Related papers: Calogero-Sutherland Particles as Quasisemions
Coupled dark sector models have gained significant attention, motivated by recent advances in cosmology and the pressing need to address unresolved puzzles. In this work, we study coupled scalar dark sector models inspired by…
Some first principles that, we believe, could serve as foundation for quantum theory of extended particles are formulated. It is also shown that in the point-like particles limit the non-relativistic quantum mechanics can be restored. As an…
Split-UED allows for the possibility that the lowest lying KK excitations of the Standard Model fermions can be much lighter than the corresponding gauge or Higgs KK states. This can happen provided the fermion bulk masses are chosen to be…
We introduce a generalization of variations of Hodge structures living over moduli spaces of non-commutative deformations of complex manifolds. Hodge structure associated with a point of such moduli space is an element of Sato type…
In this paper, we introduce homological structure theory of semirings and CP-semirings---semirings all of whose cyclic semimodules are projective. We completely describe semisimple, Gelfand, subtractive, and anti-bounded, CP-semirings. We…
We construct orbifolds with quasitoric boundary and show that they have stable almost complex structure. We show that a quasitoric orbifold is complex cobordant to finite disjoint copies of complex orbifold projective spaces. Finally some…
An approximate but straight forward projection method to molecular many alpha-particle states is proposed and the overlap to the shell model space is determined. The resulting space is in accordance with the shell model, but still contains…
We consider here quasiperiodic potentials on the plane, which can serve as a "transitional link" between ordered (periodic) and chaotic (random) potentials. As can be shown, in almost any family of quasiperiodic potentials depending on a…
It is shown that the Calogero-Moser models based on all root systems of the finite reflection groups (both the crystallographic and non-crystallographic cases) with the rational (with/without a harmonic confining potential), trigonometric…
These lectures study two correspondences between gauge theories and integrable many-body systems. The first arises from infinite-dimensional Hamiltonian reduction and relates gauge-theoretic dynamics directly to Calogero--Moser-type systems…
The idea that dark matter may be a composite state of a hidden nonabelian gauge sector has received great attention in recent years. Frameworks such as asymmetric dark matter motivate the idea that dark matter may have similar mass to the…
We express the Hamiltonian of the quantum trigonometric Calogero-Sutherland model related to the Lie algebra $D_4$ in terms of a set of Weyl-invariant variables, namely, the characters of the fundamental representations of the Lie algebra.…
We provide a rigorous construction of a large class of generalized spin-boson models with ultraviolet-divergent form factors. This class comprises various models of many possibly non-identical atoms with arbitrary but finite numbers of…
In the present paper we prove the compactness theorem with respect to partial structures and quasi-truth, using the technique of ultraproducts. Partial structures and quasi-truth are two notions developed within the partial structures…
We study the so-called closed and splitting subsemimodules and submodules of a given semimodule or module, respectively. We describe lattices of subsemimodules and of closed subsemimodules and posets of splitting subsemimodules and…
A full-quantum approach is used to study quantum nonlinear properties of a compound Michelson-Sagnac interferometer optomechanical system. The effective Hamiltonian shows that both dissipative and dispersive couplings possess imaginary- and…
Starting from the Hamiltonian formulation of supersymmetric Calogero models associated with the classical $A_n$, $B_n$, $C_n$ and $D_n$ series we construct the ${\cal N}{=}\,2$ and ${\cal N}{=}\,4$ supersymmetric extensions of the their…
The properties of the quantum universe on extremely small spacetime scales are studied in the semi-classical approach to the well-defined quantum model. It is shown that near the initial cosmological singularity point quantum gravity…
The symmetric group on 4 letters has the reflection group $D_{3}$ as an isomorphic image. This fact follows from the coincidence of the root systems $A_{3}$ and $D_{3}$. The isomorphism is used to construct an orthogonal basis of…
One considers quasihomogeneous isolated singularities of hypersurfaces in arbitrary dimensions through the lenses of three apparently quite apart themes: syzygies, singularity invariants, and foliations. In the first of these, one adds to…