalar matter and the scale factor of a Robertson-Walker universe are derived from a minisuperspace action. As for the minimally coupled case, it is shown that the entire…
A modification of the covariant theory is proposed in which the self-energy of the system, corresponding to time-like degrees of freedom in the configuration space, preserves the classical law of change in quantum theory. As a result,…
In previous works, we showed that both time and space can emerge from entanglement within a globally constrained quantum Universe, with no background coordinates. By extending the Page and Wootters quantum time formalism to include both…
The time evolution operator (Schr\"odinger functional) of quantum field theory can be expressed in terms of first quantised particles moving on the orbifold $S^1/Z_2$. We give a graphical derivation of this that generalises to second…
We study the quantum field theory (QFT) of a scalar field in the Schr\"odinger picture in the functional formulation. We derive a formula for the evolution kernel in a flat expanding metric. We discuss a transition between Riemannian and…
One of the main challenges in physics today is to merge quantum theory and the theory of general relativity into a unified framework. Various approaches towards developing such a theory of quantum gravity are pursued, but the lack of…
The three original publications in this thesis encompass various aspects in the still developing area of noncommutative quantum field theory, ranging from fundamental concepts to model building. One of the key features of noncommutative…
Planck-scale physics challenges the classical smooth-spacetime picture by introducing quantum fluctuations that imply a nontrivial spacetime microstructure. We present a framework that encodes these fluctuations by promoting local scale…
We study the Schr\"odinger equation in quantum field theory (QFT) in its functional formulation. In this approach quantum correlation functions can be expressed as classical expectation values over (complex) stochastic processes. We obtain…
Quantum measurement and quantum operation theory is developed here by taking the relational properties among quantum systems, instead of the independent properties of a quantum system, as the most fundamental elements. By studying how the…
We argue that the problem of time is not a crucial issue inherent in the quantum picture of the universe evolution. On the minisuperspace model example with the massless scalar field, we demonstrate four approaches to the description of…
Several quantum gravity scenarios lead to physics below the Planck scale characterised by nonlocal, Lorentz invariant equations of motion. We show that such non-local effective field theories lead to a modified Schr\"odinger evolution in…
The proper time of an observer can be introduced as a degree of freedom in quantum cosmology, additional to the existing fields. We review two arguments for using the Schr\"odinger equation to evolve the corresponding wavefunction. We…
The "problem of time" in present physics substantially consists in the fact that a straightforward quantization of the general relativistic evolution equation and constraints generates for the Universe wave function the Wheeler-De Witt…
We present a simple proof of the minimum time for the quantum evolution between two arbitrary states. This proof is performed in the absence of any geometrical arguments. Then, being in the geometric framework of quantum evolutions based…
Can a simple microscopic model of space and time demonstrate Special Relativity as the macroscopic (aggregate) behavior of an ensemble ? The question will be investigated in three parts. First, it is shown that the Lorentz transformation…