Speaker
Description
The aim of the work:
To prove the following conjecture: The largest maximal subgroup of shifts of a multi-permutation system in a Moran covering is isomorphic to the maximal discrete group of displacements (branchings) of Γ(c). To do this, prove the lemma 〖lim〗(n→∞) lim(k→∞)=#Aut(Γ)=ord(1/k)log#G_(n,k)
Equivalent to this conjecture is the following statement: the vacuum expectation value of the Wilson loop reduces to the vacuum expectation value for the maximal compact subgroup of the symmetry group G, that is, 𝑊((𝐶)) ̅.
Results:
1. Examples of invariant knots in SO(4) are constructed.
2. The Inono-Wigner contraction for the symmetry group of SO(4) is performed using methods of the theory of non-commutative algebras.
3. A new proof of the Brouwer shift theorem for a periodic point on the "disk" set is found.
4. The Chern-Simons action is modified using the Cartan exterior form method, and it is shown that translationally invariant components of the Lie algebra can describe a topologically invariant contortion tensor.
5. Based on the polysymbolic formalism for describing the Cachazo-Ye-Yuan equation, a new method for calculating Wilson loops is derived, as applied to three-amplitude fermion Feynman diagrams. is a contact structure.
6. It is proved that elliptic symplectic compact sets have the specification property.
7. The properties of the symplectic time ordering operator are studied.
8. It is proved that the sum of multi-permutation subshifts of a topological Markov chain on the Moran covering on the Carathéodory structure in the projective limit converges to a motion invariant of the Randemeister type.
9. It is shown that the extended locality criterion for loops allows one to construct form factors based on a sequence of p-addic numbers.
10. Ward identities are modified for the old covariant approach in the Chan-Paton model, which allows one to describe Reeb fields in a general form.
11. The equivalence of the definitions of homeomorphism on pseudoholomorphic curves on elliptic sets for different classes of symplectic capacities is proved.
12. An equivalent formulation of the Chern-Simons term is created, which, when substituted into the Kauffman bracket in the Lax representation,
| Тематическая секция | Физика фундаментальных взаимодействий |
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