Related papers: The Scalar Field Kernel in Cosmological Spaces
In flat spacetime, two inequivalent vacuum states which arise rather naturally are the Rindler vacuum (R) and the Minkowski vacuum (M). We disuss several aspects of the Rindler vacuum, concentrating on the propagator and Schwinger (heat)…
Scalar fields in curved backgrounds are assumed to be composite objects. As an example realizing such a possibility we consider a model of the massless tensor field $l_{\mu\nu}(x)$ in a 4-dim. background $g_{\mu\nu}(x)$ with spontaneously…
Among the available perturbative approaches in quantum field theory, heat kernel techniques provide a powerful and geometrically transparent framework for computing effective actions in nontrivial backgrounds. In this work, resummation…
We implement an all-optical setup demonstrating kernel-based quantum machine learning for two-dimensional classification problems. In this hybrid approach, kernel evaluations are outsourced to projective measurements on suitably designed…
We present a new covariant method of construction of the (position space) propagators in the $N$-dimensional (Euclidean) anti-de Sitter background for any gravitational theory with the Lagrangian that is an analytic expression in the…
We link the notion causality with the orientation of the 2-complex on which spin foam models are based. We show that all current spin foam models are orientation-independent, pointing out the mathematical structure behind this independence.…
We study spinor field theories as an origin to induce space-time evolution. Self-interacting spinor fields with canonical and non-canonical kinetic terms are considered in a Friedman-Robertson-Walker universe. The deceleration parameter is…
The present matter density of the Universe, while highly inhomogeneous on small scales, displays approximate homogeneity on large scales. We propose that whereas it is justified to use the Friedmann-Lemaitre-Robertson-Walker (FLRW) line…
We study the Moyal commutators and their expectation values between vacuum states and non-vacuum states for free scalar field on noncommutative spacetime. Then from the Moyal commutators, we find that the microcausality is satisfied for the…
We consider conditions on a given system $\mathcal{F}$ of vectors in Hilbert space $\mathcal{H}$, forming a frame, which turn $\mathcal{H}$ into a reproducing kernel Hilbert space. It is assumed that the vectors in $\mathcal{F}$ are…
We investigate the nonlinear evolution of cosmological perturbations in theories with scale-dependent perturbation growth, first in general and then focusing on Horndeski gravity. Within the framework of standard perturbation theory, we…
We study an extension of the classical Paley-Wiener space structure, which is based on bilinear expansions of integral kernels into biorthogonal sequences of functions. The structure includes both sampling expansions and Fourier-Neumann…
The analytic structure of the quark propagator in Minkowski space is more complex than in Euclidean space due to the possible existence of poles and branch cuts at timelike momenta. These singularities impose enormous complications on the…
In a previous paper we have presented a general formalism for computing Feynman diagrams for scalar fields in curved spacetime at any loop order using heat kernel methods. The main technique used is the expansion of the fully off-diagonal…
Developing our understanding of how correlations evolve during inflation is crucial if we are to extract information about the early Universe from our late-time observables. To that end, we revisit the time evolution of scalar field…
The Schwinger--DeWitt expansion for the evolution operator kernel is used to investigate analytical properties of the Schr\"odinger equation solution in time variable. It is shown, that this expansion, which is in general asymptotic,…
Quantum field theory in the $4$-dimensional de Sitter space-time is constructed in the ambient space formalism in a rigorous mathematical framework. This work is based on the group representation theory and the analyticity of the…
Using the Zwanzig projection-operator formalism, we derive a causal two-point spatiotemporal kernel for heat conduction, defined microscopically as a space-resolved equilibrium heat-flux time-correlation function, that encodes temporal…
Scalar-tensor gravitational theories are important extensions of standard general relativity, which can explain both the initial inflationary evolution, as well as the late accelerating expansion of the Universe. In the present paper we…
We study the scattering behavior of scalar and spinor fields in the background of a gravitating cosmic string spacetime. The model explored here for the background vortex is non-abelian, becoming abelian in an appropriate limiting case. We…