arXiv subjects

M. V. Takook

Publications and source records attributed to M. V. Takook.

At least 19 recordsLinked to original sources

arXiv2026

Krein Space Quantization and a Spectral Interpretation of the Riemann $ξ$-Function

The invariant two-point function of a scalar field in de Sitter spacetime can be expressed in terms of Legendre functions via Lorentzian harmonic analysis. Using this structure together with the Mehler--Fock transform, we obtain an integral representation of the completed Riemann $ξ$-function in which the Legendre kernel appears naturally. Motivated by this correspondence, we introduce a retarded propagator whose spectral weight is given by the $ξ$-function and analyze it within the framework of Krein space quantization, where sign-indefinite spectral measures are admissible. This construction yields a geometric and spectral interpretation of the $ξ$-function restricted to the critical line and relates the asymptotic spacing of its zeros to a mass--time scaling in de Sitter geometry. The results provide a novel interpretive framework linking de Sitter quantum field theory, harmonic analysis, and analytic number theory.

math-ph↗

arXiv2025

Photon decaying in de Sitter universe

The interaction between three photons is studied in de Sitter ambient space formalism. As a special case the half harmonic generator is considered, {\it i.e.} one photon decays to two same-energy photons. The scattering matrix elements are presented which define the indirect gravitational effect on quantum field theory. The null curvature limit of scattering matrix is obtained for comparing it with its Minkowskian counterpart. The Hamiltonian of this interaction, in Minkowski space-time, was presented by using the quantum vacuum fluctuation in the one-loop approximation.

gr-qc↗

arXiv2025

Krein space quantization and New Quantum Algorithms

Krein space quantization and the ambient space formalism have been successfully applied to address challenges in quantum geometry (e.g., quantum gravity) and the axiomatic formulation of quantum Yang-Mills theory, including phenomena such as color confinement and the mass gap. Building on these advancements, we aim to extend these methods to develop novel quantum algorithms for quantum computation, particularly targeting underdetermined or ill-conditioned linear systems of equations, as well as quantum systems characterized by non-unitary evolution and open quantum dynamics. This approach represents a significant step beyond commonly used techniques, such as Quantum Singular Value Decomposition, Sz.-Nagy dilation, and Unitary Operator Decomposition. The proposed algorithm has the potential to establish a unified framework for quantum algorithms.

gr-qc↗

arXiv2023

Asymptotic states and $S$-matrix operator in de Sitter ambient space formalism

Within the de Sitter ambient space framework, the two different bases of the one-particle Hilbert space of the de Sitter group algebra are presented for the scalar case. Using field operator algebra and its Fock space construction in this formalism, we discuss the existence of asymptotic states in de Sitter QFT under an extension of the adiabatic hypothesis and prove the Fock space completeness theorem for the massive scalar field. We define the quantum state in the limit of future and past infinity on the Sitter hyperboloid in an observer-independent way. These results allow us to examine the existence of the $S$-matrix operator for de Sitter QFT in ambient space formalism, a question usually obscure in spacetime with a cosmological event horizon for a specific observer. Some similarities and differences between QFT in Minkowski and de Sitter spaces are discussed.

hep-th↗

arXiv2022

Axiomatic de Sitter quantum Yang-Mills theory with color confinement and mass gap

The analyticity property of de Sitter's quantum Yang-Mills theory in the framework of Kerin space quantization, including quantum metric fluctuation, is demonstrated. This property completes our previous work regarding quantum Yang-Mills theory in de Sitter's ambient space formalism, and we can construct an axiomatic quantum field theory similar to Wightman's axioms. The color confinement is proven for the general case, which was previously approved in the early universe. It is shown by using the interaction between gluon fields and the conformal sector of the gravitational field, which is a massless minimally coupled scalar gauge field. The gluon mass results from the interaction between the gluon fields and the massless minimally coupled scalar field as a conformal sector of the gravitational field and then the symmetry-breaking setting due to the vacuum expectation value of the scalar field.

gr-qc↗

arXiv2022

Scalar and vector gauges unification in de Sitter ambient space formalism

We consider the massless minimally coupled scalar field in the de Sitter ambient space formalism as a gauge potential or connection field. We construct the scalar gauge theory by helping an arbitrary constant five-vector field $B^α$ analogous to the standard gauge theory. The Lagrangian density of the interaction between the scalar and spinor fields is presented in this framework. The Yukawa potential can be extracted from this Lagrangian density at the null curvature limit by an appropriate choice of a constant five-vector field. It is shown that the de Sitter ambient space formalism permits us to unify the scalar and vector gauge fields. By choosing a matrix form for the constant five-vector field $B^α$, the unification of scalar and vector gauge fields in the spectral action of noncommutative geometry can be rewritten. We discuss that if the scalar gauge field is considered as a conformal sector of the background metric field, it may be interpreted as the connection field between the different de Sitter hyperboloids in the quantum geometry from the classical point of view.

