scholarly journals Canonical quantization of the covariant fields on de Sitter space–times

2018 ◽  
Vol 33 (08) ◽  
pp. 1830007 ◽  
Author(s):  
Ion I. Cotaescu
Keyword(s):  
Isometry Group ◽  
Canonical Quantization ◽  
Principal Series ◽  
De Sitter Space ◽  
Fermion Mass ◽  
Dirac Field ◽  
De Sitter ◽  
Covariant Quantum ◽  
Covariant Representations ◽  
Casimir Operators

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 covariant representation, transforming the Dirac field under de Sitter isometries, is equivalent with a direct sum of two unitary irreducible representations of the [Formula: see text] group, transforming alike the particle and antiparticle field operators in momentum representation. Their basis generators and Casimir operators are written down finding that the covariant representations are equivalent with unitary irreducible ones from the principal series whose canonical weights are determined by the fermion mass and spin.

scholarly journals Isometry generators in momentum representation of the Dirac theory on the de Sitter spacetime

2015 ◽  
Vol 30 (38) ◽  
pp. 1550208 ◽  
Author(s):  
Ion I. Cotăescu ◽  
Doru-Marcel Băltăţeanu
Keyword(s):  
Principal Series ◽  
Fermion Mass ◽  
Dirac Field ◽  
Momentum Representation ◽  
De Sitter ◽  
Covariant Representation ◽  
Dirac Theory ◽  
Sitter Spacetime ◽  
Casimir Operators ◽  
First Time

In this paper, it is shown that the covariant representation (CR) 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 alike the particle and antiparticle field operators in momentum representation. Their basis generators and Casimir operators are written down for the first time finding that these representations are equivalent to an UIR from the principal series whose canonical labels are determined by the fermion mass and spin. The properties of the conserved observables (i.e. one-particle operators) associated to the de Sitter isometries via Noether theorem and of the corresponding Pauli–Lubanski type operator are also pointed out.

scholarly journals An invitation to the principal series

2020 ◽  
Vol 9 (3) ◽  
Author(s):  
Tarek Anous ◽  
Jim Skulte
Keyword(s):  
Isometry Group ◽  
Hamiltonian Formulation ◽  
Series Representation ◽  
Principal Series ◽  
Scalar Fields ◽  
De Sitter Space ◽  
Late Time ◽  
De Sitter ◽  
Principal Series Representation ◽  
Massive Scalar Field

Scalar unitary representations of the isometry group of dd-dimensional de Sitter space SO(1,d)SO(1,d) are labeled by their conformal weights \DeltaΔ. A salient feature of de Sitter space is that scalar fields with sufficiently large mass compared to the de Sitter scale 1/\ell1/ℓ have complex conformal weights, and physical modes of these fields fall into the unitary continuous principal series representation of SO(1,d)SO(1,d). Our goal is to study these representations in d=2d=2, where the relevant group is SL(2,\mathbb{R})SL(2,ℝ). We show that the generators of the isometry group of dS_22 acting on a massive scalar field reproduce the quantum mechanical model introduced by de Alfaro, Fubini and Furlan (DFF) in the early/late time limit. Motivated by the ambient dS_22 construction, we review in detail how the DFF model must be altered in order to accommodate the principal series representation. We point out a difficulty in writing down a classical Lagrangian for this model, whereas the canonical Hamiltonian formulation avoids any problem. We speculate on the meaning of the various de Sitter invariant vacua from the point of view of this toy model and discuss some potential generalizations.

scholarly journals COVARIANT REPRESENTATIONS OF THE DE SITTER ISOMETRY GROUP

2013 ◽  
Vol 28 (09) ◽  
pp. 1350033 ◽  
Author(s):  
ION I. COTĂESCU
Keyword(s):  
General Theory ◽  
Isometry Group ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Induced Representations ◽  
Covariant Representations ◽  
Sitter Spacetime ◽  
Technical Details ◽  
First Time

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 representations are presented here for the first time.

