Вариант Теоремы Ван Дер Вардена И Доказательство Гипотезы Мищенко Для Гомоморфизмов Локально Компактных Групп

Shtern, A. I.; Shtern, A. I.

doi:10.4213/im2599

Izv. RAN. Ser. Mat.

2008

DOI: 10.4213/im2599

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Вариант Теоремы Ван Дер Вардена И Доказательство Гипотезы Мищенко Для Гомоморфизмов Локально Компактных Групп

A. I. Shtern¹,

A. I. Shtern²

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Cited by 19 publications

References 48 publications

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An Analogue of the Coleman–Mandula Theorem for Quantum Field Theory in Curved Spacetimes

Fewster

2017

Commun. Math. Phys.

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Abstract:The Coleman-Mandula (CM) theorem states that the Poincaré and internal symmetries of a Minkowski spacetime quantum field theory cannot combine nontrivially in an extended symmetry group. We establish an analogous result for quantum field theory in curved spacetimes, assuming local covariance, the timeslice property, a local dynamical form of Lorentz invariance, and additivity. Unlike the CM theorem, our result is valid in dimensions n ≥ 2 and for free or interacting theories. It is formulated for theories defined on a category of all globally hyperbolic spacetimes equipped with a global coframe, on which the restricted Lorentz group acts, and makes use of a general analysis of symmetries induced by the action of a group G on the category of spacetimes. Such symmetries are shown to be canonically associated with a cohomology class in the second degree nonabelian cohomology of G with coefficients in the global gauge group of the theory. Our main result proves that the cohomology class is trivial if G is the universal cover S of the restricted Lorentz group. Among other consequences, it follows that the extended symmetry group is a direct product of the global gauge group and S, all fields transform in multiplets of S, fields of different spin do not mix under the extended group, and the occurrence of noninteger spin is controlled by the centre of the global gauge group. The general analysis is also applied to rigid scale covariance.

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An Analogue of the Coleman–Mandula Theorem for Quantum Field Theory in Curved Spacetimes

Fewster

2017

Commun. Math. Phys.

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The structure of homomorphisms of connected locally compact groups into compact groups

Shtern

2011

Izv. Math.

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The crystallization, microstructure, and soft magnetic properties of Fe 52 Co 34 Hf 7 B 6 Cu 1 alloy are studied. Amorphous Fe 52 Co 34 Hf 7 B 6 Cu 1 alloys are first treated by a pulsed magnetic field with a medium frequency, and then annealed at 100 • C-400 • C for 30 min in a vacuum. The rise in temperature during the treatment by a pulsed magnetic field is measured by a non-contact infrared thermometer. The soft magnetic properties of specimens are measured by a vibrating sample magnetometer (VSM). The microstructure changes of specimens are observed by a Mössbauer spectroscopy and transmission electron microscope (TEM). The results show the medium-frequency pulsating magnetic field will promote nanocrystallization of the amorphous alloy with a lower temperature rise. The nanocrystalline phase is α-Fe(Co) with bcc crystal structure, and the grain size is about 10 nm. After vacuum annealing at 100 • C for 30 min, scattering nanocrystalline phases become more uniform, the coercive force and the saturation magnetization of the specimens are 41.98 A/m and 185.15 emu/g.

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The structure of locally bounded finite-dimensional representations of connected locally compact groups

Shtern¹

2014

Sb. Math.

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Вариант Теоремы Ван Дер Вардена И Доказательство Гипотезы Мищенко Для Гомоморфизмов Локально Компактных Групп

Cited by 19 publications

References 48 publications

An Analogue of the Coleman–Mandula Theorem for Quantum Field Theory in Curved Spacetimes

An Analogue of the Coleman–Mandula Theorem for Quantum Field Theory in Curved Spacetimes

The structure of homomorphisms of connected locally compact groups into compact groups

The structure of locally bounded finite-dimensional representations of connected locally compact groups

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