| 1. |
- Abedin, R., et al.
(författare)
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Topological Manin pairs and (n, s)-type series
- 2023
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Ingår i: Letters in Mathematical Physics. - 0377-9017 .- 1573-0530. ; 113:3
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Tidskriftsartikel (refereegranskat)abstract
- Lie subalgebras of L = g((x)) x g[x]/x(n)g[x], complementary to the diagonal embedding Delta of g[x] and Lagrangian with respect to some particular form, are in bijection with formal classical r-matrices and topological Lie bialgebra structures on the Lie algebra of formal power series g[x]. In this work we consider arbitrary subspaces of L complementary to Delta and associate them with so-called series of type (n, s). We prove that Lagrangian subspaces are in bijection with skew-symmetric (n, s)-type series and topological quasi-Lie bialgebra structures on g[x]. Using the classificaiton of Manin pairs we classify up to twisting and coordinate transformations all quasi-Lie bialgebra structures. Series of type (n, s), solving the generalized classical Yang-Baxter equation, correspond to subalgebras of L. We discuss their possible utility in the theory of integrable systems.
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| 2. |
- Albeverino, S., et al.
(författare)
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Pseudo-Differential Operators with Point Interactions
- 1997
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Ingår i: Letters in Mathematical Physics. - 0377-9017 .- 1573-0530. ; 41, s. 79-92
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Tidskriftsartikel (refereegranskat)abstract
- Point interactions for pseudo-differential operators are studied. Necessary and sufficient conditions for a pseudo-differential operator to have nontrivial point perturbations are given. The results are applied to the construction of relativistic spin zero Hamiltonians with point interactions.
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| 3. |
- Albeverio, S., et al.
(författare)
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Symmetries of Schrödinger operator with point interactions
- 1998
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Ingår i: Letters in Mathematical Physics. - 0377-9017 .- 1573-0530. ; 45, s. 33-47
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Tidskriftsartikel (refereegranskat)abstract
- The transformations of all the Schrödinger operators with point interactions in dimension one under space reflection P, time reversal T and (Weyl) scaling Wλ are presented. In particular, those operators which are invariant (possibly up to a scale) are selected. Some recent papers on related topics are commented upon
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| 4. |
- Andersen, Jørgen Ellegaard, et al.
(författare)
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Reducibility of quantum representations of mapping class groups
- 2010
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Ingår i: Letters in Mathematical Physics. - : Springer. - 0377-9017 .- 1573-0530. ; 91:3, s. 215-239
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we provide a general condition for the reducibility of the Reshetikhin–Turaev quantum representations of the mapping class groups. Namely, for any modular tensor category with a special symmetric Frobenius algebra with a non-trivial genus one partition function, we prove that the quantum representations of all the mapping class groups built from the modular tensor category are reducible. In particular, for SU(N) we get reducibility for certain levels and ranks. For the quantum SU(2) Reshetikhin–Turaev theory we construct a decomposition for all even levels. We conjecture this decomposition is a complete decomposition into irreducible representations for high enough levels.
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| 5. |
- Arnlind, Joakim, et al.
(författare)
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A noncommutative catenoid
- 2018
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Ingår i: Letters in Mathematical Physics. - : Springer Netherlands. - 0377-9017 .- 1573-0530. ; 108:7, s. 1601-1622
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Tidskriftsartikel (refereegranskat)abstract
- A noncommutative algebra corresponding to the classical catenoid is introduced together with a differential calculus of derivations. We prove that there exists a unique metric and torsion-free connection that is compatible with the complex structure, and the curvature is explicitly calculated. A noncommutative analogue of the fact that the catenoid is a minimal surface is studied by constructing a Laplace operator from the connection and showing that the embedding coordinates are harmonic. Furthermore, an integral is defined and the total curvature is computed. Finally, classes of left and right modules are introduced together with constant curvature connections, and bimodule compatibility conditions are discussed in detail.
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| 6. |
- Arnlind, Joakim, et al.
(författare)
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Eigenvalue Dynamics off the Calogero-Moser system
- 2004
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Ingår i: Letters in Mathematical Physics. - : Springer. - 0377-9017 .- 1573-0530. ; 68:2, s. 121-129
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Tidskriftsartikel (refereegranskat)abstract
- By finding N(N-1)/2 suitable conserved quantities, free motions of real symmetric N x N matrices X(t), with arbitrary initial conditions, are reduced to nonlinear equations involving only the eigenvalues of X-in contrast to the rational Calogero-Moser system, for which [X(0), X(0)] has to be purely imaginary, of rank one.
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| 7. |
- Arnlind, Joakim, et al.
(författare)
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Goldfish geodesics and hamiltonian reduction of matrix dynamics
- 2008
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Ingår i: Letters in Mathematical Physics. - : Springer Science and Business Media LLC. - 0377-9017 .- 1573-0530. ; 84:1, s. 89-98
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Tidskriftsartikel (refereegranskat)abstract
- We describe the Hamiltonian reduction of a time-dependent real-symmetric NxN matrix system to free vector dynamics, and also provide a geodesic interpretation of Ruijsenaars-Schneider systems. The simplest of the latter, the goldfish equation, is found to represent a flat-space geodesic in curvilinear coordinates.
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| 8. |
- Arnlind, Joakim, et al.
(författare)
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Noncommutative Minimal Surfaces
- 2016
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Ingår i: Letters in Mathematical Physics. - : Springer Science and Business Media LLC. - 0377-9017 .- 1573-0530. ; 106:8, s. 1109-1129
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Tidskriftsartikel (refereegranskat)abstract
- We define noncommutative minimal surfaces in the Weyl algebra, and give a method to construct them by generalizing the well-known Weierstrass representation.
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| 9. |
- Arnlind, Joakim, et al.
(författare)
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Pseudo-Riemannian Geometry in Terms of Multi-Linear Brackets
- 2014
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Ingår i: Letters in Mathematical Physics. - : Springer Verlag (Germany). - 0377-9017 .- 1573-0530. ; 104:12, s. 1507-1521
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Tidskriftsartikel (refereegranskat)abstract
- We show that the pseudo-Riemannian geometry of submanifolds can be formulated in terms of higher order multi-linear maps. In particular, we obtain a Poisson bracket formulation of almost (para-)Kahler geometry.
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| 10. |
- Arnlind, Joakim, et al.
(författare)
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Trace Extensions, Determinant Bundles, and Gauge Group Cocycles
- 2002
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Ingår i: Letters in Mathematical Physics. - : Springer. - 0377-9017 .- 1573-0530. ; 62:2, s. 101-110
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Tidskriftsartikel (refereegranskat)abstract
- We study the geometry of determinant line bundles associated with Dirac operators on compact odd-dimensional manifolds. Physically, these arise as (local) vacuum line bundles in quantum gauge theory. We give a simplified derivation of the commutator anomaly formula using a construction based on noncyclic trace extensions and associated nonmultiplicative renormalized determinants.
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