Научные публикации сотрудников
https://dspace.kpfu.ru/xmlui/handle/net/6052
Wed, 31 May 2023 19:55:59 GMT2023-05-31T19:55:59ZFlexible extra dimensions
https://dspace.kpfu.ru/xmlui/handle/net/175940
Flexible extra dimensions
Petryakova Polina; Popov Arkadiy Aleksandrovich; Rubin Sergey Georgievich
This paper discusses the origin of the small parameters with the aim of explaining the Hierarchy problem. The flexible extra dimensions are an essential tool in the process by which physical parameters are formed. The evolution of a multidimensional metric starts at the Planck scale and is completed with the static extra-dimensional metric and the 4-dim de Sitter space at high energies, where the exponential production of causally disconnected universes begins. Quantum fluctuations independently distort the metric within these universes, causing inflationary processes within them. Some of these universes tend asymptotically towards states characterised by small Hubble parameters. The effective parameter reduction applied to the Higgs sector of the Standard Model is explained by the presence of small-amplitude distributions of a scalar field in a fraction of these universes.
Sun, 01 Jan 2023 00:00:00 GMThttps://dspace.kpfu.ru/xmlui/handle/net/1759402023-01-01T00:00:00ZCommutators in $C*$-algebras and traces
https://dspace.kpfu.ru/xmlui/handle/net/175256
Commutators in $C*$-algebras and traces
Bikchentaev Airat Midkhatovich
Let $\mathcal{H}$ be a Hilbert space, $\dim \mathcal{H}= +\infty$. Let $X=U|X|$ be the polar decomposition of an
operator $X\in \mathcal{B}(\mathcal{H})$. Then $X$ is a non-commutator if and only if both $U$ and $|X|$ are non-commutators. A Hermitian operator $X\in \mathcal{B}(\mathcal{H})$ is a commutator if and only if the Cayley transform $\mathcal{K}(X)$ is a commutator.
Let $\mathcal{H}$ be a Hilbert space and $\dim mathcal{H}\leq +\infty$, $A,B, P\in \mathcal{B}(\mathcal{H})$ and $P=P^2$.
If $AB=\lambda BA$ for some $\lambda \in \mathbb{C}\setminus\{1\}$ then the operator $AB$ is a commutator.
The operator $AP$ is a commutator if and only if $PA$ is a commutator.
Sun, 01 Jan 2023 00:00:00 GMThttps://dspace.kpfu.ru/xmlui/handle/net/1752562023-01-01T00:00:00ZThe algebra of thin measurable operators is directly finite
https://dspace.kpfu.ru/xmlui/handle/net/175023
The algebra of thin measurable operators is directly finite
Bikchentaev Airat Midkhatovich
Let $\mathcal{M}$ be a semifinite von Neumann algebra on a Hilbert space $\cH$ equipped with a faithful normal semifinite trace $\tau$, $S(\mathcal{M},\tau)$ be the ${}^*$-algebra of all $\tau$-measurable operators. Let $S_0(\mathcal{M},\tau)$ be the ${}^*$-algebra of all $\tau$-compact operators and
$T(\mathcal{M},\tau)=S_0(\mathcal{M},\tau)+\mathbb{C}I$ be the ${}^*$-algebra of all operators $X=A+\lambda I$
with $A\in S_0(\mathcal{M},\tau)$ and $\lambda \in \mathbb{C}$. We prove that every operator of $T(\mathcal{M},\tau)$ that is left-invertible in $T(\mathcal{M},\tau)$ is in fact invertible in $T(\mathcal{M},\tau)$.
It is a generalization of Sterling Berberian theorem (1982) on the subalgebra of thin operators in $\cB (\cH)$.
For the singular value function $\mu(t; Q)$ of $Q=Q^2\in S(\mathcal{M},\tau)$ we have $\mu(t; Q)\in \{0\}\bigcup
[1, +\infty)$ for all $t)0$. It gives the positive answer to the question posed by Daniyar Mushtari in 2010.
Sun, 01 Jan 2023 00:00:00 GMThttps://dspace.kpfu.ru/xmlui/handle/net/1750232023-01-01T00:00:00ZVacuum Polarization of a Quantized Scalar Field in the Thermal State on the Short Throat Wormhole Background
https://dspace.kpfu.ru/xmlui/handle/net/173728
Vacuum Polarization of a Quantized Scalar Field in the Thermal State on the Short Throat Wormhole Background
Попов Аркадий Александрович; Лисенков Дмитрий Сергеевич
Vacuum polarization of a scalar field on the short throat wormhole background is investigated.
The scalar field is assumed to be massless, having an arbitrary coupling to the scalar curvature of spacetime. In addition, it is supposed that the field is in a thermal state with an \mbox{arbitrary temperature.
Sun, 01 Jan 2023 00:00:00 GMThttps://dspace.kpfu.ru/xmlui/handle/net/1737282023-01-01T00:00:00Z