相关论文: Two disjoint aspects of the deformation programme:…

Starting from noncommutative generalization of Minkowski space we consider quantum deformed relativistic symmetries which lead to the modification of kinematics of special relativity. The noncommutative field theory framework described by…

A proper deformation of the underlying coordinate and momentum commutation relations in quantum mechanics provides a phenomenological approach to account for the influence of gravity on small scales. Introducing the squared momentum term…

The quantization scheme based on reduction of the physical states \cite{Park:2014tia} is extended to two gravity-matter systems and pure dS gravity. For the gravity-matter systems we focus on quantization in a flat background for…

We use Anti-de Sitter quantum field theory to prove a new class of identities between hypergeometric functions related to the K\"all\'en-Lehmann representation of products of two Anti-de Sitter two-point functions. A rich mathematical…

The paper concerns the fictitious entanglement of the so-called ``singularities'' in problems, pertaining to quantum gravity, due, in point of fact, to the way we try to employ, in that context, differential geometry, the latter being…

We provide and discuss complex analytic methods for overcoming the formal character of formal deformation quantization. This is a necessity for returning to physically meaningful statements, and accounts for the fact that the formal…

The purpose of this brief article is to clarify certain distortions of the history of ideas about the quantum theory of de Sitter space that have appeared in recent literature.

We derive a noncovariant but simple representation for the self-energy of a conformally transformed graviton field on the cosmological patch of de Sitter. Our representation involves four structure functions, as opposed to the two that…

The deformation star product of smooth functions on the momentum phase space of covariant (polysymplectic) Hamiltonian field theory is introduced.

We study some two-dimensional dilaton gravity models using the formal theory of partial differential equations. This allows us to prove that the reduced phase space is two-dimensional without an explicit construction. By using a convenient…

Linear quantum mechanics can be regarded as a particular example of a nonlinear Nambu-type theory. Some elements of this approach are presented.

Physical geometry studies mutual disposition of geometrical objects and points in space, or space-time, which is described by the distance function d, or by the world function \sigma =d^{2}/2. One suggests a new general method of the…

Recently, it has been proposed that the dimension of the Hilbert space of quantum gravity in deSitter space is finite and moreover it is expressed in terms of the coupling constants by using the entropy formula. A weaker conjecture would be…

There is a vast literature showing the connection between a deformed relativistic kinematics and a curved momentum space, and, in particular, how the former can be obtained from the geometrical properties of the latter. However, there is…

We give a pedagogical introduction to certain aspects of supersymmetric field theories in anti-de Sitter space. Among them are the presence of masslike terms in massless wave equations, irreducible unitary representations and the phenomenon…

We develop a complete theory of non-formal deformation quantization exhibiting a nonzero minimal uncertainty in position. An appropriate integral formula for the star-product is introduced together with a suitable space of functions on…

In this paper we establish a notion of deformation quantization of a surjective submersion which is specialized further to the case of a principal fibre bundle: the functions on the total space are deformed into a right module for the star…

It has been proposed that a quantum group structure underlies de Sitter/Conformal field theory duality. These ideas are used to give a microscopic operator counting interpretation for the entropy of two-dimensional dilaton de Sitter space.…

We show that the warped de Sitter compactifications are possible under certain conditions in D-dimensional gravitational theory coupled to a dilaton, a form field strength, and a cosmological constant. We find that the solutions of field…

After picking out what may seem more realistic minimal gravitational deformation of quantum mechanics, we study its back reaction on gravity. The large distance behaviour of Newtonian potential coincides with the result obtained by using of…