hep-th↗

arXiv2022

Polarization tensor in de Sitter gauge gravity

The gauge theory of the de Sitter group, SO$(1,4)$, in the ambient space formalism has been considered in this article. This method is essential to constructing the de Sitter super-conformal gravity and Quantum gravity. $10$ gauge vector fields are needed, corresponding to $10$ generators of the de Sitter group. Using the gauge-invariant Lagrangian, the field equation of these vector fields has been obtained. The gauge vector field solutions are recalled. Then, the spin-$2$ gauge potentials are constructed from the gauge vector field. There are two possibilities for presenting this tensor field: rank-$2$ symmetric and mixed symmetry rank-$3$ tensor fields. To preserve the conformal transformation, a spin-$2$ field must be represented by a mixed symmetry rank-$3$ tensor field, $\mathcal {K}_{αβγ}$. This tensor field has been rewritten using a generalized polarization tensor field and a de Sitter plane wave. This generalized polarization tensor field has been calculated as a combination of vector polarization, $\mathcal {E}_α$, and tensor polarization of rank-$2$, $\mathcal {E}_{αβ}$, which can be used in the gravitational wave consideration. For the construction of this polarization tensor, the arbitrary constant vector fields appear. We fix it so that, in the limit, $H=0$, one obtains the polarization tensor in Minkowski space-time. It has been shown that under some simple conditions, the spin-$2$ mixed symmetry rank-$3$ tensor field can be simultaneously transformed by the unitary irreducible representation of de Sitter and conformal groups, SO$(2,4)$.

gr-qc↗

arXiv2022

Conceptual and technical challenges of quantum gravity

The appearance of infinity together with collapsing quantum state due to the observation or interaction, which are two challenging features of quantum field theory, become very serious problems in quantum gravity as well as in quantum geometry of space-time. These problems can be divided into two categories: technical and conceptual parts. In the technical aspect, the biggest problem comes from the definition of the point, which constructs classical geometry. By changing the point definition, the technical problem may be approximately bypassed, and a mathematical formulation of quantum geometry may be found. On the other hand, the conceptual problem comes from the quantum state collapse due to the observation since the entanglement between the observer and gravity cannot be eliminated in the presence of gravity. The conceptual part does not depend on the techniques which are employed. As much as possible, we try to discuss these problems by rediscovering the perception and understanding of a phenomenon for an observer in quantum theory.

gr-qc↗

arXiv2022

"Krein" regularization method

The "Krein" regularization method of quantum field theory is studied, inspired by the Krein space quantization and quantum metric fluctuations. It was previously considered in the one-loop approximation, and this paper is generalized to all orders of perturbation theory. We directly recover the physical results previously obtained starting from the standard QFT by imposing the renormalization conditions. By applying our approach to the QFT in curved space-time and quantum linear gravity, we discuss that there is no need for the higher derivative of the metric tensor for the renormalization of the theory. The advantage of our method compared to the previous ones is that the linear quantum gravity is renormalizable in all orders of perturbation theory.

hep-th↗

arXiv2022

Quantum Yang-Mills theory in de Sitter ambient space formalism

We present the quantum Yang-Mills theory in the four-dimensional de Sitter ambient space formalism. In accordance with the SU$(3)$ gauge symmetry the interaction Lagrangian is formulated in terms of interacting color charged fields in curved space-time. The gauge-invariant field equations are obtained in an independent coordinate description, and their corresponding color conserved currents are computed. Faddeev-Popov ghost fields are shown to be equivalent to their Minkowski counterparts. We obtain that the free ghost fields are massless minimally coupled scalar fields. The problems of the vacuum state, namely the breaking of de Sitter invariance, and the appearance of infrared divergence in its quantization procedure, are discussed. The existence of an axiomatic quantum Yang-Mills theory within the framework of the Krein space quantization is examined. The infrared divergence regularization of the interaction between the gauge vector fields and the ghost fields is studied in the one-loop approximation. Two different regularization methods are discussed: cut-off regularization and Krein space regularization. A mass term for the gauge vector fields is obtained, which may explain the mass gap and the color confinement problems at the quantum level in de Sitter background. The large curvature limit at the early universe or inflationary epoch is considered.

hep-th↗

arXiv2021

Electron-photon interaction in de Sitter ambient space formalism

The electron-photon interaction (the spinor-vector field interaction) in the de Sitter ambient space formalism is investigated in the first (leading order) approximation. The interaction Lagrangian and the scattering matrix are presented. In this approximation, the scattering matrix can be written as a expansion of the interaction Lagrangian. The tree-diagram of electron-photon scattering amplitude is calculated. Finally the Minkowski limit is considered.

