Speaker
Description
In this paper, a proof of the theorem on the global hyperbolicity of space-time M on the sphere $S^4$ is proposed based on the topology of open light cones; the work uses the so-called concrete approach to the construction of the Haag-Araki axiomatics.
The properties of causal geodesic structures on the paracompact complement of space-time are investigated.1. A description of quasi-equivalent sectors has been created within the framework of super selection rules\
2. It is proven that each layer on a star-shaped surface is a projective limit for a tubular region in axiomatic field theory on a factor space\
3. It is proved that the temporal ordering operator of the causal geodesic structure in the symplectic case
- The advantages from the point of view of physical motivation for choosing the criterion of extended isotonia are indicated \
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A superstructure on the Bowen-Waters ultrametrics has been introduced in relation to axylmatic quantum field theory.\
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A new proof of the generalized Cook's criterion for $\omega_o$ states of the system has been found, based on the SEM (condition for positive energy on the symplectic layer).
- It is shown that the Markovian time ordering operator $T_{\grave{\omega}\lambda}^*$ has a closed spectrum
The author has proven the following theorem
Let there be a pseudo-Riemannian metric E with signature $(+, -, + -)$ in class $C^p$ on which there is an isomorphism defining an almost complex structure $(E, \sigma)$ with gauge function $ \sigma$, which defines a family of symplectic forms of the form $d\lambda^n$ . This theorem can be reformulated like this:\par\textit{A symplectic structure based on the 1-form $d\sigma$ in the class $C^p$ has a contractible fiber .
For this purpose, an auxiliary lemma was proved. \
\textit{Lemma 1. $\exists$ at least 1 vector $v_b^a \perp TM$ non-orthogonal to the timelike surface }
In order to find an object suitable for proving Lemma 1, it is necessary to prove the following theorem
\begin{theorem}
The paracompact complement of spacetime $\grave{M}$ is a non-extensible globally hyperbolically complete spacetime
