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The main result describes the Brauer-Nesbitt reduction of unipotent representations of a finite group of Lie type, expressing it as an explicit linear combination of the restriction of Weyl modules from the algebraic group to the group of…
Gaussian unitaries, generated by quadratic Hamiltonians, are fundamental in quantum optics and continuous-variable computing. Their structures correspond to symplectic (bosons) and orthogonal (fermions) groups, but physical realizations…
We discuss a Poincar\'e invariant coupled-channel formalism which is based on the point-form of relativistic quantum mechanics. Electromagnetic scattering of an electron by a 2-body bound state is treated as a 2-channel problem for a…
The Polaron is the quantum of a "Polarization" field originated by the "contact" interaction [D1][D2] of a massive polarizable particle with a photon. We prove that this process produces bound states. Each bound state carries a…
Triangle Feynman diagrams can be considered as describing form factors of states bound by a zero-range interaction. These form factors are calculated for scalar particles and compared to point-form and non-relativistic results. By examining…
We show that the open unit ball of the space of operators from a finite dimensional Hilbert space into a separable Hilbert space (we call it "operator ball") has a restricted form of normal structure if we endow it with a hyperbolic metric…
We study the behavior of exciton polaritons in an optical microcavity with an embedded semiconductor quantum well. We use two-component exciton-photon approach formulated in terms of path integral formalism. In order to describe spatial…
We obtain determinant representations for the form factors of the monodromy matrix entries in quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing $GL(3)$-invariant $R$-matrix. These representations can be…
A relative position 4-vector is constructed for two spin-zero particles. Some advantages of this relative position over Bakamjian-Thomas are pointed out. The centre-of-mass (CM) and relative positions and momenta are an explicit realisation…
We study two Hamiltonian models, based on infrared approximations which render them solvable, in order to obtain an operator formulation of the soft-photon corrections to the scattering of a single electron, as given in Quantum…
We present a dual 5D braneworld picture of a recently suggested model for a microcanonical description of a 4D cosmology driven by a conformal field theory with a large number of quantum fields. The 5D side of the duality relation is…
In this review, we have reached from the most basic definitions in the theory of groups, group structures, etc. to representation theory and irreducible representations of the Poincar'e group. Also, we tried to get a more comprehensible…
In this paper, we consider the relation between two nonabelian Fourier transforms. The first one is defined in terms of the Langlands-Kazhdan-Lusztig parameters for unipotent elliptic representations of a split p-adic group and the second…
Quantum chromodynamics in two spacetime dimensions admits a finite non-invertible symmetry described mathematically by a fusion category. This symmetry is spontaneously broken at long distances, leading to distinct vacua. When the theory…
Hamiltonian models based on two different infrared approximations are studied in order to obtain an explicit comparison with the standard analysis of the infrared contributions, occurring in the relativistically covariant perturbative…
Using the multisymplectic Hamiltonian formalism, we propose a Poisson bracket for the electromagnetic field that, in addition to satisfying the restricted principle of relativity, reproduces well-established results from the standard…
The Einstein equations are non-linear and the particles of which the gravitational effect is described by these equations are lastly unknown. If renormalizable fields are assumed, then results are obtained only in the case of a at space.…
The electromagnetic form factors of the proton are obtained using a particular realization of QCD in the large $N_c$ limit (${QCD}_{\infty}$), which sums up the infinite number of zero-width resonances to yield an Euler's Beta function…
In standard quantum field theory, the one-particle states are classified by unitary representations of the Poincar\'e group, whereas the causal fields' classification employs the finite dimensional (non-unitary) representations of the…
We study the representations of the three-dimensional Euclidean Snyder-de Sitter algebra. This algebra generates the symmetries of a model admitting two fundamental scales (Planck mass and cosmological constant) and is invariant under the…