Related papers: Path Integral of Bianchi I models in Loop Quantum …
We describe a path-integral ground-state quantum Monte Carlo method for light nuclei in continuous space. We show how to efficiently update and sample the paths with spin-isospin dependent and spin-orbit interactions. We apply the method to…
Using the ADM formalism in the minisuperspace, we obtain the commutative and noncommutative exact classical solutions and exact wave function to the Wheeler-DeWitt equation with an arbitrary factor ordering, for the anisotropic Bianchi type…
Physical path integral formulation of motion of particles in Riemannian spaces is outlined and extended to deduce the corresponding field theoretical formulation. For the special case of a zero rest mass particle in Minkowski manifold, it…
We demonstrate that it is possible to produce different isotropic embeddings of anisotropic Loop Quantum Cosmology, resulting to "lattice refinement" in the isotropic system. To introduce the general approach, we first use a simple model…
We follow the Feynman procedure to obtain a path integral formulation of loop quantum cosmology starting from the Hilbert space framework. Quantum geometry effects modify the weight associated with each path so that the effective measure on…
Using noncommutative deformed canonical commutation relations, a model describing a noncommutative complex scalar field theory is considered. Using the path integral formalism, the noncommutative free and exact propagators are calculated to…
In this work, the quantization of the most general Bianchi Type I geometry, with and without a cosmological constant, is considered. In the spirit of identifying and subsequently removing as many gauge degrees of freedom as possible, a…
We show how to construct path integrals for quantum mechanical systems where the space of configurations is a general non-compact symmetric space. Associated with this path integral is a perturbation theory which respects the global…
We study integrable models in the Bianchi I metric case with scalar fields minimally and non-minimally coupled with gravity and the correspondence between their general solutions. Using the model with a minimally coupled scalar field and a…
We study the qualitative properties of the class of spatially homogeneous Bianchi VI_o cosmological models containing a perfect fluid with a linear equation of state, a scalar field with an exponential potential and a uniform cosmic…
The improved dynamics of loop quantum cosmology is extended to include the Bianchi type II model. Because these space-times admit both anisotropies and non-zero spatial curvature, certain technical difficulties arise over and above those…
We study the scalar modes of linear perturbations in loop quantum cosmology. This is done on a lattice where each cell is taken to be homogeneous and isotropic and can be quantized via standard homogeneous loop quantum cosmology techniques.…
An approach to quantum cosmology, relying on strengths of both canonical and path integral formalisms, is applied to the cosmological model, Bianchi type IX. Physical quantum states are constructed on the maximal slice of the cosmological…
A coarse graining technique akin to block spin transformations that groups together fiducial cells in a homogeneous and isotropic universe has been recently developed in the context of loop quantum cosmology. The key technical ingredient…
We study the hybrid quantization of the linearly polarized Gowdy $T^3$ model with a massless scalar field with the same symmetries as the metric. For simplicity, we quantize its restriction to the model with local rotational symmetry. Using…
The quantum evolution equation of Loop Quantum Cosmology (LQC) -- the quantum Hamiltonian constraint -- is a difference equation. We relate the LQC constraint equation in vacuum Bianchi I separable (locally rotationally symmetric) models…
A self-consistent system of interacting spinor and scalar fields is considered within the scope of Bianchi type VI cosmological model filled with a perfect fluid. The contribution of the cosmological constant ($\Lambda$-term) is taken into…
I study several aspects of the path(st) integral we formulated in previous papers on energetic causal sets with Cortes and others. The focus here is on quantum field theories, including the standard model of particle physics. I show that…
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…
We propose a phase-space path integral formulation of noncommutative quantum mechanics, and prove its equivalence to the operatorial formulation. As an illustration, the partition function of a noncommutative two-dimensional harmonic…