Related papers: The Scalar Field Kernel in Cosmological Spaces
It is generally known that linear (free) field theories are one of the few QFT that are exactly soluble. In the Schroedinger functional description of a scalar field on flat Minkowski spacetime and for flat embeddings, it is known that the…
The theory of positive kernels and associated reproducing kernel Hilbert spaces, especially in the setting of holomorphic functions, has been an important tool for the last several decades in a number of areas of complex analysis and…
The method of 'covariant perturbation theory' allowed for the computation of the kernel of the evolution equation on a spin Riemannian manifold. The proposed axiomatic definition of the effective action introduces the universal scale…
In this paper, we consider fermionic systems in discrete spacetime evolving with a strict notion of causality, meaning they evolve unitarily and with a bounded propagation speed. First, we show that the evolution of these systems has a…
Inspiral of binary black holes occurs over a time-scale of many orbits, far longer than the dynamical time-scale of the individual black holes. Explicit evolutions of a binary system therefore require excessively many time steps to capture…
We build a systematic calculational method for the covariant expansion of the two-point heat kernel $\hat K(\tau|x,x')$ for generic minimal and non-minimal differential operators of any order. This is the expansion in powers of dimensional…
We have obtained propagators in the position space as an expansion over Landau levels for the charged scalar particle, fermion, and massive vector boson in a constant external magnetic field. The summation terms in the resulting expressions…
It is proven that the kernel of the fermionic projector of regularized Dirac sea vacua in Minkowski Space is $L^4$-integrable. The proof is carried out in the specific setting of a continuous exponentially-decaying cutoff in momentum space.…
It is shown that Weyl spinors in 4D Minkowski space are composed of primary fields of half-integer conformal weights. This yields representations of fermionic 2-point functions in terms of correlators of primary fields with a factorized…
We study the heat kernel for the Laplace type partial differential operator acting on smooth sections of a complex spin-tensor bundle over a generic $n$-dimensional Riemannian manifold. Assuming that the curvature of the U(1) connection…
We investigate scalar-induced gravitational waves (SIGWs) in the framework of spatially covariant gravity (SCG), a broad class of Lorentz-violating modified gravity theories respecting only spatial diffeomorphism invariance. Extending…
We study mapping properties of operators with kernels defined via a combination of continuous and discrete orthogonal polynomials, which provide an abstract formulation of quantum (q-) Fourier type systems. We prove Ismail conjecture…
In this paper, we investigate cosmological particle production using quantum field theory (QFT). We will consider how production of scalar particles can occur in an expanding universe. By introducing a time-dependent energy parameter…
The framework of the relativistic quantum mechanics on spatially flat FLRW space-times is considered for deriving the analytical solutions of the Dirac equation in different local charts of these manifolds. Systems of commuting conserved…
In this paper we investigate massless scalar field theory on non-degenerate algebraic curves. The propagator is written in terms of the parameters appearing in the polynomial defining the curve. This provides an alternative to the language…
The article is a natural continuation of our paper {\em Quantum scalar field in FRW Universe with constant electromagnetic background}, Int. J. Mod. Phys. {\bf A12}, 4837 (1997). We generalize the latter consideration to the case of massive…
We calculate quantum fluctuations of a free scalar field in the Schwarzschild-de Sitter space-time, adopting the planar coordinates that is pertinent to the presence of a black hole in an inflationary universe. In a perturbation approach,…
We solve analytically the low-frequency s-wave dynamics of a massless scalar field propagating on a Schwarzschild-de Sitter black hole background. A rigorous application of the method of matched asymptotic expansions allows us to connect…
In this paper, we adopt the method of quantum fields in curved spacetime to quantize a free scalar matter field in the braneworld background whose warped factor is of the form that could generate P\"{o}schl-Teller potential. Then we…
The classical and quantum models of the Friedmann universe originally filled with a scalar field and radiation have been studied. The radiation has been used to specify a reference frame that makes it possible to remove ambiguities in…