| 1. |
- Arnlind, Joakim, et al.
(author)
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Eigenvalue Dynamics off the Calogero-Moser system
- 2004
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In: Letters in Mathematical Physics. - : Springer. - 0377-9017 .- 1573-0530. ; 68:2, s. 121-129
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Journal article (peer-reviewed)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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| 2. |
- Arnlind, Joakim, et al.
(author)
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Trace Extensions, Determinant Bundles, and Gauge Group Cocycles
- 2002
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In: Letters in Mathematical Physics. - : Springer. - 0377-9017 .- 1573-0530. ; 62:2, s. 101-110
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Journal article (peer-reviewed)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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| 3. |
- Graf, G. M., et al.
(author)
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No zero energy states for the supersymmetric x(2)y(2) potential
- 2002
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In: Letters in Mathematical Physics. - 0377-9017 .- 1573-0530. ; 60:2, s. 191-196
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Journal article (peer-reviewed)abstract
- We show that the positive supersymmetric matrix-valued differential operator H = p(x)(2) + p(y)(2) + x(2)y(2) + xsigma(3) + ysigma(1) has no zero modes, i.e., Hpsi = 0 implies psi = 0. The result depends on a virial type argument for the corresponding supercharge. The model may be regarded as a simple relative of dimensional reductions of supersymmetric Yang Mills theories.
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| 4. |
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| 5. |
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| 6. |
- Langmann, Edwin
(author)
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Anyons and the elliptic Calogero-Sutherland model
- 2000
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In: Letters in Mathematical Physics. - 0377-9017 .- 1573-0530. ; 54:4, s. 279-289
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Journal article (peer-reviewed)abstract
- We obtain a second quantization of the elliptic Calogero-Sutherland (eCS) model by constructing a quantum field theory model of anyons on a circle and at a finite temperature. This yields a remarkable identity involving anyon correlation functions and providing an algorithm for solving of the eCS model. The eigenfunctions obtained define an elliptic generalization of the Jack polynomials.
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| 7. |
- Matsubara, Keizo, et al.
(author)
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Invariant Star Products on S 2 and the Canonical Trace
- 2004
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In: Letters in Mathematical Physics. - : Springer Science and Business Media LLC. - 0377-9017 .- 1573-0530. ; 70:2, s. 109-120
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Journal article (peer-reviewed)abstract
- We calculate the canonical trace and use the Fedosov–Nest–Tsygan index theorem to obtain the characteristic class for a star product on S 2. We show how, for this simple example, it is possible to extract the relevant information needed to use the Fedosov–Nest–Tsygan index theorem from a local calculation.
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| 8. |
- Albeverio, S, et al.
(author)
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Point interactions: PT-Hermiticity and reality of the spectrum
- 2002
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In: Letters in Mathematical Physics. - 0377-9017. ; 59:3, s. 227-242
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Journal article (peer-reviewed)abstract
- General point interactions for the second derivative operator in one dimension are studied. In particular, cal PT-self-adjoint point interactions with the support at the origin and at points +/-l are considered. The spectrum of such non-Hermitian operators is investigated and conditions when the spectrum is pure real are presented. The results are compared with those for standard self-adjoint point interactions.
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| 9. |
- Kurasov, Pavel, et al.
(author)
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On field theory methods in singular perturbation theory
- 2003
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In: Letters in Mathematical Physics. - 0377-9017. ; 64:2, s. 171-184
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Journal article (peer-reviewed)abstract
- Singular and supersingular finite rank perturbations of self-adjoint operators are studied using methods from renormalization theory for quantum fields. It is shown that the ideas from dimensional and Pauli-Villars regulatizations can be applied to determine uniquely certain finite rank supersingular perturbations. Approach is based on the regularization of homogeneous singular quadratic forms.
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| 10. |
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