In differential geometry, given a spin structure on an -dimensional orientable Riemannian manifold one defines the spinor bundle to be the complex vector bundle associated to the corresponding principal bundle of spin frames over and the spin representation of its structure group on the space of spinors .
A section of the spinor bundle is called a spinor field.
Let be a spin structure on a Riemannian manifold that is, an equivariant lift of the oriented orthonormal frame bundle with respect to the double covering of the special orthogonal group by the spin group.
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The goal of the course is to introduce relativistic quantum field theory as the conceptual and mathematical framework describing fundamental interactions.
Presentation of Wightman's axiomatic framework to QFT as well as to the necessary mathematical objects to their understanding (Hilbert analysis, distributions, group representations,...).Proofs of
The goal of the course is to introduce relativistic quantum field theory as the conceptual and mathematical framework describing fundamental interactions such as Quantum Electrodynamics.
In differential geometry, a spin structure on an orientable Riemannian manifold (M, g) allows one to define associated spinor bundles, giving rise to the notion of a spinor in differential geometry. Spin structures have wide applications to mathematical physics, in particular to quantum field theory where they are an essential ingredient in the definition of any theory with uncharged fermions. They are also of purely mathematical interest in differential geometry, algebraic topology, and K theory.
In mathematics the spin group Spin(n) is a Lie group whose underlying manifold is the double cover of the special orthogonal group SO(n) = SO(n, R), such that there exists a short exact sequence of Lie groups (when n ≠ 2) The group multiplication law on the double cover is given by lifting the multiplication on . As a Lie group, Spin(n) therefore shares its dimension, n(n − 1)/2, and its Lie algebra with the special orthogonal group. For n > 2, Spin(n) is simply connected and so coincides with the universal cover of SO(n).
In mathematics, spin geometry is the area of differential geometry and topology where objects like spin manifolds and Dirac operators, and the various associated index theorems have come to play a fundamental role both in mathematics and in mathematical physics. An important generalisation is the theory of symplectic Dirac operators in symplectic spin geometry and symplectic topology, which have become important fields of mathematical research.
alpha-RuCl3 is a promising candidate material to realize the so far elusive quantum spin liquid ground state. However, at low temperatures, the coexistence of different exchange interactions couple the effective pseudospins into an antiferromagnetically zi ...
NATURE PORTFOLIO2022
We study the asymptotic behavior of the N-clock model, a nearest neighbors ferromagnetic spin model on the d-dimensional cubic epsilon-lattice in which the spin field is constrained to take values in a discretization S-N of the unit circle S-1 consisting o ...
2021
This PhD thesis aims at testing one of the fundamental properties of the Standard Model (SM) of particle physics: the lepton flavour universality (LFU), which states that W and Z bosons are equally coupled to the three lepton generations. In this work, ...