The mode solutions of the Dirac equation on $N$-dimensional de Sitter space-time ($dS_{N}$) with $(N-1)$-sphere spatial sections are obtained by analytically continuing the spinor eigenfunctions of the Dirac operator on the $N$-sphere ($S^{N}$). The analogs of flat space-time positive frequency modes are identified and a vacuum is defined. The transformation properties of the mode solutions under the de Sitter group double cover (Spin($N$,1)) are studied. We reproduce the expression for the massless spinor Wightman two-point function in closed form using the mode-sum method. By using this closed-form expression and taking advantage of the maximal symmetry of $dS_{N}$ we find an analytic expression for the spinor parallel propagator. The latter is used to construct the massive Wightman two-point function in closed form.
We construct the Wightman function for symmetric traceless tensors and Dirac fermions in dS$_{d+1}$ in a coordinate and index free formalism using a $d+2$ dimensional ambient space. We expand the embedding space formalism to cover spinor and tensor fields in any even or odd dimension. Our goal is to furnish a self-contained toolkit for the study of fields of arbitrary spin in de Sitter, with applications to cosmological perturbation theory. The construction for spinors is shown in extensive detail. Concise expressions for the action of isometry generators on generic bulk fields, the 2-point fu…
We consider massless fields of arbitrary spin in de Sitter space. We introduce a spinor-helicity formalism, which encodes the field data on a cosmological horizon. These variables reduce the free S-matrix in an observer's causal patch, i.e. the evolution of free fields from one horizon to another, to a simple Fourier transform. We show how this result arises via twistor theory, by decomposing the horizon<->horizon problem into a pair of (more symmetric) horizon<->twistor problems.
Discrete symmetries, parity, time reversal, antipodal, and charge conjugation transformations for spinor field in de Sitter space, are presented in the ambient space notation, i.e. in a coordinate independent way. The PT and PCT transformations are also discussed in this notation. The five-current density is studied and their transformation under the discrete symmetries is discussed.
Cosmology of ELKO and Lorentz Invariant NSS has been investigated using dynamical system method starting from the proposal of Boehmer et al [arXiv:1003.3858]. Some different results have been obtained by a different approach. The exact solutions described by fixed points of the dynamical system and their stability have been discussed. Some stable solutions corresponding to de Sitter universes have been obtained.
$CPT$ groups for spinor fields in de Sitter and anti-de Sitter spaces are defined in the framework of automorphism groups of Clifford algebras. It is shown that de Sitter spaces with mutually opposite signatures correspond to Clifford algebras with different algebraic structure that induces an essential difference of $CPT$ groups associated with these spaces. $CPT$ groups for charged particles are considered with respect to phase factors on the various spinor spaces related with real subalgebras of the simple Clifford algebra over the complex field (Dirac algebra). It is shown that $CPT$ group…
Recalling the universal covering group of de Sitter, the transformation properties of the spinor fields $ψ(x)$ and ${\barψ}(x)$, in the ambient space notation, are presented in this paper. The charge conjugation symmetry of the de Sitter spinor field is then discussed in the above notation. Using this spinor field and charge conjugation, de Sitter supersymmetry algebra in the ambient space notation has been established. It is shown that a novel dS-superalgebra can be attained by the use of spinor field and charge conjugation in the ambient space notation.
