Ion I. Cotăescu

West University of Timisoara · Department of Physics

The Dirac theory of free massive fermions is reconstructed around the new conserved spin operator and its corresponding position one proposed initially by Pryce long time ago and redefined recently by using suitable spectral representations [I. I. Cotȃescu, Eur. Phys. J. C (2022) 82:1073]. This approach is generalized here associating to any integr...

The discrete symmetries of Dirac’s free field on the de Sitter manifold are studied, taking into account that this has two portions that can play the role of physical space-times, namely an expanding and a collapsing universe. The proper discrete isometries which preserve the portion have a physical meaning, in contrast to the improper ones, which...

New conserved spin and orbital angular momentum operators of Dirac's theory on spatially flat FLRW spacetimes are proposed generalizing thus recent results concerning the role of Pryce's spin operator in the flat case [I. I. Cot\u aescu, Eur. Phys. J. C (2022) 82:1073]. These operators split the conserved total angular momentum generating the new s...

The discrete symmetries of the Dirac field on the de Sitter manifold are studied taking into account that this has two portions that can play the role of physical space-times, namely the expanding and a collapsing universes. The proper discrete isometries which preserve the portion have a physical meaning in contrast to the improper ones which chan...

It is shown that the components of Pryce’s spin operator of Dirac’s theory are SU (2) generators of a representation carried by the space of Pauli’s spinors determining the polarization of the plane wave solutions of Dirac’s equation. These operators are conserved via Noether’s theorem such that new conserved polarization operators can be defined f...

It is shown that the components of Pryce's spin operator of Dirac's theory are SU(2) generators of a representation carried by the space of Pauli's spinors determining the polarization of the plane wave solutions of Dirac's equation. These operators are conserved via Noether theorem such that new conserved polarization operators can be defined for...

The processes in the first order of perturbations of de Sitter quantum electrodynamics (QED) in Coulomb gauge are studied but setting our recently proposed rest frame vacuum of the Dirac field instead of the traditional adiabatic one. This vacuum gives rise to a new phenomenology favouring the transitions between neutral states, i.e. the pair creat...

Metrics of dynamical point particles embedded in spatially flat FLRW space-times are derived as isotropic solutions of the Einstein equations with the energy–momentum tensor of a perfect fluid. These particles are produced by central singularities of the fluid density but without changing the pressure of the asymptotic FLRW space-times. It is shown...

The propagation of the packets of left-handed plane wave solutions of the massless Dirac equation is studied in spatially flat Friedmann–Lemaître–Robertson–Walker (FLRW) space-times. Assuming that the observations are performed in physical frames with Painlevé–Gullstrand coordinates, the current and energy–momentum tensor are derived, emphasising t...

A new type of dynamical black holes is defined in manifolds with flat space sections having the asymptotic behaviour of spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) space-times. These black holes are no longer vacuum solutions of the Einstein equations but preserve the isotropy of the flat space sections of the asymptotic FLRW manifold...

The classical and quantum theory of the Maxwell free field (or perturbation) minimally coupled to the gravity of local-Minkowskian spatially flat Friedmann–Lemaître–Robertson–Walker (FLRW) space-times is constructed in conformal local charts (herein called frames) where the Maxwell equations have the same form as in special relativity. Taking into...

The classical and quantum theory of the Maxwell field minimally coupled to the gravity of local-Minkowskian spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) space-times is constructed in conformal local charts (called here frames) where the Maxwell equations have the same form as in special relativity. Taking into account that the conforma...

We derive for the first time the form of the spiral null geodesics around the photon sphere of the Reissner–Nordstrom black hole in the de Sitter expanding universe. Moreover, we obtain the principal parameter we need for deriving, according to our method [I. I. Cotăescu, Eur. Phys. J. C 81, 32 (2021)], the black hole shadow and the related redshif...

The quantum theory of the Maxwell free field in Coulomb gauge on the de Sitter expanding universe is completed with the technical elements needed for building a coherent quantum theory of redshift. Paying special attention to the conserved observables and defining the projection operator selecting the detected momenta it is shown that the expectati...

We study for the first time the propagation of the Maxwell wave packets in the de Sitter expanding universe as detected by an observer staying at rest in his proper frame with physical de Sitter- Painlev\' e coordinates. This observes an accelerate propagation of the wave packet along to a null geodesic, laying out an exponential decay during propa...

