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Factoriality of von Neumann algebras connected with general commutation relations-finite dimensional case

Ilona Królak (2006)

Banach Center Publications

We study a certain class of von Neumann algebras generated by selfadjoint elements $ω_{i} = a_{i} + a ⁺_{i}$ , where $a_{i}, a ⁺_{i}$ satisfy the general commutation relations: $a_{i} a ⁺_{j} = \sum_{r, s} t_{j}^{i} r_{s} a ⁺_{r} a_{s} + δ_{i j} I d$ . We assume that the operator T for which the constants $t_{j}^{i} r_{s}$ are matrix coefficients satisfies the braid relation. Such algebras were investigated in [BSp] and [K] where the positivity of the Fock representation and factoriality in the case of infinite dimensional underlying space were shown. In this paper we prove that under certain conditions on the number of generators...

Faster than Hermitian time evolution.

Bender, Carl M. (2007)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Feynman diagrams and large order estimates for the exponential anharmonic oscillator

Stephen Breen (1987)

Annales de l'I.H.P. Physique théorique

Feynman diagrams and the quantum stochastic calculus

John Gough (2006)

Banach Center Publications

We present quantum stochastic calculus in terms of diagrams taking weights in the algebra of observables of some quantum system. In particular, we note the absence of non-time-consecutive Goldstone diagrams. We review recent results in Markovian limits in these terms.

Feynman maps, Cameron-Martin formulae and anharmonic oscillators

David Elworthy, Aubrey Truman (1984)

Annales de l'I.H.P. Physique théorique

Feynman path integral as spectral decomposition

Souček, J., Souček, V., Janiš, V. (1981)

Abstracta. 9th Winter School on Abstract Analysis

Feynman path integrals on phase space and the metaplectiv representation.

Joel Robbin, Dietmar Salamon (1996)

Mathematische Zeitschrift

Field theory on curved noncommutative spacetimes.

Schenkel, Alexander, Uhlemann, Christoph F. (2010)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

From multi-instantons to exact results

Jean Zinn-Justin (2003)

Annales de l’institut Fourier

In these notes, conjectures about the exact semi-classical expansion of eigenvalues of hamiltonians corresponding to potentials with degenerate minima, are recalled. They were initially motivated by semi-classical calculations of quantum partition functions using a path integral representation and have later been proven to a large extent, using the theory of resurgent functions. They take the form of generalized Bohr--Sommerfeld quantization formulae. We explain here their...