Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Local martingales associated with Schramm-Loewner evolutions with internal symmetry
View through CrossRef
We consider Schramm-Loewner evolutions (SLEs) with internal degrees of freedom that are associated with representations of affine Lie algebras, following group theoretical formulation of SLEs. We reconstruct the SLEs considered by Bettelheim et al. [Phys. Rev. Lett. 95, 251601 (2005)] and Alekseev et al. [Lett. Math. Phys. 97, 243–261 (2011)] in correlation function formulation. We also explicitly formulate stochastic differential equations on internal degrees of freedom for Heisenberg algebras and the affine sl2. Our formulation enables us to find several local martingales associated with SLEs with internal degrees of freedom from computation on a representation of an affine Lie algebra. Indeed, we formulate local martingales associated with SLEs with internal degrees of freedom described by Heisenberg algebras and the affine sl2. We also find an affine sl2 symmetry of a space of SLE local martingales for the affine sl2.
Title: Local martingales associated with Schramm-Loewner evolutions with internal symmetry
Description:
We consider Schramm-Loewner evolutions (SLEs) with internal degrees of freedom that are associated with representations of affine Lie algebras, following group theoretical formulation of SLEs.
We reconstruct the SLEs considered by Bettelheim et al.
[Phys.
Rev.
Lett.
95, 251601 (2005)] and Alekseev et al.
[Lett.
Math.
Phys.
97, 243–261 (2011)] in correlation function formulation.
We also explicitly formulate stochastic differential equations on internal degrees of freedom for Heisenberg algebras and the affine sl2.
Our formulation enables us to find several local martingales associated with SLEs with internal degrees of freedom from computation on a representation of an affine Lie algebra.
Indeed, we formulate local martingales associated with SLEs with internal degrees of freedom described by Heisenberg algebras and the affine sl2.
We also find an affine sl2 symmetry of a space of SLE local martingales for the affine sl2.
Related Results
Frequency of Common Chromosomal Abnormalities in Patients with Idiopathic Acquired Aplastic Anemia
Frequency of Common Chromosomal Abnormalities in Patients with Idiopathic Acquired Aplastic Anemia
Objective: To determine the frequency of common chromosomal aberrations in local population idiopathic determine the frequency of common chromosomal aberrations in local population...
Fundamental Symmetries and Symmetry Violations from High Resolution Spectroscopy
Fundamental Symmetries and Symmetry Violations from High Resolution Spectroscopy
AbstractAfter an introductory survey, we introduce the seven fundamental symmetries of physics in relation to the group of the molecular Hamiltonian and the current standard model ...
Automated Symmetry Exploitation in Engineering Analysis
Automated Symmetry Exploitation in Engineering Analysis
It is well known that one can exploit symmetry to speed-up engineering analysis and improve accuracy, at the same time. Not surprisingly, most CAE systems have standard ‘provisions...
Brain Activity in Response to Visual Symmetry
Brain Activity in Response to Visual Symmetry
A number of studies have explored visual symmetry processing by measuring event related potentials and neural oscillatory activity. There is a sustained posterior negativity (SPN) ...
A Framework for Detection of Exact Global and Partial Symmetry in 3D CAD Models
A Framework for Detection of Exact Global and Partial Symmetry in 3D CAD Models
The most common way to retrieve symmetry information (i.e., the planes and axes of symmetry) in 3D CAD models is through visual recognition by engineers. However, engineers are not...
Bilateral Symmetry of Jumping and Agility in Professional Basketball Players: Differentiating Performance Levels and Playing Positions
Bilateral Symmetry of Jumping and Agility in Professional Basketball Players: Differentiating Performance Levels and Playing Positions
Although functional asymmetry is very common and normal in professional athletes, the better interlimb symmetry between dominant and nondominant sides (bilateral symmetry) could co...
Symmetry and symmetry breaking in science and arts
Symmetry and symmetry breaking in science and arts
In this review article, symmetry and symmetry breaking are considered as complementary principles in science and arts. It starts with symmetry and symmetry breaking in early world ...
Symmetry and Symmetry Breaking in Science and Arts
Symmetry and Symmetry Breaking in Science and Arts
In this review article, symmetry and symmetry breaking are considered as complementary principles in science and arts. It starts with symmetry and symmetry breaking in early world ...