We analyze the Abraham–Minkowski problem known from classical electrodynamics from two different perspectives. First, we follow a formal approach, implying use of manifolds with curved space sections in accordance with Fermat’s principle, emphasizing that the resulting covariant and contravariant components of the photon four-momentum are a propert...

The quantum theory of the Maxwell free field in Coulomb gauge on the de Sitter expanding universe is completed with the technical elements needed for building a coherent quantum theory of redshift. Paying a special attention to the conserved observables and defining the projection operator selecting the detected momenta it is shown that the expecta...

The kinematics on spatially flat FLRW space-times is presented for the first time in co-moving local charts with physical coordinates, i. e. the cosmic time and Painlev\' e-type Cartesian space coordinates. It is shown that there exists a conserved momentum which determines the form of the covariant four-momentum on geodesics in terms of physical c...

A new method is applied for deriving simultaneously the redshift and shadow of a Schwarzschild black hole moving freely in the de Sitter expanding universe as recorded by a remote co-moving observer. This method is mainly algebraic, focusing on the transformation of the conserved quantities under the de Sitter isometry relating the black hole co-mo...

A new redshift formula is obtained considering the longitudinal Doppler effect in the de Sitter expanding universe where the relative geodesic motion is governed by the Lorentzian isometries of our new de Sitter relativity [I. I. Cotăescu, Eur. Phys. J. C 77, 485 (2017)]. This formula combines in a nontrivial manner the well-known cosmological cont...

The light from the Reissner-Nordstrom black hole in de Sitter expanding universe is studied deriving for the first time the form of the spiral null geodesics around the photon sphere and the radius of the sphere hosting the apparent sources near the black hole shadow. We obtains thus the principal parameter giving the redshift and the observed blac...

We analyze the Abraham-Minkowski problem known from classical electrodynamics from two different perspectives. First, we follow a formal approach, implying use of manifolds with curved space sections in accordance with Fermat's principle, emphasizing that the resulting covariant and contravariant components of the photon four-momentum is a property...

A new method is applied for deriving the redshift and shadow of a Schwarzschild black hole moving freely in the de Sitter expanding universe as recorded by a co-moving remote observer. This method is manly algebraic focusing on the transformation of the conserved quantities under the de Sitter isometry relating the black hole proper frame to observ...

The problem of the flat limits of the scalar and spinor fields on the de Sitter expanding universe is considered in the traditional adiabatic vacuum and in the new rest frame vacuum we proposed recently, in which the frequencies are separated in the rest frames as in special relativity. It is shown that only in the rest frame vacuum can the Minkows...

A new formula of the longitudinal Doppler effect in de Sitter expanding universe is derived combining the cosmological contribution with that of the relative geodesic motion of the source with respect to a fixed observer.

We propose a method of projecting the quantum states from a state space of a given geometry into another state space generated by a different geometry, taking care of the correct normalization which is crucial in interpreting the quantum theory. Thanks to this method we can define on any spatially flat FLRW spacetime states in which genuine Minkows...

The general plane wave solutions of the Proca field in conformal charts of the de Sitter expanding universe are derived for arbitrary polarizations showing how the frequencies can be separated in rest frames, defining thus the rest frame vacuum of this field.

The relativistic quantum mechanics of the free Dirac field in spatially flat FLRW spacetimes is considered as the framework for deriving the analytical solutions of the Dirac equation in different local charts of these manifolds. Different systems of commuting conserved operators are used for giving physical meaning to the integration constants as...

The quantum electrodynamics (QED) in a spatially flat (1+3)-dimensional Friedmann-Lemaître-Robertson-Walker (FLRW) space-time with a Milne-type scale factor is outlined focusing on the amplitudes of the allowed processes in the first order perturbations. The definition of the transition rates is reconsidered such that an appropriate angular behavio...

The problem of the flat limits of the scalar and spinor fields on the de Sitter expanding universe is considered in the rest frame vacuum where the frequencies are separated in rest frames as in special relativity. The phases of the fundamental solutions of these fields are regularized in order to obtain Minkowskian flat limits. In this manner the...

The general plane wave solutions of the Proca field in conformal charts of the de Sitter expanding universe are derived for arbitrary polarizations showing how the frequencies can be separated in rest frames, defining thus the rest frame vacuum of this field.

We propose a method of projecting the quantum states from a state space of a given geometry into another state space generated by a different geometry, taking care on the correct normalization which is crucial in interpreting the quantum theory. Thanks to this method we can define on any spatially flat FLRW spacetime states in which genuine Minkows...

