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For conformal boundary operators associated with the Paneitz operator, we introduce a rigorous definition of the biharmonic Poisson kernel consisting of a pair of kernel functions and derive its explicit representation formula. With this…
It is shown that flat spacetime can be dressed with a real scalar field that satisfies the nonlinear Klein-Gordon equation without curving spacetime. Surprisingly, this possibility arises from the nonminimal coupling of the scalar field…
We investigate here various kinds of semi-product subgroups of Poincar\'e group in the scheme of Cohen-Glashow's very special relativity along the deformation approach by Gibbons- Gomis-Pope. For each proper Poincar\'e subgroup which is a…
Grassmann variables are used to formally transform a system with constraints into an unconstrained system. As a result, the Schr\"{o}dinger equation arises instead of the Wheeler-DeWitt one. The Schr\"{o}dinger equation describes a system's…
The product space configuration $AdS_2\times S_2$ (with $l$ and $r$ being radiuses of the components) carrying the electric charge $Q$ is demonstrated to be an exact solution of the semiclassical Einstein equations in presence of the…
We derived the second-order perturbations of the Einstein equations and the Klein-Gordon equation for a generic situation in terms of gauge-invariant variables. The consistency of all the equations is confirmed. This confirmation implies…
We introduce the spinor representations for osp(m|2n). These generalize the spinors for so(m) and the symplectic spinors for sp(2n) and correspond to representations of the supergroup with supergroup pair (Spin(m) x Mp(2n),osp(m|2n)). We…
We establish a correspondence between a conformally invariant complex scalar field action (with a conformal self-interaction potential) and the action of a phantom scalar field minimally coupled to gravity (with a cosmological constant). In…
A canonical realization of the BMS (Bondi-Metzner-Sachs) algebra is given on the phase space of the classical real Klein-Gordon field . By assuming the finiteness of the generators of the Poincar\'e group, it is shown that a countable set…
A system of generalized coherent states for the de Sitter group obeying the Klein-Gordon equation and corresponding to the massive spin zero particles over the de Sitter space is considered. This allows us to construct the quantized scalar…
We study the Klein--Gordon (KG) oscillator in a doubly special relativity (DSR) framework, where the mass-shell condition is deformed through a linear--fractional (M\"obius-type) modification of the Casimir invariant. This is induced by a…
Inspired by the structural unification of unitary groups (quantum field theory) with orthogonal groups (relativity) proposed recently through a non-division algebra, we construct a hypercomplex field theory with an internal symmetry that…
Let $ G $ be a connected semisimple Lie group with finite center. We prove a formula for the inner product of two cuspidal automorphic forms on $ G $ that are given by Poincar\'e series of $ K $-finite matrix coefficients of an integrable…
A discrete version of Lagrangian reduction is developed in the context of discrete time Lagrangian systems on $G\times G$, where $G$ is a Lie group. We consider the case when the Lagrange function is invariant with respect to the action of…
We study conformal properties of the quantum kinetic equations in curved spacetime. A transformation law for the covariant Wigner function under conformal transformations of a spacetime is derived by using the formalism of tangent bundles.…
We investigate the properties of kappa-Minkowski spacetime by using representations of the corresponding deformed algebra in terms of undeformed Heisenberg-Weyl algebra. The deformed algebra consists of kappa-Poincare algebra extended with…
We discuss scalar quantum field theories in a Lorentz-invariant three-dimensional noncommutative space-time. We first analyze the one-loop diagrams of the two-point functions, and show that the non-planar diagrams are finite and have…
We seek to introduce a mathematical method to derive the Klein-Gordon equation and a set of relevant laws strictly, which combines the relativistic wave functions in two inertial frames of reference. If we define the stationary state wave…
A bosonic Laplacian, which is a generalization of Laplacian, is constructed as a second order conformally invariant differential operator acting on functions taking values in irreducible representations of the special orthogonal group,…
We study the consequences of twisting the Poincare invariance in a quantum field theory. First, we construct a Fock space compatible with the twisting and the corresponding creation and annihilation operators. Then, we show that a covariant…