arXiv subjects

Cosmin Crucean

Publications and source records attributed to Cosmin Crucean.

At least 19 recordsLinked to original sources

arXiv2025

Early Universe production of $W$ bosons in neutrino decays

In this paper we study, via perturbative methods, the rates of production of $W$ bosons emitted in neutrino decays during the early stages of the Universe. We compute the transition amplitude corresponding to the first order of de Sitter electroweak perturbation theory and study its various limiting cases. The transition rates are derived using minimal subtraction and dimensional regularization. In the end we attempt to obtain the density number of $W$ bosons produced in perturbative transitions in de Sitter spacetime, using the rates obtained in this paper and in previous ones, and analyze the density number with respect to the particle momenta and renormalisation mass $\mu$.

hep-ph↗

arXiv2025

Dirac fermions under imaginary rotation

In the present study, we investigate the properties of an ensemble of free Dirac fermions, at finite inverse temperature $\beta$ and finite chemical potential $\mu$, undergoing rigid rotation with an imaginary angular velocity $\Omega=i\Omega_I$. Our purpose is to establish the analytical structure of such states, as well as the prospects (and dangers) of extrapolating results obtained under imaginary rotation to the case of real rotation. We show that in the thermodynamic limit, the state of the system is akin to a stationary system with modified inverse temperature $\beta_q = q\beta$ and the same chemical potential, where $q$ is the denominator of the irreducible fraction $\nu = \beta \Omega_I / 2\pi = p/q$. The temperature of the system becomes a fractal function of the rotation parameter, as in the case of the scalar field. The chemical potential breaks the fractalization of fermions. We also compute the thermodynamic potential $\Phi$ and associated thermodynamic functions, showing that they also exhibit fractal behavior. Finally, we evaluate the axial and helical fluxes through the transverse plane, generated through the vortical effects, and show that they diverge in the thermodynamic limit, in the case when $\nu = 1/q$ and $q \to \infty$.

hep-th↗

arXiv2025

Emission of $W$ bosons by electrons and decays of $W$ bosons in the early universe

In this paper we study the transition rates for the decay of $W^{\pm}$ bosons into leptons in de Sitter spacetime. From the results obtained in the de Sitter geometry we recover the Minkowski limits of the transition rates. We also study the emission of $W^{\pm}$ bosons by leptons, a process which is possible only in the large expansion conditions of the early universe. These results are obtainable due to perturbative methods which allow us to compute the transition amplitudes in the first order of perturbation theory. The resulting probabilities and rates depend on the particle masses and the Hubble parameter. In order to establish finite expressions for the probabilities and transition rates, we make use of dimensional regularization and the minimal substraction method.

hep-th↗

arXiv2022

Production of massive $W^{\pm}$ bosons and fermion-antifermion pairs from vacuum in the de Sitter Universe

In this paper we study the charged electro-weak interactions in the de Sitter geometry. We develop the reduction formalism for the Proca field with the help of the solutions for the interacting fields. Perturbation theory is used for obtaining the definition of the transition amplitudes in the first order. We apply our formalism to the study of spontaneous vacuum emission of fermions, anti-fermions and $W^{\pm}$ bosons in the expanding de Sitter universe. Our results are generalizations of the Weinberg-Salam electro-weak theory to curved space-time, in the case of $W^{\pm}$ boson interaction with leptons. The probability and transition amplitude are found to be a quantities which depend on the Hubble parameter. Our analytical and graphical results prove that such perturbative processes are possible only for the large expansion conditions of the early Universe. The total probability and rate of transition are obtained for the case of large expansion and we use dimensional regularization and Pauli-Villars regularization for the momenta integrals. In the end we recover the Minkowski limit, where our probabilities vanish, thus confirming the well known fact that spontaneous vacuum emission of $W^{\pm}$ bosons and fermions is forbidden in flat space-time due to energy-momentum conservation.

gr-qc↗

arXiv2022

A perturbative production of massive Z bosons and fermion-antifermion pairs from the vacuum in the de Sitter Universe