A new type of integral representation is proposed for the propagators of the massive Klein–Gordon field minimally coupled to gravity of the de Sitter expanding universe. This representation encapsulates the effects of the Heaviside step functions of the Feynman propagators, making possible for the first time the calculation of Feynman diagrams invo...

In quantum theory of the free Dirac field on spatially flat FLRW spacetimes we introduce a new type of vacuum able to separate the positive and negative frequencies in the rest frames. This is called here the rest frame vacuum showing that this differs from the adiabatic vacuum apart from the Minkowski spacetime where these two vacua coincide.

In quantum theory of the free Dirac field on spatially flat FLRW spacetimes we introduce a new type of vacuum able to separate the positive and negative frequencies in the rest frames. This is refereed as the rest frame vacuum shoving that this differs from the adiabatic vacuum apart from the Minkowski spacetime where these two vacua coincide.

The \((1+3)\)-dimensional Dirac equation of the fermions moving in ideal Aharonov–Bohm rings in the de Sitter expanding universe is used for deriving the exact expressions of the general relativistic partial currents and corresponding energies. In the de Sitter geometry, these quantities depend on time but these are related each other just as in th...

The $(1+3)$-dimensional Dirac equation of the fermions moving in ideal Aharonov-Bohm rings in the de Sitter expanding universe is used for deriving the exact expressions of the general relativistic partial currents and corresponding energies. In the de Sitter geometry, these quantities depend on time but these are related each other just as in the...

The quantum electrodynamics (QED) on a spatially flat $(1+3)$-dimensional Friedmann-Lema\^ itre-Robertson-Walker (FLRW) spacetime with a Milne-type scale factor is outlined focusing on the amplitudes of the allowed effects in the first order of perturbations. The definition of the transition rates is reconsidered obtaining an appropriate angular be...

The general formalism of the free Dirac fermions on spatially flat (1+3)-dimensional Friedmann-Lemaître–Robertson–Walker (FLRW) space–times is developed in momentum representation. The mode expansions in terms of the fundamental spinors satisfying the charge conjugation and normalization conditions are used for deriving the structure of the anticom...

A new type of integral representation is proposed for the propagators of the massive Klein-Gordon field minimally coupled to the gravity of the de Sitter expanding universe.

The asymptotic form of Dirac spinors in the field of a Schwarzschild black hole is used for deriving analytically for the first time the phase shifts of the partial wave analysis of Dirac fermions scattered from massive spherical bodies, imagined as black holes surrounded by a surface producing total reflection. A simple model is analyzed by using...

The asymptotic form of Dirac spinors in the field of a Schwarzschild black hole is used for deriving analytically for the first time the phase shifts of the partial wave analysis of Dirac fermions scattered from massive spherical bodies, imagined as black holes surrounded by a surface producing total reflection. A simple model is analyzed by using...

We consider the theory of the free Dirac fermions on spatially flat $(1+3)$-dimensional Friedmann-Lema\^ itre-Robertson-Walker (FLRW) spacetimes, developing a general formalism independent on the concrete form of the Dirac spinors in particular geometries. The general form of the fundamental spinors satisfying the charge conjugation an normalizatio...

The propagators of the Dirac fermions on the expanding portion of the (1+3)-dimensional de Sitter spacetime are considered as mode sums in momentum representation with a fixed vacuum of Bunch-Davies type. The principal result reported here is a new integral representation of the Feynman propagators of the massive and left-handed massless Dirac fiel...

The propagators of the Dirac fermions on the expanding portion of the \((1+3)\)-dimensional de Sitter spacetime are considered as mode sums in momentum representation with a fixed vacuum of Bunch–Davies type. The principal result reported here is a new integral representation of the Feynman propagators of the massive and left-handed massless Dirac...

The method of Koksma and Prokopec [Class. Quant. Grav. {\bf 26}, 125003 (2009)] is applied for studying the propagators of the Dirac fermions on the expanding portion of the $(1+3)$-dimensional de Sitter spacetime with a fixed vacuum of Bunch-Davies type. The propagators of massive fermions are recovered as a particular case but for the left-handed...

The properties of the covariant quantum fields on de Sitter space-times are investigated focusing on the isometry generators and Casimir operators in order to establish the equivalence among the covariant representations and the unitary irreducible ones of the de Sitter isometry group. For the Dirac quantum field, it is shown that the spinor covari...

