相关论文: Dynamical Vector Fields on the Manifold of Quantum…
Massive Klein-Gordon theory is quantized on a timelike hyperplane in Minkowski space using the framework of general boundary quantum field theory. In contrast to previous work, not only the propagating sector of the phase space is…
Dynamical evolution of the quantum ground state (vacuum) is analyzed for time variant harmonic oscillators characterized by asymptotically constant frequency. The oscillatory density matrix in the asymptotic future is uniquely determined by…
Quantum de Sitter geometry is discussed using elementary field operator algebras in Krein space quantization from an observer-independent point of view, {\it i.e.} ambient space formalism. In quantum geometry, the conformal sector of the…
We provide a diagrammatic formulation of perturbative quantum field theory in a finite interval of time $\tau $, on a compact space manifold $\Omega $. We explain how to compute the evolution operator $U(t_{\text{f}},t_{\text{i}})$ between…
In the framework of deterministic finslerian models, a mechanism producing dissipative dynamics at the Planck scale is discussed. It is based on a geometric evolution from Finsler to Riemann structures defined on the fiber bundle ${ TM}\to…
Dynamical evolution is described as a parallel section on an infinite dimensional Hilbert bundle over the base manifold of all frames of reference. The parallel section is defined by an operator-valued connection whose components are the…
An exterior derivative, inner derivation, and Lie derivative are introduced on the quantum group $GL_{q}(N)$. $SL_{q}(N)$ is then found by constructing matrices with determinant unity, and the induced calculus is found.
We consider an optomechanical quantum system composed of a single cavity mode interacting with N mechanical resonators. We propose a scheme for generating continuous-variable graph states of arbitrary size and shape, including the so-called…
We present a group of transformations in the quantum configuration space of loop quantum gravity that contains the set of all transformations generated by the flux variables.
Using the notion of distribution on an infinite dimensional space defined in our previous paper, we give definition of a version of dynamical evolution in quantum field theory, motivated by heuristic formulas involving path integrals.
If we develop into perturbation series the evolution operator of the Heisenberg equation in the infinite dimensional Weyl algebra, say, for the $\phi^4$ model of field theory, then the arising integrals almost coincide with the usual…
We construct two-dimensional non-commutative topological quantum field theories (TQFTs), one for each Hecke algebra corresponding to a finite Coxeter system. These TQFTs associate an invariant to each ciliated surface, which is a Laurent…
In this work, we apply the generalised Feshbach Villars transformation (GFVT) to spin-0 scalar fields in a Schwarzschild gravitational background. Starting from the covariant Klein Gordon equation, we reformulate the dynamics in the FV…
A scalar field theory with 4-derivative kinetic terms and 4-derivative cubic and quartic couplings is presented as a proxy for quantum quadratic gravity (QQG). The scalar theory is renormalizable and asymptotically free and the remaining…
Quantum gravity was born as that branch of modern theoretical physics that tries to unify its guiding principles, i.e., quantum mechanics and general relativity. Nowadays it is providing new insight into the unification of all fundamental…
We study the evolution of a quantum scalar field in a toy universe which has three stages of evolution, viz., (i) an early (inflationary) de Sitter phase (ii) radiation dominated phase and (iii) late-time (cosmological constant dominated)…
We propose an extended quantum mechanical formalism that is based on a wave operator $\vr$, which is related to the ordinary density matrix via $\rho=\vr\vr^\dagger$. This formalism allows a (generalized) unitary evolution between pure and…
A class of vector states on a von Neumann algebra is constructed. These states belong to a deformed exponential family. One specific deformation is considered. It makes the exponential function asymptotically linear. Difficulties arising…
We study homogeneous quantum L\'{e}vy processes and fields with independent additive increments over a noncommutative *-monoid. These are described by infinitely divisible generating state functionals, invariant with respect to an…
The transition from a classical to quantum theory is investigated within the context of orthogonal and symplectic Clifford algebras, first for particles, and then for fields. It is shown that the generators of Clifford algebras have the…