Since horizon formation in global anti-de Sitter spacetime is dual to thermalization of a conformal field theory on a compact space, whether generic initial data is stable or unstable against gravitational collapse is of great interest. We argue that all the known stable initial data for massless scalars are dominated by single scalar eigenmodes, specifically providing strong numerical evidence consistent with the interpretation that initial data with equal energies in two modes collapse on time scales of order the inverse square of the amplitude. We further scan the parameter space for massiv…
The scalar-spinor interaction Lagrangian is presented by the Yukawa potential. In dS ambient space formalism, the interaction Lagrangian of scalar-spinor fields was obtained from a new transformation which is very similar to the guage theory. The interaction of massless minimally coupled scalar and spinor fields was investigated. The Minkowski limit of the massless minimally coupled scalar field and massive spinor field interaction in the ambient space formalism of de Sitter space time is calculated. The interaction Lagrangian and massless minimally coupled scalar field in the null curvature l…
The interaction of massless minimally coupled scalar field and spinor field $ \left( Ψ+ Φ_m \rightarrow Ψ+ Φ_m \right) $ is investigated and the behavior of interaction and scattering matrix in Minkowski limit is studied. It is seen that the massless minimally coupled scalar field operator, the interaction Lagrangian and the scattering matrix become zero. Also the incoming and outgoing spinor fields, which in de Sitter space-time are different and are interacted with massless minimally coupled scalar field, in null curvature limit are the same and no interaction seen. In other word, the massle…
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 $B^α$, …
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 for the particles at rest in the moving local charts where the modes of the helicity basis remain undefined. Under quantization these modes lead to a basis in which the one-particle operators keep their usual forms apart from the energy operator whic…
We considered a new renormalization condition for the vacuum expectation values of the scalar and spinor currents induced by a homogeneous and constant electric field background in de Sitter spacetime. Following a semiclassical argument, the condition named maximal subtraction imposes the exponential suppression on the massive charged particle limit of the renormalized currents. The maximal subtraction changes the behaviors of the induced currents previously obtained by the conventional minimal subtraction scheme. The maximal subtraction is favored for a couple of physically decent predictions…
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 vac…
We investigate the possibility that, in a combined theory of quantum mechanics and gravity, de Sitter space is described by finitely many states. The notion of observer complementarity, which states that each observer has complete but complementary information, implies that, for a single observer, the complete Hilbert space describes one side of the horizon. Observer complementarity is implemented by identifying antipodal states with outgoing states. The de Sitter group acts on S-matrix elements. Despite the fact that the de Sitter group has no nontrivial finite-dimensional unitary representat…
In this paper a quantum N = 4 super Yang-Mills theory perturbed by dilaton-coupled scalars and spinor fields is considered. The induced effective action for such a theory is calculated on a dilaton-gravitational background using the conformal anomaly found via the AdS/CFT correspondence. Considering such an effective action (using the large N method) as a quantum correction to the classical gravity action with cosmological constant, we study the effect from the dilaton on the scale factor (this corresponds to an inflationary universe without dilaton). It is shown that, depending on the initial…
In this work, we study quantum fluctuations in the stress energy tensor of spinor fields evolving in general FRW spacetimes. We quantify these fluctuations by the noise kernel of spinor fields. For the particular case of de Sitter spacetime, we place the spinor field in what is called the fermionic Bunch Davies vacuum and study the variation of the noise kernel with the mass of the field. We then make use of the conformal invariance of massless spinor fields and employ an equivalence that relates a massless spinor field in any given FRW spacetime with a corresponding massless spinor field in d…
Quantization of spinor and vector free fields in 4-dimensional de Sitter space-time, in the ambient space notation, has been studied in the previous works. Various two-points functions for the above fields are presented in this paper. The interaction between the spinor field and the vector field is then studied by the abelian gauge theory. The U(1) gauge invariant spinor field equation is obtained in a coordinate independent way notation and their corresponding conserved currents are computed. The solution of the field equation is obtained by use of the perturbation method in terms of the Gree…
We propose an unified theory for spinor fields on extended Weyl manifolds taking into account self-interactions to obtain the Relativistic dynamics on a general curved Riemannian background as continuation of the Relativistic Quantum Geometry program, recently introduced. We focuss our attention separately on both, massless and matter fields. We study an example of confined gravitons on a de Sitter (dS) background at Planckian scales.
We explore the possibility that the expansion of the universe can be driven by a condensate of spinors which are free of interactions on a 5D relativistic vacuum defined on an extended de Sitter spacetime which is Riemann-flat. The extra coordinate is considered as noncompact. After making a static foliation on the extra coordinate, we obtain an effective 4D (inflationary) de Sitter expansion which describes an inflationary universe. We found that the condensate of spinors here studied could be an interesting candidate to explain the presence of dark energy in the early universe. The dark ener…
We study the decay of charged scalar and spinor fields around Reissner-Nordstrom black holes in de Sitter spacetime through calculations of quasinormal frequencies of the fields. The influence of the parameters of the black hole (charge, mass), of the decaying fields (charge, spin), and of the spacetime (cosmological constant) on the decay is analyzed. The analytic formula for calculation quasinormal frequencies for a large multipole number (eikonal approximation) is derived both for the spinor and scalar fieldss.