The geosesics on de Sitter and anti-de Sitter spacetimes of any dimensions are derived in terms of conserved quantities. With their help the mesoscopic systems on these manifolds are studied finding the general solutions of the Boltzmann-Marle model in both these cases.

The covariant free fields of any spin on anti-de Sitter (AdS) spacetimes are studied, pointing out that these transform under isometries according to covariant representations (CRs) of the AdS isometry group, induced by those of the Lorentz group. Applying the method of ladder operators, it is shown that the CRs with unique spin are equivalent with...

The relative geodesic motion in static (and spherically symmetric) local charts on the \((1+3)\)-dimensional de Sitter spacetimes is studied in terms of conserved quantities. The Lorentzian isometries are derived, relating the coordinates of the local chart of a fixed observer with the coordinates of a mobile chart considered as the rest frame of a...

It is shown that the stereographic coordinates on the $(1+3)$-dimensional de Sitter spacetime induce, in the parametric equations of all the timelike geodesics, artificial singularities which do not have any physical motivation.

Our recent results concerning the transformation under isometries of the conserved quantities on de Sitter manifolds, allow us to define the rest frame and study the relative geodesic motion in terms of conserved momentum, revealing thus various relativistic effects [I. I. Cotaescu, arXiv:1701.08499]. Here we discuss the time dilation (of the twin...

The geodesics on the $(1+3)$-dimensional de Sitter spacetime are considered studying how their parameters are determined by the conserved quantities in the conformal Euclidean, Friedmann-Lema\^itre-Robertson-Walker, de Sitter-Painlev\'e and static local charts with Cartesian space coordinates. Moreover, it is shown that there exist a special static...

The covariant free fields of any spin on anti-de Sitter spacetimes are studied, pointing out that these transform under isometries according to covariant representations of the anti-de Sitter isometry group, induced by those of the Lorentz group. Applying the method of ladder operators it is shown that the covariant representations with unique spin...

The relative geodesic motion in central charts (i.e. static and spherically symmetric) on the $(1+3)$-dimensional de Sitter spacetimes is studied in terms of conserved quantities. The Lorentzian isometries are derived, relating the coordinates of the local chart of a fixed observer with the coordinates of a mobile chart considered as the rest frame...

The relative geodesic motion on anti-de Sitter spacetimes is studied in terms of conserved quantities by adapting the Nachtmann boosting method created initially for the de Sitter spacetimes. In this approach the Lorentzian isometriy is derived, relating the coordinates of the local chart of a fixed observer with the coordinates of a mobile chart c...

Our recent results concerning the transformation under isometries of the conserved quantities on de Sitter manifolds, allow us to define the rest frame and study the relative geodesic motion in terms of conserved momentum, revealing thus various relativistic effects [I. I. Cotaescu, arXiv:1701.08499]. Here we discuss the time dilation (of the twin...

The geodesic motion on anti-de Sitter spacetimes is studied pointing out how the trajectories are determined by the ten independent conserved quantities associated to the specific $SO(2,3)$ isometries of these manifolds. The new result is that there are two conserved $SO(3)$ vectors which play the same role as the Runge-Lenz vector of the Kepler pr...

It is shown that the Nachtmann boosting method of introducing coordinates on de Siter manifolds can be completed with suitable gauge transformations able to keep under control the transformation under isometries of the conserved quantities. With this method the rest local charts (or natural frames) are defined pointing out the role of the conserved...

The asymptotic form of Dirac spinors in the field of the Reissner–Nordström black hole is derived for the scattering states (with \(E>mc^2\)) obtaining the phase shifts of the partial wave analysis of Dirac fermions scattered from charged black holes. Elastic scattering and absorption are studied giving analytic formulas for the partial amplitudes...

The exact solutions of the complete (1+3)-dimensional Dirac equation of fermions moving in ideal Aharonov-Bohm (AB) rings and cylinders are used for deriving the exact expressions of the relativistic partial currents. It is shown that these currents can be related to the derivative of the fermion energy with respect to the flux parameter, just as i...

We consider rigidly rotating states in thermal equilibrium on static spherically symmetric spacetimes. Using the Maxwell-Juttner equilibrium distribution function, onstructed as a solution of the relativistic Boltzmann equation, the equilibrium particle flow four-vector, stress-energy tensor and the transport coefficients in the Marle model are com...

