Related papers: Stochastic quantization of two-dimensional $P(\Phi…
In this article we propose a `second quantization' scheme especially suitable to deal with non-trivial, highly symmetric phase spaces, implemented within a more general Group Approach to Quantization, which recovers the standard Quantum…
In a series of seminal papers, Laddha and Varadarajan have developed in depth the quantisation of Parametrised Field Theory (PFT) in the kind of discontinuous representations that are employed in Loop Quantum Gravity (LQG). In one spatial…
We study fluctuations of the metric in the postquantum theory of classical gravity, a covariant theory which couples a classical spacetime with quantum matter fields. Mathematical consistency requires spacetime to evolve stochastically.…
Quantum gravity is studied nonperturbatively in the case in which space has a boundary with finite area. A natural set of boundary conditions is studied in the Euclidean signature theory, in which the pullback of the curvature to the…
An oscillating, compact Friedmann universe with a massive conformally coupled scalar field is studied in the framework of quantum cosmology. The scalar field is treated as a perturbation and we look for solutions of the Wheeler-DeWitt…
We find that, in presence of the Snyder geometry, the notion of translational invariance needs to be modified, allowing a momentum dependence of this symmetry. This step is necessary to build the maximally localized states and the Feynman…
We describe quantum-field-theoretical (QFT) techniques for mapping quantum problems onto c-number stochastic problems. This approach yields results which are identical to phase-space techniques [C.W. Gardiner, {\em Quantum Noise} (1991)]…
We construct a relativistically covariant stochastic model for systems of non-interacting spinless particles whose number undergoes random fluctuations. The model is compared with the canonical quantization of the free scalar field in the…
We study non-perturbative quantization of 3d gravity with positive cosmological constant (de Sitter space being the prototype vacuum solution, whose Euclideanization of course gives the three sphere) on the background topology of lens…
The canonical quantum theory of a free field using arbitrary foliations of a flat two-dimensional spacetime is investigated. It is shown that dynamical evolution along arbitrary spacelike foliations is unitarily implemented on the same Fock…
We construct an effective Quantum Field Theory for the wrapping effects in 1+1 dimensional models of factorised scattering. The recently developed graph-theoretical approach to TBA gives the perturbative desctiption of this QFT. For the…
Four-dimensional quantum field theories generally require regularization to be well defined. This can be done in various ways, but here we focus on Pauli--Villars (PV) regularization and apply it to nonperturbative calculations of bound…
We unify Brownian motion and quantum mechanics in a single mathematical framework. In particular, we show that non-relativistic quantum mechanics of a single spinless particle on a flat space can be described by a Wiener process that is…
Non-equilibrium quantum field theory studies time dependence of processes which are not available for the S-matrix description. One of the new methods of investigation in non-equilibrium quantum theory is the stochastic limit method. This…
Scattering transform is a well known powerful tool for quantisation of field theories in (1+1) dimensions. Conventionally only those models whose classical counterparts admit a Lax pair (origin of which is always mysterious) have been…
We embed Nelson's stochastic quantization in the Schwartz-Meyer second order geometry framework. The result is a non-perturbative theory of quantum mechanics on (pseudo)-Riemannian manifolds. Within this approach, we derive stochastic…
A model of state reduction in relativistic quantum field theory involving a nonlinear stochastic extension of Schr\"odinger's equation is outlined. The eigenstates of the annihilation operator are chosen as the preferred basis onto which…
We analyze the transformation of quantum fields under conformal coordinate transformations from inertial to accelerated frames, in the simple case of scalar massless fields in a two-dimensional spacetime, through the transformation of…
Gauge theory on the q-deformed two-dimensional Euclidean plane R^2_q is studied using two different approaches. We first formulate the theory using the natural algebraic structures on R^2_q, such as a covariant differential calculus, a…
We consider the Einstein-Cartan theory with the tetrad $e_{\mu}^{a}$ and spin connection $\omega_{\mu ab}$ taken as being independent fields. Diffeomorphism invariance and local Lorentz invariance result in there being two distinct gauge…