Related papers: Ground state and functional integral representatio…
The linearly polarized Gowdy $T^3$ model is paradigmatic for studying technical and conceptual issues in the quest for a quantum theory of gravity since, after a suitable and almost complete gauge fixing, it becomes an exactly soluble…
We show that the emergence of time evolution in an otherwise timeless nonrelativistic closed quantum system -- viewed as a poor man's model of generally covariant quantum theory -- can be understood from the perspective of the path integral…
It is shown that the $n$-point functions of scalar massive free fields on the noncommutative Minkowski space are distributions which are boundary values of analytic functions. Contrary to what one might expect, this construction does not…
A functional integral representation is given for a large class of quantum mechanical models with a non--L2 ground state. As a prototype the particle in a periodic potential is discussed: a unique ground state is shown to exist as a state…
By using the localized character of canonical coherent states, we give a straightforward derivation of the Bargmann integral representation of Wigner function (W). A non-integral representation is presented in terms of a quadratic form…
Neural network representations are often analyzed as vectors in a fixed Euclidean space. However, their coordinates are not uniquely defined. If a hidden representation is transformed by an invertible linear map, the network function can be…
In the language of Feynman path integrals the quantization of gauge theories is most easily carried out with the help of the Schr\"odinger Functional (SF). Within this formalism the essentially unique gauge fixing condition is $A_{\circ} =…
We study energy functionals associated with non-local quasi-linear Schr\"odinger operators, and develop a ground state representation. Our main focus is on infinite graphs but we also consider non-local quasi-linear Schr\"odinger operators…
The exact and stable evolutions of generalized coherent states (GCS) for quantum systems are considered by making use of the time-dependent integrals of motion method and of the Klauder approach to the relationship between quantum and…
Starting from the observation that in Yang-Mills theory the Schroedinger state functional in the momentum representation is not gauge invariant, we investigate the reversed question: Which are the representations for the operators of a…
A C*-algebra containing the CCR and CAR algebras as its subalgebras and naturally described as the semidirect product of these algebras is discussed. A particular example of this structure is considered as a model for the algebra of…
The homogeneous Friedman-Lema\^\i tre-Robertson-Walker (FLRW) cosmology of a free scalar field with vanishing cosmological constant was recently shown to be invariant under the one-dimensional conformal group $\textrm{SL}(2,\mathbb{R})$…
Recent work on the quantization of Maxwell theory has used a non-covariant class of gauge-averaging functionals which include explicitly the effects of the extrinsic-curvature tensor of the boundary, or covariant gauges which, unlike the…
Generalized Fourier transformation between the position and the momentum representation of a quantum state is constructed in a coordinate independent way. The only ingredient of this construction is the symplectic (canonical) geometry of…
Two algorithms are proposed to simulate space-time Gaussian random fields with a covariance function belonging to an extended Gneiting class, the definition of which depends on a completely monotone function associated with the spatial…
We present a local framework for investigating non-unitary evolution groups pertinent to effective field theories in general semi-classical spacetimes. Our approach is based on a rigorous local stability analysis of the algebra of…
We discuss canonical transformations in Quantum Field Theory in the framework of the functional-integral approach. In contrast with ordinary Quantum Mechanics, canonical transformations in Quantum Field Theory are mathematically more subtle…
A novel exact dynamical real space renormalization group for a Langevin equation derivable from a Euclidean Gaussian action is presented. It is demonstrated rigorously that an algebraic temporal law holds for the Green function on arbitrary…
We develop generalized coherent states for a class of nonlinear oscillators with position-dependent effective mass in the context of the Gazeau-Klauder formalism and discuss some of their properties. In order to investigate the temporal…
Affine quantum gravity involves (i) affine commutation relations to ensure metric positivity, (ii) a regularized projection operator procedure to accomodate first- and second-class quantum constraints, and (iii) a hard-core interpretation…