Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userComposite bundles in Clifford algebras. Gravitation theory. Part I
187
0
0.0
(
0
)
Added by
Gennady Sardanashvily
Publication date
2015
fields
Physics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
Based on a fact that complex Clifford algebras of even dimension are isomorphic to the matrix ones, we consider bundles in Clifford algebras whose structure group is a general linear group acting on a Clifford algebra by left multiplications, but not a group of its automorphisms. It is essential that such a Clifford algebra bundle contains spinor subbundles, and that it can be associated to a tangent bundle over a smooth manifold. This is just the case of gravitation theory. However, different these bundles need not be isomorphic. To characterize all of them, we follow the technique of composite bundles. In gravitation theory, this technique enables us to describe different types of spinor fields in the presence of general linear connections and under general covariant transformations.
rate research
Read More
The Minkowski spacetime quantum Clifford algebra structure associated with the conformal group and the Clifford-Hopf alternative k-deformed quantum Poincare algebra is investigated in the Atiyah-Bott-Shapiro mod 8 theorem context. The resulting algebra is equivalent to the deformed anti-de Sitter algebra U_q(so(3,2)), when the associated Clifford-Hopf algebra is taken into account, together with the associated quantum Clifford algebra and a (not braided) deformation of the periodicity Atiyah-Bott-Shapiro theorem.
A new variational principle for General Relativity, based on an action functional $I/(Phi, abla)/$ involving both the metric $Phi/$ and the connection $ abla/$ as independent, emph{unconstrained/} degrees of freedom is presented. The extremals of $I/$ are seen to be pairs $/(Phi, abla)/$ in which $Phi/$ is a Ricci flat metric, and $ abla/$ is the associated Riemannian connection. An application to Kaluzas theory of interacting gravitational and electromagnetic fields is discussed.
In the framework of J-bundles a vielbein formulation of unified Einstein-Maxwell theory is proposed. In the resulting scheme, field equations matching the gravitational and electromagnetic fields are derived by constraining a five-dimensional variational principle. No dynamical scalar field is involved.
It is shown that a certain representation of the Heisenberg type Krichever-Novikov algebra gives rise to a state field correspondence that is quite similar to the vertex algebra structure of the usual Heisenberg algebra. Finally a definition of Krichever-Novikov type vertex algebras is proposed and its relation to vertex algebras is discussed.
We construct new families of spin chain Hamiltonians that are local, integrable and translationally invariant. To do so, we make use of the Clifford group that arises in quantum information theory. We consider translation invariant Clifford group transformations that can be described by matrix product operators (MPOs). We classify the translation invariant Clifford group transformations that consist of a shift operator and an MPO of bond dimension two -- this includes transformations that preserve locality of all Hamiltonians; as well as those that lead to non-local images of particular operators but nevertheless preserve locality of certain Hamiltonians. We characterise the translation invariant Clifford group transformations that take single-site Pauli operators to local operators on at most five sites -- examples of Quantum Cellular Automata -- leading to a discrete family of Hamiltonians that are equivalent to the canonical XXZ model under such transformations. For spin chains solvable by algebraic Bethe Ansatz, we explain how conjugating by a matrix product operator affects the underlying integrable structure. This allows us to relate our results to the usual classifications of integrable Hamiltonians. We also treat the case of spin chains solvable by free fermions.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
