Representation and design of wavelets using unitary circuits [PDF]
, 2016 The representation of discrete, compact wavelet transformations (WTs) as circuits of local unitary gates is discussed. We employ a similar formalism as used in the multiscale representation of quantum many-body wave functions using unitary circuits ...
G. Evenbly, S. White
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On Constructing Informationally Complete Covariant Positive Operator-Valued Measures
Entropy, 2023 We study a projective unitary representation of the product G=G˜×G, where G is a locally compact Abelian group and G^ is its dual consisting of characters on G.
Grigori Amosov
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Topological Boundaries of Unitary Representations [PDF]
International Mathematics Research Notices, 2020 AbstractWe introduce and study a generalization of the notion of the Furstenberg boundary of a discrete group $\Gamma $ to the setting of a general unitary representation $\pi : \Gamma \to B(\mathcal H_\pi )$. This space, which we call the “Furstenberg–Hamana boundary” (or "FH-boundary") of the pair $(\Gamma , \pi )$, is a $\Gamma $-invariant subspace ...
Bearden, Alex, Kalantar, Mehrdad
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Minimal unitary representation of SU(2,2) and its deformations as massless conformal fields and their supersymmetric extensions [PDF]
, 2009 We study the minimal unitary representation (minrep) of SO(4,2) over a Hilbert space of functions of three variables, obtained by quantizing its quasiconformal action on a five dimensional space.
S. Fernando, M. Gunaydin
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Integral formula of the unitary inversion operator for the minimal representation of $O(p, q)$
Proceedings of the Japan Academy Series A: Mathematical Sciences, 2007 Toshiyuki Kobayashi
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SU(2) deformations of the minimal unitary representation of OSp(8*|2N) as massless 6D conformal supermultiplets [PDF]
, 2010 Minimal unitary representation of SO ⁎ ( 8 ) ≃ SO ( 6 , 2 ) realized over the Hilbert space of functions of five variables and its deformations labeled by the spin t of an SU ( 2 ) subgroup correspond to massless conformal fields in six dimensions as was
S. Fernando, M. Gunaydin
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Hamiltonian Quantization of Chern-Simons theory with SL(2,C) Group [PDF]
, 2002 We analyze the hamiltonian quantization of Chern-Simons theory associated to the universal covering of the Lorentz group SO(3,1). The algebra of observables is generated by finite dimensional spin networks drawn on a punctured topological surface.
Alekseev A Yu +22 more
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The Minimal Unitary Representation of E_8(8) [PDF]
, 2001 We give a new construction of the minimal unitary representation of the exceptional group E8(8) on a Hilbert space of complex functions in 29 variables. Due to their manifest covariance with respect to the E7(7) subgroup of E8(8) our formulas are simpler
M. Günaydin, K. Koepsell, H. Nicolai
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A note on cocycles of unitary representations [PDF]
Proceedings of the American Mathematical Society, 1976 Given a unitary representation U U of a locally compact abelian group G G , we investigate the relationship between two cocycles a 1 , a 2 : V a 1
Parry, W., Schmidt, K.
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Covariant catalysis requires correlations and good quantum reference frames degrade little [PDF]
Quantum, 2023 Catalysts are quantum systems that open up dynamical pathways between quantum states which are otherwise inaccessible under a given set of operational restrictions while, at the same time, they do not change their quantum state.
Lauritz van Luijk +2 more
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