What is the physical origin of dark energy? Could this energy be originated by other fields than the inflaton? In this work we explore the possibility that the expansion of the universe can be driven by a condensate of spinors. These spinors are free of interactions on 5D relativistic vacuum in an extended de Sitter spacetime. The extra coordinate is considered as noncompact. After making a static foliation on the extra coordinate, we obtain an effective 4D (inflationary) de Sitter expansion which describes an inflationary universe. In view of our results we conclude that the condensate of spi…
Anti-de Sitter space with identified points give rise to black-hole structures. This was first pointed out in three dimensions, and generalized to higher dimensions by Aminneborg et al. In this paper, we analyse several aspects of the five dimensional anti-de Sitter black hole including, its relation to thermal anti-de Sitter space, its embedding in a Chern-Simons supergravity theory, its global charges and holonomies, and the existence of Killing spinors.
We obtain the exact solutions to the field equations for massless scalar and massless spinor fields on quantized two-dimensional anti-de Sitter space. We then apply the AdS/CFT correspondence principle to get exact answers for the two point correlation functions of the associated operators on the boundary. The results support the conclusion that conformal symmetry on the boundary is not spoiled by quantization of the bulk. Moreover, quantization of the bulk has no effect on the spinor two-point correlation function, while it induces an overall re-scaling in the scalar two-point correlation fun…
Utilizing the conformal-flatness nature of 3-dim. Anti-de Sitter (AdS_3) black hole solution of Banados, Teitelboim and Zanelli, the quantisation of conformally-coupled scalar and spinor fields in this background spacetime is explicitly carried out. In particular, mode expansion forms and propagators of the fields are obtained in closed forms. The vacuum in this conformally-coupled field theories in AdS_3 black hole spacetime, which is conformally-flat, is the conformal vacuum which is unique and has global meaning. This point particularly suggests that now the particle production by AdS_3 bla…
The massless minimally coupled scalar field in de Sitter ambient space formalism might play a similar role to what the Higgs scalar field accomplishes within the electroweak standard model. With the introduction of a "local transformation" for this field, the interaction Lagrangian between the scalar field and the spinor field can be made similar to a gauge theory. In the null curvature limit, the Yukawa potential can be constructed from that Lagrangian. Finally the one-loop correction of the scalar-spinor interaction is presented, which is free of any infrared divergence.
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. New expressions of scalar mode functions or Dirac spinors reaching natural flat limits are given in the rest frame vacuum and suitable approximate formulas are proposed. In this manner the flat limit is correctly defined for the entire quantum theory since the one-part…
The thick brane model supported by a nonlinear spinor field is constructed. The different cases with the various values of the cosmological constant $Λ(< = >) 0$ are investigated. It is shown that regular analytical spinor thick brane solutions with asymptotically Minkowski (at $Λ=0$) or anti-de Sitter spacetimes (at $Λ<0$) do exist.
Using an exact expression for the bi-spinor of parallel transport, we construct the Feynman propagator for Dirac fermions in the vacuum state on anti-de Sitter space-time. We compute the vacuum expectation value of the stress-energy tensor by removing coincidence-limit divergences using the Hadamard method. We then use the vacuum Feynman propagator to compute thermal expectation values at finite temperature. We end with a discussion of rigidly rotating thermal states.
We show that the Dirac equation on de Sitter background can be analytically solved in a special static frame where the energy eigenspinors can be expressed in terms of usual angular spinors known from special relativity, and a pair of radial wave functions.
The tetrad gauge invariant theory of the free Dirac field in two special moving charts of the de Sitter spacetime is investigated pointing out the operators that commute with the Dirac one. These are the generators of the symmetry transformations corresponding to isometries that give rise to conserved quantities according to the Noether theorem. With their help the plane wave spinor solutions of the Dirac equation with given momentum and helicity are derived and the final form of the quantum Dirac field is established. It is shown that the canonical quantization leads to a correct physical int…
We study the space of Killing fields on the four dimensional AdS spacetime $AdS^{3,1}$. Two subsets $\mathcal{S}$ and $\mathcal{O}$ are identified: $\mathcal{S}$ (the spinor Killing fields) is constructed from imaginary Killing spinors, and $\mathcal{O}$ (the observer Killing fields) consists of all hypersurface orthogonal, future timelike unit Killing fields. When the cosmology constant vanishes, or in the Minkowski spacetime case, these two subsets have the same convex hull in the space of Killing fields. In presence of the cosmology constant, the convex hull of $ \mathcal{O}$ is properly co…
We study massive spinor fields in the geometry of a straight cosmic string in a de Sitter background. We find a hidden N=2 supersymmetry in the fermionic solutions of the equations of motion. We connect the zero mode solutions to the heat-kernel regularized Witten index of the supersymmetric algebra.