gr-qc↗

arXiv2021

Scalar spinor fields interaction in de Sitter ambient space formalism

In de Sitter ambient space formalism, the massless minimally coupled scalar field can be constructed from a massless conformally coupled scalar field and a constant five-vector $A^α$. Also, a constant five-vector $B^α$ appears in the interaction Lagrangian of massless minimally coupled scalar and spinor fields in this formalism. These constant five-vector fields can be fixed in the interaction case in the null curvature limit. Here we will calculate the $\cal S$ matrix elements of scalar-spinor fields interaction in the tree level approximation. Then the constant five-vectors $A^α$ and $B^α$, will be fixed by comparing the $\cal S$ matrix elements in the null curvature limits with the Minkowskian counterparts.

gr-qc↗

arXiv2017

de Sitter super-gravity in ambient space formalism

In the de Sitter ambient space formalism the massless fields, which include the linear gravity and massless minimally coupled scalar field, can be written in terms of two separate parts: a massless conformally coupled scalar field and a polarization tensor(-spinor) part. Therefore due to the massless conformally coupled scalar field, there exist an unique Bunch-Davies vacuum state for quantum field theory in the de Sitter space time. In the de Sitter ambient space formalism one can show that the massless fields with spin $s\geq 1$ are gauge invariant. By coupling the massless gauge spin-$2$ and the massless gauge spin-$3/2$ fields and using the super-symmetry algebra in de Sitter ambient space formalism, one can naturally construct a unitary de Sitter super-gravity on Bunch-Davies vacuum state.

gr-qc↗

arXiv2017

Quantum de Sitter-black hole in ambient space formalism

Two important problems in studying the quantum black hole, namely the construction of the Hilbert space and the definition of the time evolution operator on such Hilbert space, are discussed using the de Sitter background field method for an observer far from the black hole. This is achieved through the ambient space formalism. Remarkably, in this approximation (distant observer), the theory preserves unitarity and analyticity, it is free from any infrared divergence, and it renders a quantum black hole entropy that turns out to be finite.

gr-qc↗

arXiv2017

Linear Gravity in de Sitter universe

We give in this paper an explicit construction of the covariant quantization of the rank-two massless tensor field on de Sitter space (linear covariant quantum gravity on a de Sitter background). The main ingredient of the construction is an indecomposable representation of de Sitter group. We here make the choice of a specific simple gauge fixing. We show that our gauge fixing eliminates any infrared divergence in the two-point function for the traceless part of this field. But it is not possible to do the same for the pure trace part (conformal sector). We describe the related Krein space structure and covariant field operators. This work is in the continuation of our previous ones concerning the massless minimally coupled scalar fields and the massive tensor field on de Sitter.

gr-qc↗

arXiv2017

Quantum Linear Gravity in de Sitter Universe On Bunch-Davies vacuum state

In de Sitter ambient space formalism, the linear gravity can be written in terms of a minimally coupled scalar field and a polarization tensor. In this formalism, the massless minimally coupled scalar field can be quantized on Bunch-Davies vacuum state, that preserves the de Sitter invariance, the analyticity and removes the infrared divergence. The de Sitter quantum linear gravity is then constructed on Bunch-Davies vacuum state, which is also covariant, analytic and free of any infrared divergences. We will conclude that the unique Bunch-Davies vacuum state can be used adequately to constructing the quantum field theory in de Sitter universe.

gr-qc↗

arXiv2016

Super-gauge Field in de Sitter Universe

The Gupta-Bleuler triplet for vector-spinor gauge field is presented in de Sitter ambient space formalism. The invariant space of field equation solutions is obtained with respect to an indecomposable representation of the de Sitter group. By using the general solution of the massless spin-$\frac{3}{2}$ field equation, the vector-spinor quantum field operator and its corresponding Fock space is constructed. The quantum field operator can be written in terms of the vector-spinor polarization states and a quantum conformally coupled massless scalar field, which is constructed on Bunch-Davies vacuum state. The two-point function is also presented, which is de Sitter covariant and analytic.

gr-qc↗

arXiv2016

Quantum Linear Gravity in de Sitter Universe On Gupta-Bleuler vacuum state

Application of Krein space quantization to the linear gravity in de Sitter space-time have constructed on Gupta-Bleuler vacuum state, resulting in removal of infrared divergence and preserving de Sitter covariant. By pursuing this path, the non uniqueness of vacuum expectation value of the product of field operators in curved space-time disappears as well. Then the vacuum expectation value of the product of field operators can be defined properly and uniquely.

gr-qc↗