IRIS Pol. Torinohttps://iris.polito.itIl sistema di repository digitale IRIS acquisisce, archivia, indicizza, conserva e rende accessibili prodotti digitali della ricerca.Sat, 28 Mar 2020 12:45:20 GMT2020-03-28T12:45:20Z10321Zeta-function regularization of one-loop effective potentials in anti-de Sitter spacetimehttp://hdl.handle.net/11583/2497955Titolo: Zeta-function regularization of one-loop effective potentials in anti-de Sitter spacetime
Abstract: We use the zeta-function technique to calculate the one-loop effective potential for a scalar field in anti-de Sitter (AdS) space. The zeta function is computed exactly on the four-dimensional hyperbolic space H-4, the Euclidean section appropriate for AdS space. The structure of the ultraviolet divergences is shown to agree with previous calculations where Pauli-Villars or some version of dimensional regularization was used. The finite part of the effective potential is given explicitly by an integral over a variable related to the spectrum of the Laplace-Beltrami operator on H-4.
Tue, 01 Jan 1991 00:00:00 GMThttp://hdl.handle.net/11583/24979551991-01-01T00:00:00ZA Generalization of a Theorem of Mammanahttp://hdl.handle.net/11583/2424025Titolo: A Generalization of a Theorem of Mammana
Abstract: We prove that any linear ordinary differential operator with complex-valued coefficients continuous in an interval I can be factored into a product of first-order operators globally defined on I. This generalizes a theorem of Mammana for the case of real-valued coefficients.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/11583/24240252011-01-01T00:00:00ZStress-energy tensors in anti-de Sitter spacetimehttp://hdl.handle.net/11583/2497954Titolo: Stress-energy tensors in anti-de Sitter spacetime
Abstract: The stress-energy tensors are computed for scalar and spinor fields with arbitrary mass in anti-de Sitter spacetime using the ζ-function technique. The results are compared with those obtained by Pauli-Villars regularization. It is found that they agree with one another. The trace anomaly for the Wess-Zumino model (the scalar supermultiplet) in anti-de Sitter spacetime is studied. It is concluded that the trace anomaly must take the "conventional" value in this model although the physical significance of the stress-energy tensor is not clear in anti-de Sitter spacetime. The relation between the ζ-function and Pauli-Villars methods in an arbitrary space is also clarified.
Wed, 01 Jan 1992 00:00:00 GMThttp://hdl.handle.net/11583/24979541992-01-01T00:00:00ZThe biradial Paley-Wiener theorem for the Helgason Fourier transform on Damek-Ricci spaceshttp://hdl.handle.net/11583/2549738Titolo: The biradial Paley-Wiener theorem for the Helgason Fourier transform on Damek-Ricci spaces
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/11583/25497382014-01-01T00:00:00ZA fresh look at linear ordinary differential equations with constant coefficients. Revisiting the impulsive response method using factorizationhttp://hdl.handle.net/11583/2659525Titolo: A fresh look at linear ordinary differential equations with constant coefficients. Revisiting the impulsive response method using factorization
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/11583/26595252016-01-01T00:00:00ZThe Helgason Fourier transform for homogeneous vector bundles over compact Riemannian symmetric spaces--the local theoryhttp://hdl.handle.net/11583/1398370Titolo: The Helgason Fourier transform for homogeneous vector bundles over compact Riemannian symmetric spaces--the local theory
Abstract: The Helgason Fourier transform on noncompact Riemannian symmetric spaces $G/K$
is generalized to the homogeneous vector bundles over the compact dual spaces
$U/K$. The scalar theory on $U/K$ was considered by Sherman
(the local theory for $U/K$ of arbitrary rank, and the global theory for $U/K$
of rank one). In this paper we extend the local theory of Sherman to
arbitrary homogeneous vector bundles on $U/K$.
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/11583/13983702005-01-01T00:00:00ZGeodesic spheres and non radial eigenfunctions on Damek-Ricci spaceshttp://hdl.handle.net/11583/2507450Titolo: Geodesic spheres and non radial eigenfunctions on Damek-Ricci spaces
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/11583/25074502013-01-01T00:00:00ZOn the analytic continuation of the Minakshisundaram-Pleijel zeta function for compact symmetric spaces of rank onehttp://hdl.handle.net/11583/1398362Titolo: On the analytic continuation of the Minakshisundaram-Pleijel zeta function for compact symmetric spaces of rank one
Wed, 01 Jan 1997 00:00:00 GMThttp://hdl.handle.net/11583/13983621997-01-01T00:00:00ZA generalization of the Cartan-Helgason theorem for Riemannian symmetric spaces of rank onehttp://hdl.handle.net/11583/1398371Titolo: A generalization of the Cartan-Helgason theorem for Riemannian symmetric spaces of rank one
Abstract: Let $U/K$ be a compact Riemannian symmetric space with $U$ simply connected and
$K$ connected. Let $G/K$ be the noncompact dual space, with
$G$ and $U$ analytic subgroups of the
simply connected complexification $G^{\mathbb{C}}$. Let $G=KAN$ be an Iwasawa
decomposition of $G$, and let $M$ be the centralizer of $A$ in $K$.
For $\d\in\widehat{U}$, let $\m$ be the highest restricted weight of $\d$, and let
$\s$ be the $M$-type acting in the highest restricted weight subspace of $H_{\d}$.
Fix a $K$-type $\tau$. In \cite{CAMPO} the following result was proved. Assume $U/K$ has rank one.
Then $\d|_K$ contains $\tau$
if and only if 1) $\tau|_M$ contains $\s$ and 2) $\m\in\m_{\s,\tau}+\L_{sph}$, where $\L_{sph}$ is the
set of highest restricted spherical weights, and $\m_{\s,\tau}$ is a suitable element of
$\mathfrak{a}^{\ast}$
uniquely determined by $\s$ and $\tau$. In this paper we obtain an explicit formula for this element
in the case of $U/K=S^n,\,P^n(\mathbb{C}),\,P^n(\mathbb{H})$. This
gives a generalization of the Cartan-Helgason theorem to arbitrary $K$-types
on these rank one symmetric spaces.
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/11583/13983712005-01-01T00:00:00ZThe Helgason Fourier transform for homogeneous vector bundles over Riemannian symmetric spaceshttp://hdl.handle.net/11583/1398361Titolo: The Helgason Fourier transform for homogeneous vector bundles over Riemannian symmetric spaces
Wed, 01 Jan 1997 00:00:00 GMThttp://hdl.handle.net/11583/13983611997-01-01T00:00:00Z