Related papers: Continuous spin field in the $\mathbf{AdS_6}$ spac…
Contemporary presentation of the version 1 demonstrates briefly the development of our investigations and our future goals. The improved free of difficulties in interpretation and printing errors version is presented. The 256-dimensional…
We consider a 5-dimensional Chern-Simons gauge theory for the isometry group of Anti-de-Sitter spacetime, $\operatorname{AdS}_{4+1}\simeq\operatorname{SO}(4,2)$, and invoke different dimensional reduction schemes in order to relate it to…
It is shown that a covariant derivative on any d-dimensional manifold M can be mapped to a set of d operators acting on the space of functions on the principal Spin(d)-bundle over M. In other words, any d-dimensional manifold can be…
By calculating the second-order pole in the operator product expansion (OPE) between the spin-3 Casimir operator and the spin-4 Casimir operator known previously, the spin-5 Casimir operator is obtained in the coset model based on…
We revisit the problem of consistent free propagation of higher-spin fields in nontrivial backgrounds, focusing on symmetric tensor(-spinor)s. The Fierz-Pauli equations for massive fields in flat space form an involutive system, whose…
The notion of the eigenvalue problem in the Fock space with polynomial eigenfunctions is introduced. This problem is classified by using the finite-dimensional representations of the $\mathfrak{sl}(2)$-algebra in Fock space. In the complex…
We study maximal representations of nonnegative sesquilinear forms in real or complex Hilbert spaces, that are not necessarily closed or even closable. We associate positive self-adjoint operators with such forms, in a sense similar to…
AdS space is the universal covering of a hyperboloid. We consider the action of the deck transformations on a classical string worldsheet in $AdS_5\times S^5$. We argue that these transformations are generated by an infinite linear…
We present a covariant quantization of the free "massive" spin-3/2 fields in four-dimensional de Sitter space-time based on analyticity in the complexified pseudo-Riemannian manifold. The field equation is obtained as an eigenvalue equation…
Taking into account the Schuster-Toro action and its fermionic analogue discovered by us, we supersymmetrize unconstrained formulation of the continuous spin gauge field theory. Afterwards, building on the Metsaev actions, we…
The unconstrained frame-like formulation of an infinite tower of completely symmetric tensor gauge fields is reviewed and examined in the limit where the cosmological constant goes to zero. By partially fixing the gauge and solving the…
The Estabrook-Wahlquist prolongation method is applied to the (compact and noncompact) continuous isotropic Heisenberg model in 1 + 1 dimensions. Using a special realization (an algebra of the Kac-Moody type) of the arising incomplete…
It is shown that the deformed Heisenberg algebra involving the reflection operator R (R-deformed Heisenberg algebra) has finite-dimensional representations which are equivalent to representations of paragrassmann algebra with a special…
The exterior algebra of Minkowski space naturally has the structure of a sixteen-dimensional Clifford algebra representation, and so can be used as the space of spinors. We examine plane, circular, and spherical solutions to the free Dirac…
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 ${\cal…
We construct massless infinite spin irreducible representations of the six-dimensional Poincar\'{e} group in the space of fields depending on twistor variables. It is shown that the massless infinite spin representation is realized on the…
We propose to describe higher spins as invariant subspaces of the Casimir operators of the Poincar\'{e} Group, P^{2}, and the squared Pauli-Lubanski operator, W^{2}, in a properly chosen representation, \psi(p) (in momentum space), of the…
We construct a candidate for the most general chiral higher spin theory with AdS$_3$ boundary conditions. In the Chern-Simons language, on the left it has the Drinfeld-Sokolov reduced form, but on the right all charges and chemical…
We formulate the equations of motion of a free scalar field in the flat and $AdS$ space of an arbitrary dimension in the form of some "higher spin" covariant constancy conditions. Klein-Gordon equation is interpreted as a non-trivial…
The AdS_5 superalgebra PSU(2,2|4) has an infinite dimensional extension, which we denote by hs(2,2|4). We show that the gauging of hs(2,2|4) gives rise to a spectrum of physical massless fields which coincides with the symmetric tensor…