In this paper we study the problem of neutral electro-weak interactions in a de Sitter geometry. We develop the formalism of reduction for the Proca field with the help of the solutions for the interacting fields and by using perturbative methods we obtain the definition of the transition amplitudes in the first order of perturbation theory. As an application to our formalism we study the generation of massive fermions and Z bosons from vacuum in the expanding de Sitter universe. Our results are the generalization to the curved geometry of the Weinberg-Salam electro-weak theory for the case of Z boson interaction with leptons. The probability is found to be a quantity that depends on the Hubble parameter and we prove that such perturbative processes are possible only for large expansion regime of the early Universe. The total probability and rate of transition are obtained for the case of large expansion and we use the dimensional regularization for extract finite results from the momenta integrals. In the Minkowski limit we obtain that the probability of particle generation from vacuum is vanishing recovering the well known result that forbids particle production in flat space-time due to the momentum-energy conservation.

hep-th↗

arXiv2020

Z boson emission by a neutrino in de Sitter expanding universe

Production of Z bosons in emission processes by neutrinos in the expanding de Sitter universe is studied by using perturbative methods. The total probability and transition rate for the spontaneous emission of a Z boson by a neutrino is computed analytically, then we perform a graphical analysis in terms of the expansion parameter. Our results prove that this process is possible only for large expansion conditions of the early Universe. Finally the density number of Z bosons is defined and we obtain a quantitative estimation of this quantity in terms of the density number of neutrinos.

hep-th↗

arXiv2019

Total probability and number of particles for fermion production in external electric and magnetic fields in de Sitter universe

In this paper we present a method for computing the total probability corresponding to the processes of fermion pair production in dipole magnetic field and external Coulomb field in a de Sitter geometry. For that we rewrite the functions that define the amplitudes in terms of oscillatory functions and we use the Taylor expansion of these functions for arriving at the final form of the momenta integrals. The total probability is analysed in terms of the ratio between the mass of the fermion and expansion parameter and we recover the Minkowski limit when the expansion parameter is vanishing. Finally it is proven that from our results we can compute the number of fermions in terms of expansion parameter.

hep-th↗

arXiv2018

Production of Z bosons and neutrinos in early universe

Production of Z bosons and neutrinos is studied in the expanding de Sitter universe. The expression of the transition amplitudes in the case of Z boson interaction with leptons is established by using perturbative methods. Then the amplitude and probability for the spontaneous generation from vacuum of a Z boson a neutrino and an antineutrino are computed analytically and a graphical analysis is performed in terms of the expansion parameter. We found that the probability for this process is nonvanishing only for large expansion conditions of the early Universe. We discuss the Minkowski limit and obtain that in this limit the amplitude is zero, result which corresponds to the well established fact that spontaneous particle generation from vacuum in Minkowski space-time is forbidden by the simultaneous energy and momentum conservation in perturbative processes. The total probability of the process is computed and we prove that this quantity is important only for the regime of large expansion from early universe and is vanishing in the Minkowski limit.

hep-th↗

arXiv2017

Perturbative approach to the problem of particle production in electric field on de Sitter universe

In this letter we study the problem of scalar particle production in external electric field in de Sitter geometry. The total probability is calculated using the previously obtained result in Ref.\cite{6} for transition amplitude in external electric field on de Sitter space. Then we make a graphical study of the total probability in terms of the ratio mass of the particle/expansion factor. Our results show that the probability depend of the direction in which the particles are emitted and that the probability becomes maxim when particles are emitted on the direction of the electric field. In the Minkowski limit we obtain that the probability is vanishing.

gr-qc↗

arXiv2017

Reply to the "Comment on Fermion production in a magnetic field in a de Sitter Universe"

In this paper we study the problem of gauge invariance of the first order transition amplitudes in de Sitter QED in Coulomb gauge. We consider the gauge transformations which preserve the Coulomb gauge, that contain the gradient of the gauge function. The final results prove that the first order transition amplitudes do not change at a gradient transformation of the vector potential because the only allowed transformation is $Λ=0$. Our results suggest that the remarks made in the comment by Nicolaevici and Farkas {\em Phys. Rev. D} \textbf{95}, are not directly applicable to the results in our paper since their proposed gauge transformations do not preserve the Coulomb gauge.

gr-qc↗

arXiv2016

Fermion production in a magnetic field in a de Sitter Universe

The process of fermion production in the field of a magnetic dipole on a de Sitter expanding universe is analyzed. The amplitude and probability for production of massive fermions are obtained using the exact solution of the Dirac equation written in the momentum-helicity basis. We found that the most probable transitions are those that generate the fermion pair perpendicular to the direction of the magnetic field. The behavior of the probability is graphically studied for large/small values of the expansion factor, and a detailed analysis of the probability in terms of the angle between the momenta vectors of the particle and antiparticle is performed. The phenomenon of fermion production is significant only at large expansion which corresponds to the conditions from the early Universe. When the expansion factor vanishes we recover the Minkowski limit where this process is forbidden by the simultaneous energy-momentum conservation.