The Nachtmann boosting method is completed with gauge transformations in order to be applied to the study of the relative geodesic motion on the de Sitter spacetimes, finding how the conserved quantities transform under isometries and defining the rest frames of massive mobiles.

Asymptotic analytic solutions of the Dirac equation, giving the scattering modes (of the continuous energy spectrum, E>mc2) in Schwarzschild's chart and Cartesian gauge, are used for building the partial wave analysis of Dirac fermions scattered by black holes. The contribution of the bound states to absorption and possible resonant scattering is n...

The properties of the covariant fields on the de Sitter spacetimes are investigated focusing on the isometry generators and Casimir operators in order to establish the equivalence among the covariant representations and the unitary irreducible ones of the de Sitter isometry group. For the Dirac field it is shown that the spinor covariant representa...

These pedagogical lecture notes address to the students in theoretical physics for helping them to understand the mechanisms of the linear operators defined on finite-dimensional vector spaces equipped with definite or indefinite inner products. The importance of the Dirac conjugation is pointed out presenting its general theory and a version of th...

The relativistic theory of the Dirac fermions moving on Aharonov-Bohm cylinders is built starting with a suitably restricted Dirac equation whose spin degrees of freedom are not affected. The exact solutions of this equation on finite or infinite cylinders in Aharonov-Bohm field allow one to derive the relativistic circular and transversal currents...

It is shown that on the de Sitter manifolds the tachyonic geodesics are restricted such that the classical tachyons cannot exist on this manifold at any time. On the contrary, the theory of the scalar quantum tachyons is free of any restriction.

It is shown that the covariant representation transforming the Dirac field under de Sitter isometries is equivalent to a direct sum of two unitary irreducible representations (UIRs) of the $Sp(2,2)$ group transforming the particle and antiparticle field operators in momentum representation. Their basis generators and Casimir operators are written d...

The exact solutions of the complete Dirac equation for fermions moving in Aharonov-Bohm rings are used for deriving the exact expressions of the relativistic partial currents. It is show that only in the non-relativistic limit these currents can be related to the derivative of the fermion energy with respect of the flux parameter. A specific relati...

Aspects of the ambiguity in defining quantum modes on de Sitter spacetime using a commuting system composed only of differential operators are discussed. Discrete symmetries and their actions on the wavefunction in commonly used coordinate charts are reviewed. It is argued that the system of commuting operators can be supplemented by requiring the...

Approximative analytic solutions of the Dirac equation in the Schwarzschild geometry are used for building the partial wave analysis of the Dirac fermions scattered by black holes. The analytic expressions of the differential cross section and induced polarization degree are derived in terms of scattering angle, mass of the black-hole, energy and m...

We revisit the principal arguments for interpreting the free quantum fields on anti-de Sitter or de Sitter spacetimes of any dimensions as oscillators or respectively anti-oscillators. In addition, we point out that there exists a chart on the de Sitter background where the free Dirac field becomes a genuine anti-oscillator in the non-relativistic...

We propose a definition of uniform accelerated frames in de Sitter spacetimes applying the Nachtmann method of introducing coordinates using suitable point-dependent isometries. In order to recover the well-known Rindler approach in the flat limit, we require the transformation between the static frame and the accelerated one to depend continuously...

We propose a definition of the accelerated frames in de Sitter spacetime which recovers the Rindler conjecture in the flat limit.

The action of the discrete symmetries on the scalar mode functions of the de Sitter spacetime is studied. The invariance with respect to a combination of discrete symmetries is put forward as a criterion to select a certain vacuum out of a family of vacua. The implications of the choices for eigenfunctions of various common sets of commuting operat...

How to kill the Unruh effect? Very simple, by requiring the Rindler transformation to behave continuously for vanishing acceleration. Then the Unruh effect disappears as we show in the case of the massive scalar quantum field. The main point is that the continuity condition restricts the integral of the mode expansion to the positive energy spectru...

The scalar mode functions on the spatially flat FLRW chart of the de Sitter spacetime are redefined in order to obtain a natural frequencies separation in the special local charts where the momentum vanishes, called here (natural) rest frames. This can be done since in such frames the mode functions are eigenfunctions of the energy operator. Moreov...

We outline the de Sitter QED in Coulomb gauge assuming that the vacuum is sta8 ble and invariant, independent on the local coordinates. Then we proceed in traditional manner postulating the appropriate equal-time commutators and anti-commutators of the interacting fields and deriving the perturbation expansion of the scattering operator. In this ap...