Based on some recent work of the authors, we focus on the relationship between the Casimir energy of a Majorana spinor field for a Euclidean Einstein universe $S^4\times R$ and for a Euclidean de Sitter brane ($S^4$) embedded in AdS(5). This is for a conformally coupled massless field. Interestingly, the one brane effective potential is zero and the results are equivalent, as for the scalar case, when evaluated on the conformally related cylinder. However, using the actual metric this equivalence no longer holds because a non-trivial contribution from the path integral measure (known as the co…
In the No-Boundary Universe a primordial black hole is created from a constrained gravitational instanton. The black hole created is immersed in the de Sitter background with a positive cosmological constant. The constrained instanton is characterized not only by the external parameters, the mass parameter, charge and angular momentum, but also by one more internal parameter, the identification period in the imaginary time coordinate. Although the period has no effect on the black hole background, its inverse is the temperature of the no-boundary state of the perturbation modes perceived by an…
We provide a general technique for collectively analysing a manifestly covariant formulation of non-abelian gauge theories on both anti de Sitter as well as de Sitter spaces. This is done by stereographically projecting the corresponding theories, defined on a flat Minkowski space, onto the surface of the A(dS) hyperboloid. The gauge and matter fields in the two descriptions are mapped by conformal Killing vectors and conformal Killing spinors, respectively. A bilinear map connecting the spinors with the vector is established. Different forms of gauge fixing conditions and their equivalence ar…
The finite entropy of de Sitter space suggests that in a theory of quantum gravity there are only finitely many states. It has been argued that in this case there is no action of the de Sitter group consistent with unitarity. In this note we propose a way out of this if we give up the requirement of having a hermitian Hamiltonian. We argue that some of the generators of the de Sitter group act in a novel way, namely by mixing in- and out-states. In this way it is possible to have a unitary S-matrix that is finite-dimensional and, moreover, de Sitter-invariant. Using Dirac spinors, we construct…
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.
We investigate some issues regarding quantum corrections for de Sitter branes in a bulk AdS(5) spacetime. The one-loop effective action for a Majorana spinor field is evaluated and compared with the scalar field result. We also evaluate the cocycle function for various boundary conditions, finding that the quantum corrections naturally induce higher order curvature terms in the original action and, in general, it is not possible to eliminate the cocycle function by renormalisation. In the one brane limit care must be taken on how one extracts physical results. The effective potential is found …
We calculate the one-loop effective action for conformal matter (scalars, spinors and vectors) on spherically symmetric background. Such effective action (in large $N$ approximation and expansion on curvature) is used to study quantum aspects of Schwarzschild-de Sitter black holes (SdS BHs) in nearly degenerated limit (Nariai BH). We show that for all types of above matter SdS BHs may evaporate or anti-evaporate in accordance with recent observation by Bousso and Hawking for minimal scalars. Some remarks about energy flow for SdS BHs in regime of evaporation or anti-evaporation are also done. …
We present in this paper a covariant quantization of the ``massive'' vector field on de Sitter (dS) space based on analyticity in the complexified pseudo-Riemanian manifold. The correspondence between unitary irreducible representations of the de Sitter group and the field theory on de Sitter space-time is essential in our approach. We introduce the Wightman-Gärding axiomatic for vector field on dS space. The Hilbert space structure and the unsmeared field operators $K_α(x)$ are also defined. This work is in the direct continuation of previous one concerning the scalar and the spinor cases.
Relativistic spin-1/2 particles in curved spacetime are naturally described by Dirac theory, which is a dynamical and Lorentz-invariant field theory. In this work, we propose a non-dynamical fermion theory in 3+1 dimensions dubbed spinor topological field theory, built in terms of a spinor field and a Cartan connection related to de Sitter group. We show that our model gives rise to the Dirac theory in curved spacetime when the local de Sitter gauge invariance of the model breaks down to the Lorentz gauge invariance, providing also a geometric origin to the fermion mass. Finally, we show that …
A covariant quantization of the free spinor fields (s=1/2) in 4-dimensional de Sitter (dS) space-time based on analyticity in the complexified pseudo-Riemanian manifold is presented. We define the Wigthman two-point function ${\cal W}(x,y)$, which satisfies the conditions of: a) positivity, b) locality, c) covariance, and d) normal analyticity. Then the Hilbert space structure and the field operators $ψ(f)$ are defined. A coordinate-independent formula for the unsmeared field operator $ψ(x)$ is also given.