gr-qc↗

arXiv2016

Partial wave analysis of the Dirac fermions scattered from Reissner - Nordstr\" om charged black holes

The asymptotic form of Dirac spinors in the field of the Reissner-Nordstrom black hole are 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. The elastic scattering and absorption are studied giving analytic formulas for the partial amplitudes and cross sections. A graphical study is performed for analysing the differential cross section (forward/backward scattering) and the polarization degree as functions of scattering angle.

gr-qc↗

arXiv2015

Partial wave analysis of the Dirac fermions scattered from Schwarzschild black holes

Asymptotic analytic solutions of the Dirac equation, giving the scattering modes (of the continuous energy spectrum, $E>mc^2$) 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 neglected because of some technical difficulties related to the discrete spectrum that is less studied so far. In this framework, 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 mass of the fermion. Moreover, the closed form of the absorption cross section due to the scattering modes is derived showing that in the high-energy limit this tends to the event horizon area regardless of the fermion mass (including zero). A graphical study presents the differential cross section analyzing the forward/backward scattering (known also as glory scattering) and the polarization degree as functions of scattering angle. The graphical analysis shows the presence of oscillations in scattering intensity around forward/backward directions, phenomena known as spiral scattering. The energy dependence of the differential cross section is also established by using analytical and graphical methods.

gr-qc↗

arXiv2015

Interaction between Maxwell field and charged scalar field in de Sitter universe

We study the theory of interaction between charged scalar field and Maxwell field in de Sitter background. Solving the equation of interacting fields we define the in-out fields as asymptotic free fields and construct the reduction formalism for scalar field. Then we derive the perturbation expansion of the scattering operator. The first order transition amplitudes corresponding to particle production from de Sitter vacuum and pair production in an external field are analysed. We show that all these effects are important only in strong gravitational fields and vanish in the flat limit.

gr-qc↗

arXiv2013

Fermion production by a dependent of time electric field in de Sitter universe

Fermion production by the electric field of a charge on de Sitter expanding universe is analyzed. The amplitude and probability of pair production are computed. We obtain from our calculations that the modulus of the momentum is no longer conserved and that there are probabilities for production processes where the helicity is no longer conserved. The rate of pair production in an electric field is found to be important in the early universe when the expansion factor was large comparatively with the particle mass.

gr-qc↗

arXiv2012

The de Sitter QED in Coulomb gauge: first order transition amplitudes

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 fields and deriving the perturbation expansion of the scattering operator. In this approach the $in -out$ transitions amplitudes, measured by the same global apparatus, can be calculated exactly by using the reduction formalism and the perturbation procedure as in the flat case but with significant differences due to the de Sitter geometry. A specific feature is that the gravity eliminates the constraints due to the simultaneous momentum-energy conservation giving rise to QED transitions with non-vanishing amplitudes even in the first order of perturbations. Of a special interest could be the first order amplitudes of the electromagnetic particle creation allowed by the expansion of the de Sitter universe. We show that this effect is significant only in the very strong gravity of the early universe.

gr-qc↗

arXiv2010

The quantum theory of the free Maxwell field on the de Sitter expanding universe

The theory of the free Maxwell field in two moving frames on the de Sitter spacetime is investigated pointing out that the conserved momentum and energy operators do not commute to each other. This leads us to consider new plane waves solutions of the Maxwell equation which are eigenfunctions of the energy operator. Such particular solutions complete the theory in which only the solutions of given momentum were considered so far. The energy eigenfunctions can be obtained thanks to our new time-evolution picture proposed previously for the scalar and Dirac fields. Considering both these types of modes, it is shown that the second quantization of the free electromagnetic potential in the Coulomb gauge can be done in a canonical manner as in special relativity. The principal conserved one-particle operators associated to Killing vectors are derived, concentrating on the energy, momentum and total angular momentum operators.

gr-qc↗

arXiv2008

The quantum theory of scalar fields on the de Sitter expanding universe

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 momentum basis is well-known from long time. In this enlarged framework the quantization of the scalar field can be done in canonical way obtaining the principal conserved one-particle operators and the Green functions.

gr-qc↗