We show that the induced representations of the de Sitter isometry group proposed many years ago by Nachtmann are equivalent to those derived from our general theory of external symmetry. These methods complete each other leading to a coherent theory of covariant fields with spin on the de Sitter spacetime. Some technical details of these represent...

New quantum modes of the free scalar field are derived in a special time-evolution picture that may be introduced in moving charts of de Sitter backgrounds. The wave functions of these new modes are solutions of the Klein–Gordon equation and energy eigenfunctions, defining the energy basis. This completes the scalar quantum mechanics where the mome...

Recently a new time-evolution picture of the Dirac quantum mechanics was defined in charts with spatially flat Robertson–Walker metrics, under the name of Schrödinger picture (I. I. Cotăescu, Mod. Phys. Lett. A22, 2965 (2007)). In the present paper, new Dirac quantum modes are found in moving charts of the de Sitter space–time using the technical a...

The lowest order contribution of the amplitude of Dirac–Coulomb scattering in de Sitter space–time is calculated assuming that the initial and final states of the Dirac field are described by exact solutions of the free Dirac equation on de Sitter space–time with a given energy and helicity. We find that the total energy is conserved in the scatter...

A family of relativistic geometric models is defined as a generalization of the actual anti-de Sitter (1 + 1) model of the relativistic harmonic oscillator. It is shown that all these models lead to the usual harmonic oscillator in the nonrelativistic limit, even though their relativistic behavior is quite different. Among quantum models we find a...

The Shishkin's solutions of the Dirac equation in spherical moving frames of the de Sitter spacetime are investigated pointing out the set of commuting operators whose eigenvalues determine the integration constants. It is shown that these depend on the usual angular quantum numbers and, in addition, on the value of the scalar momentum. With these...

A family of geometric models of quantum relativistic rotating oscillator is defined by using a set of one-parameter deformations of the static (3+1) de Sitter or anti-de Sitter metrics. It is shown that all these models lead to the usual isotropic harmonic oscillator in the nonrelativistic limit, even though their relativistic behavior is different...

In this paper the small relativistic correction for the energy eigenvalues of the two- and three-dimensional anisotropic quantum harmonic oscillator are calculated, using as eigenstates , for different values of the relativistic parameters βi ≡ ħwi / m0c2 with i = 1, 2 and 3.

A Lagrangian theory giving rise to a version of the Dirac-Kahler equations on curved backgrounds is considered. The principal pieces are the general fields which have values in the algebra of the Dirac matrices and satisfy a Dirac-type equation. Their components are scalar, pseudo-scalar, vector, axial-vector fields and fields strength which satisf...

It is shown that the isometry group of the de Sitter spacetime includes two different three-dimensional Abelian subgroups which transform between themselves through a discrete isometry corresponding to the time reversal in the five-dimensional Minkowski spacetime embedding the de Sitter one. The eigenfunctions of the generators of these Abelian sub...

It is shown that on the de Sitter space-time the global behavior of the free Dirac spinors in momentum representation is determined by several phases factors which are functions of momentum with special properties. Such suitable phase functions can be chosen for writing down the free Dirac quantum modes of the spin basis that are well-defined even...

The quantum theory of the vector field minimally coupled to the gravity of the de Sitter spacetime is built in a canonical manner starting with a new complete set of quantum modes of given momentum and helicity derived in the moving chart of conformal time. It is shown that the canonical quantization leads to new vector propagators which satisfy si...

We construct the de Sitter QED in Coulomb gauge assuming that the quantum modes are prepared by a global apparatus which is able to determine a stable and invariant vacuum state, independent on the local coordinates. Then we proceed in traditional manner postulating the appropriate equal-time commutators and anti-commutators of the interacting fiel...

We study the Lie algebras of the covariant representations transforming the matter fields under the de Sitter isometries. We point out that the Casimir operators of these representations can be written in closed forms and we deduce how their eigenvalues depend on the field’s rest energy and spin. For the scalar, vector and Dirac fields, which have...

The quantum theory of the vector field minimally coupled to the gravity of the de Sitter spacetime is built in a canonical manner starting with a new complete set of quantum modes of given momentum and helicity derived in the moving chart of conformal time. It is shown that the canonical quantization leads to new vector propagators which satisfy si...