We introduce and carefully define an entire class of field theories based on non-standard spinors. Their dominant interaction is via the gravitational field which makes them naturally dark; we refer to them as Dark Spinors. We provide a critical analysis of previous proposals for dark spinors noting that they violate Lorentz invariance. As a working assumption we restrict our analysis to non-standard spinors which preserve Lorentz invariance, whilst being non-local and explicitly construct such a theory. We construct the complete energy-momentum tensor and derive its components explicitly by a…
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 …
It is shown that, for spherically symmetric static backgrounds, a simple reduced Dirac equation can be obtained by using the Cartesian tetrad gauge in Cartesian holonomic coordinates. This equation is manifestly covariant under rotations so that the spherical coordinates can be separated in terms of angular spinors like in special relativity, obtaining a pair of radial equations and a specific form of the radial scalar product. As an example, we analytically solve the anti-de Sitter oscillator giving the formula of the energy levels and the form of the corresponding eigenspinors.
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-$2$ an…
The properties of the covariant quantum fields on 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 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 $Sp(2,2)$ group, transforming alike the particle and antiparticle field operators in momentum…
Starting from a Dirac equation for massless neutrino in a 5D Ricci-flat background metric, we obtain the effective 4D equation for massive neutrino in a Schwarzschild-de Sitter (SdS) background metric from an extended SdS 5D Ricci-flat metric. We use the fact that the spin connection is defined to an accuracy of a vector, so that the covariant derivative of the spinor field is strongly dependent of the background geometry. We show that the mass of the neutrino can be induced from the extra space-like dimension.
Vacuum expectation values (VEVs) of the current densities for charged scalar and Dirac spinor fields are investigated in (D+1)-dimensional de Sitter (dS) spacetime with toroidally compactified spatial dimensions. Along compact dimensions we impose quasiperiodicity conditions with arbitrary phases. In addition, the presence of a classical constant gauge field is assumed. The VEVs of the charge density and of the components for the current density along noncompact dimensions vanish. The gauge field leads to Aharonov-Bohm-like oscillations of the components along compact dimensions as functions o…
Recently, in the context of dS/CFT correspondence, quasinormal modes have been put forward to address certain features of this conjecture. In particular, it is argued that the dual states of quasi-normal modes are in fact the states of CFT$_3$ which are created by operator insertions. For a scalar field in $dS_4$, quasi-normal modes which are singular on the past horizon of the south pole and decay exponentially towards the future have been considered in \cite{Ng:2012xp, Jafferis:2013qia}, these modes lie in two complex highest-weight representation of the dS$_4$ isometry group. In this work, …
Starting with a new theory of symmetries generated by isometries in field theories with spin, one finds the generators of the spinor representation in backgrounds with a given symmetry. In this manner one obtains a collection of conserved operators from which one can chose the complete sets of commuting operators defining quantum modes. In this framework, the quantum modes of the free Dirac field on de Sitter or anti-de Sitter spacetimes can be completely derived in static or moving charts. One presents the discrete quantum modes, in the central static charts of the anti-de Sitter spacetime, w…
We establish a type of positive energy theorem for asymptotically anti-de Sitter Einstein-Maxwell initial data sets by using Witten's spinoral techniques.
The Casimir densities are investigated for a massive spinor field in de Sitter spacetime with an arbitrary number of toroidally compactified spatial dimensions. The vacuum expectation value of the energy-momentum tensor is presented in the form of the sum of corresponding quantity in the uncompactified de Sitter spacetime and the part induced by the non-trivial topology. The latter is finite and the renormalization is needed for the first part only. The asymptotic behavior of the topological term is investigated in the early and late stages of the cosmological expansion. When the comoving leng…
The fermionic projector state is a distinguished quasi-free state for the algebra of Dirac fields in a globally hyperbolic spacetime. We construct and analyze it in the four-dimensional de Sitter spacetime, both in the closed and in the flat slicing. In the latter case we show that the mass oscillation properties do not hold due to boundary effects. This is taken into account in a so-called mass decomposition. The involved fermionic signature operator defines a fermionic projector state. In the case of a closed slicing, we construct the fermionic signature operator and show that the ensuing st…