scholarly journals Fermion mass generation in de Sitter space

2006 ◽  
Vol 73 (6) ◽  
Author(s):  
Björn Garbrecht ◽  
Tomislav Prokopec
Keyword(s):  
De Sitter Space ◽  
Fermion Mass ◽  
De Sitter ◽  
Mass Generation

scholarly journals Covariant fields on anti-de Sitter spacetimes

2018 ◽  
Vol 33 (04) ◽  
pp. 1850026 ◽  
Author(s):  
Ion I. Cotăescu
Keyword(s):  
Universal Covering ◽  
Positive Energy ◽  
De Sitter ◽  
Ladder Operators ◽  
Covariant Representations ◽  
Covering Group ◽  
Ads Spacetime ◽  
Casimir Operators ◽  
Free Fields ◽  
Covariant Field

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 discrete unitary irreducible representations (UIRs) of positive energy of the universal covering group of the isometry one. The action of the Casimir operators is studied finding how the weights of these representations (reps.) may depend on the mass and spin of the covariant field. The conclusion is that on AdS spacetime, one cannot formulate a universal mass condition as in special relativity.

scholarly journals DIRAC–COULOMB SCATTERING WITH PLANE WAVE ENERGY EIGENSPINORS ON DE SITTER EXPANDING UNIVERSE

2008 ◽  
Vol 23 (09) ◽  
pp. 1351-1359 ◽  
Author(s):  
ION I. COTĂESCU ◽  
COSMIN CRUCEAN
Keyword(s):  
Dirac Equation ◽  
Plane Wave ◽  
Wave Energy ◽  
De Sitter Space ◽  
Space Time ◽  
Dirac Field ◽  
Coulomb Scattering ◽  
Final States ◽  
De Sitter ◽  
Scattering Process

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 scattering process.

HELICITY CONSERVATION IN COULOMB SCATTERING OF THE DIRAC FIELD IN THE EXPANDING DE SITTER SPACE

2011 ◽  
Vol 26 (24) ◽  
pp. 4217-4238 ◽  
Author(s):  
NISTOR NICOLAEVICI
Keyword(s):  
Scattering Amplitude ◽  
Scattering Problem ◽  
Classical Case ◽  
De Sitter Space ◽  
Complete Agreement ◽  
Dirac Field ◽  
Polarization Angle ◽  
De Sitter ◽  
Helicity Conservation ◽  
Telegdi Equation

We comment on a previous calculation1 for the scattering amplitude for the Dirac field in an external Coulomb potential in the expanding de Sitter space. The result implies that for initial and final fermion states with identical momenta |pi|=|pf| the helicity of the particle is conserved. We make a classical analysis of the scattering problem in the small scattering angle approximation using the Bargmann–Michel–Telegdi equation and show that helicity conservation also manifests in the classical case. We also show that in Minkowski space there is a complete agreement between the classical and quantum polarization angle of the scattered particle.

scholarly journals Quasinormal modes and greybody factors of the novel four dimensional Gauss–Bonnet black holes in asymptotically de Sitter space time: scalar, electromagnetic and Dirac perturbations

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
Saraswati Devi ◽  
Rittick Roy ◽  
Sayan Chakrabarti
Keyword(s):  
Black Holes ◽  
Cosmological Constant ◽  
Quasinormal Modes ◽  
De Sitter Space ◽  
Dirac Field ◽  
The Novel ◽  
De Sitter ◽  
Third Order ◽  
The Third ◽  
Different Types

Abstract We find the low lying quasinormal mode frequencies of the recently proposed novel four dimensional Gauss–Bonnet de Sitter black holes for scalar, electromagnetic and Dirac field perturbations using the third order WKB approximation as well as Padé approximation, as an improvement over WKB. We figure out the effect of the Gauss–Bonnet coupling $$\alpha $$α and the cosmological constant $$\Lambda $$Λ on the real and imaginary parts of the QNM frequencies. We also study the greybody factors and eikonal limits in the above background for all three different types of perturbations.

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