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Casimir effect for differential forms in real compact hyperbolic spaces
Mendes, V. S.;Prado, T. G.;
Brazilian Journal of Physics , 2005, DOI: 10.1590/S0103-97332005000700023
Abstract: we calculate the casimir energy associated with abelian gauge fields in real compact hyperbolic spaces. the cosmological applications of the vacuum energies are briefly considered.
Forms on Vector Bundles Over Compact Real Hyperbolic Manifolds  [PDF]
A. A. Bytsenko,A. E. Gon?alves,F. L. Williams
Physics , 2003, DOI: 10.1142/S0217751X03015465
Abstract: We study gauge theories based on abelian $p-$ forms on real compact hyperbolic manifolds. The tensor kernel trace formula and the spectral functions associated with free generalized gauge fields are analyzed.
Forms on vector bundles over compact hyperbolic manifolds and entropy bounds  [PDF]
A. A. Bytsenko,V. S. Mendes,A. C. Tort
Physics , 2003,
Abstract: We analyze gauge theories based on abelian $p-$forms in real compact hyperbolic manifolds. The explicit thermodynamic functions associated with skew--symmetric tensor fields are obtained via zeta--function regularization and the trace tensor kernel formula. Thermodynamic quantities in the high--temperature expansions are calculated and the entropy/energy ratios are established.
Estimates for the restriction of automorphic forms on hyperbolic manifolds to compact geodesic cycles  [PDF]
Jan M?llers,Bent ?rsted
Mathematics , 2013,
Abstract: We find estimates for the restriction of automorphic forms on hyperbolic manifolds to compact geodesic cycles. The geodesic cycles we study are themselves hyperbolic manifolds of lower dimension. The restriction of an automorphic form to such a geodesic cycle can be expanded into eigenfunctions of the Laplacian on the geodesic cycle. We prove exponential decay for the coefficients in this expansion.
Abelian duality on globally hyperbolic spacetimes  [PDF]
Christian Becker,Marco Benini,Alexander Schenkel,Richard J. Szabo
Mathematics , 2015,
Abstract: We study generalized electric/magnetic duality in Abelian gauge theory by combining techniques from locally covariant quantum field theory and Cheeger-Simons differential cohomology on the category of globally hyperbolic Lorentzian manifolds. Our approach generalizes previous treatments using the Hamiltonian formalism in a manifestly covariant way and without the assumption of compact Cauchy surfaces. We construct semi-classical configuration spaces and corresponding presymplectic Abelian groups of observables, which are quantized by the CCR-functor to the category of $C^*$-algebras. We demonstrate explicitly how duality is implemented as a natural isomorphism between quantum field theories. We apply this formalism to develop a fully covariant quantum theory of self-dual fields.
Forms on Vector Bundles Over Hyperbolic Manifolds and the Conformal Anomaly  [PDF]
A. A. Bytsenko,E. Elizalde,R. A. Ulhoa
Mathematics , 2003, DOI: 10.1088/0305-4470/37/6/036
Abstract: We study gauge theories based on abelian $p-$forms on real compact hyperbolic manifolds. An explicit formula for the conformal anomaly corresponding to skew--symmetric tensor fields is obtained, by using zeta--function regularization and the trace tensor kernel formula. Explicit exact and numerical values of the anomaly for $p-$forms of order up to $p=4$ in spaces of dimension up to $n=10$ are then calculated.
Cycles in hyperbolic manifolds of non-compact type and Fourier coefficients of Siegel modular forms  [PDF]
Jens Funke,John Millson
Mathematics , 2001,
Abstract: Throughout the 1980's, Kudla and the second named author studied integral transforms from rapidly decreasing closed differential forms on arithmetic quotients of the symmetric spaces of orthogonal and unitary groups to spaces of classical Siegel and Hermitian modular forms. These transforms came from the theory of dual reductive pairs and the theta correspondence. They computed the Fourier expansion of these transforms in terms of periods over certain totally geodesic cycles . This also gave rise to the realization of intersection numbers of these `special' cycles with cycles with compact support as Fourier coefficients of modular forms. The purpose of this paper is to initiate a systematic study of this transform for non rapidly decreasing differential forms by considering the case for the finite volume quotients of hyperbolic space coming from unit groups of isotropic quadratic forms over the rationals. We expect that many of the techniques and features of this case will carry over to the more general situation.
New Cases of Differential Rigidity for Non-Generic Partially Hyperbolic Actions  [PDF]
Zhenqi Wang
Mathematics , 2009,
Abstract: We prove the locally differentiable rigidity of generic partially hyperbolic abelian algebraic high-rank actions on compact homogeneous spaces obtained from split symplectic Lie groups. We also gave a non-generic action rigidity example on compact homogeneous spaces obtained from SL(2n,R) or SL(2n,C). The conclusions are based on geometric Katok-Damjanovic way and progress towards computations of the generating relations in these groups.
Valdivia compact Abelian groups  [PDF]
Wieslaw Kubi?
Mathematics , 2007, DOI: 10.1007/BF03191818
Abstract: Let R denote the smallest class of compact spaces containing all metric compacta and closed under limits of continuous inverse sequences of retractions. Class R is striclty larger than the class of Valdivia compact spaces. We show that every compact connected Abelian group which is a topological retract of a space from class R is necessarily isomorphic to a product of metric groups. This completes the result of V. Uspenskij and the author, where a compact connected Abelian group outside class R has been described.
Local Rigidity of Partially Hyperbolic Actions  [PDF]
Zhenqi Wang
Mathematics , 2009,
Abstract: We consider partially hyperbolic abelian algebraic high-rank actions on compact homogeneous spaces obtained from simple indefinite orthogonal and unitary groups. In the first part of the paper, we show local differentiable rigidity for such actions. The conclusions are based on progress towards computations of the Schur multipliers of these non-split groups, which is the main aim of the second part.
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