Related papers: Some comments on rigorous quantum field path integ…
Some symmetries can be broken in the quantization process (anomalies) and this breaking is signalled by a non-invariance of the quantum path integral measure. In this talk we show that it is possible to formulate also classical field…
The core of this thesis is the path-integral formulation of quantum field theory and its ability to describe strongly-coupled quantum many-body systems of finite size. Collective behaviors can be efficiently described in such systems…
We formulate Lagrangian descriptors (LDs) in the path integral framework. Averaging the classical LD over fluctuations about extremal trajectories defines a quantum LD that incorporates quantum effects. Invariant manifolds, which sharply…
We provide a new paradigm for quantum simulation that is based on path integration that allows quantum speedups to be observed for problems that are more naturally expressed using the path integral formalism rather than the conventional…
We present a path integral formalism for quantising gravity in the form of the spectral action. Our basic principle is to sum over all Dirac operators. The approach is demonstrated on two simple finite noncommutative geometries: the…
Path integrals represent a powerful route to quantization: they calculate probabilities by summing over classical configurations of variables such as fields, assigning each configuration a phase equal to the action of that configuration.…
We construct a quantum theory of free scalar field in 1+1 dimensions based on a `Generalized Uncertainty Principle'. Both canonical and path integral formalism are employed. Higher dimensional extension is easily performed in the path…
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…
Local path integral quantization of generic 2D dilaton gravity is considered. Locality means that we assume asymptotic fall off conditions for all fields. We demonstrate that in the absence of `matter' fields to all orders of perturbation…
The Euclidean version of Yang-Mills theory coupled to a massive dilaton is investigated. Our analytical and numerical results imply existence of infinite number of branches of globally regular, spherically symmetric, dyonic type solutions…
The coordinate-free formulation of canonical quantization, achieved by a flat-space Brownian motion regularization of phase-space path integrals, is extended to a special class of closed first-class constrained systems that is broad enough…
Effective Lagrangians containing arbitrary interactions of massive vector fields are quantized within the Hamiltonian path integral formalism. It is proven that correct Hamiltonian quantization of these models yields the same result as…
We study the convergence of the path integral for General Relativity with matter on a picewise linear (PL) spacetime that corresponds to a triangulation of a smooth manifold by using a path-integral measure that renders the pure gravity…
These notes were inspired by the course ''Quantum Field Theory from a Functional Integral Point of View'' given at the University of Zurich in Spring 2017 by Santosh Kandel. We describe Feynman's path integral approach to quantum mechanics…
A parity-conserving and Lorentz-invariant effective field theory of self-interacting massive vector fields is considered. For the interaction terms with dimensionless coupling constants the canonical quantization is performed. It is shown…
The method of geometric quantization is applied to a particle moving on an arbitrary Riemannian manifold $Q$ in an external gauge field, that is a connection on a principal $H$-bundle $N$ over $Q$. The phase space of the particle is a…
Starting from the canonical formalism of relativistic (timeless) quantum mechanics, the formulation of timeless path integral is rigorously derived. The transition amplitude is reformulated as the sum, or functional integral, over all…
Path integral formulations for gauge theories must start from the canonical formulation in order to obtain the correct measure. A possible avenue to derive it is to start from the reduced phase space formulation. In this article we review…
Coherent states path integral formalism for the simplest quantum algebras, q-oscillator, SU_q(2) and SU_q(1,1) is introduced. In the classical limit canonical structure is derived with modified symplectic and Riemannian metric. Non-constant…
We analyze on the formalism of probability measures -functional integrals on function spaces , the problem of infinities on Euclidean field theories