1,721,038 research outputs found
Thermal State with Quadratic Interaction
No full textWe consider the perturbative construction, proposed in Fredenhagen and Lindner (Commun Math Phys 332:895, 2014), for a thermal state Ω β,λV{f} for the theory of a real scalar Klein–Gordon field φ with interacting potential V{ f}. Here, f is a space-time cut-off of the interaction V, and λ is a perturbative parameter. We assume that V is quadratic in the field φ and we compute the adiabatic limit f→ 1 of the state Ω β,λV{f} . The limit is shown to exist; moreover, the perturbative series in λ sums up to the thermal state for the corresponding (free) theory with potential V. In addition, we exploit the same methods to address a similar computation for the non-equilibrium steady state (NESS) Ruelle (J Stat Phys 98:57–75, 2000) recently constructed in Drago et al. (Commun Math Phys 357:267, 2018)
On the adiabatic limit of Hadamard states
No full textWe consider the adiabatic limit of Hadamard states for free quantum Klein–Gordon fields, when the background metric and the field mass are slowly varied from their initial to final values. If the Klein–Gordon field stays massive, we prove that the adiabatic limit of the initial vacuum state is the (final) vacuum state, by extending to the symplectic framework the adiabatic theorem of Avron–Seiler–Yaffe. In cases when only the field mass is varied, using an abstract version of the mode decomposition method we can also consider the case when the initial or final mass vanishes, and the initial state is either a thermal state or a more general Hadamard state
The notion of observable and the moment problem for ∗ -algebras and their GNS representations
No full textWe address some usually overlooked issues concerning the use of ∗ -algebras in quantum theory and their physical interpretation. If A is a ∗ -algebra describing a quantum system and ω: A→ C a state, we focus, in particular, on the interpretation of ω(a) as expectation value for an algebraic observable a= a∗∈ A, studying the problem of finding a probability measure reproducing the moments {ω(an)}n∈N. This problem enjoys a close relation with the selfadjointness of the (in general only symmetric) operator πω(a) in the GNS representation of ω and thus it has important consequences for the interpretation of a as an observable. We provide physical examples (also from QFT) where the moment problem for {ω(an)}n∈N does not admit a unique solution. To reduce this ambiguity, we consider the moment problem for the sequences {ωb(an)}n∈N, being b∈ A and ωb(·) : = ω(b∗· b). Letting μωb(a) be a solution of the moment problem for the sequence {ωb(an)}n∈N, we introduce a consistency relation on the family {μωb(a)}b∈A. We prove a 1-1 correspondence between consistent families {μωb(a)}b∈A and positive operator-valued measures (POVM) associated with the symmetric operator πω(a). In particular, there exists a unique consistent family of {μωb(a)}b∈A if and only if πω(a) is maximally symmetric. This result suggests that a better physical understanding of the notion of observable for general ∗ -algebras should be based on POVMs rather than projection-valued measure
Classical KMS Functionals and Phase Transitions in Poisson Geometry
Full text linkWe study the convex cone of not necessarily smooth measures satisfying the
classical KMS condition within the context of Poisson geometry. We discuss the
general properties of KMS measures and its relation with the underlying Poisson
geometry in analogy to Weinstein's seminal work in the smooth case. Moreover,
by generalizing results from the symplectic case, we focus on the case of
-Poisson manifolds, where we provide an almost complete characterization of
the convex cone of KMS measures.Comment: 47 page
Fundamental solutions for the wave operator on static Lorentzian manifolds with timelike boundary
No full textWe consider the wave operator on static, Lorentzian manifolds with timelike boundary, and we discuss the existence of advanced and retarded fundamental solutions in terms of boundary conditions. By means of spectral calculus, we prove that answering this question is equivalent to studying the self-adjoint extensions of an associated elliptic operator on a Riemannian manifold with boundary (M, g). The latter is diffeomorphic to any constant time hypersurface of the underlying background. In turn, assuming that (M, g) is of bounded geometry, this problem can be tackled within the framework of boundary triples. These consist of the assignment of two surjective, trace operators from the domain of the adjoint of the elliptic operator onto an auxiliary Hilbert space h, which is the third datum of the triple. Self-adjoint extensions of the underlying elliptic operator are in one-to-one correspondence with self-adjoint operators Θ on h. On the one hand, we show that, for a natural choice of boundary triple, each Θ can be interpreted as the assignment of a boundary condition for the original wave operator. On the other hand, we prove that, for each such Θ , there exists a unique advanced and retarded fundamental solution. In addition, we prove that these share the same structural property of the counterparts associated with the wave operator on a globally hyperbolic spacetime
The algebra of Wick polynomials of a scalar field on a Riemannian manifold
No full textOn a connected, oriented, smooth Riemannian manifold without boundary we consider a real scalar field whose dynamics is ruled by E, a second-order elliptic partial differential operator of Laplace type. Using the functional formalism and working within the framework of algebraic quantum field theory and of the principle of general local covariance, first we construct the algebra of locally covariant observables in terms of equivariant sections of a bundle of smooth, regular polynomial functionals over the affine space of the parametrices associated to E. Subsequently, adapting to the case in hand a strategy first introduced by Hollands and Wald in a Lorentzian setting, we prove the existence of Wick powers of the underlying field, extending the procedure to smooth, local and polynomial functionals and discussing in the process the regularization ambiguities of such procedure. Subsequently we endow the space of Wick powers with an algebra structure, dubbed E-product, which plays in a Riemannian setting the same role of the time-ordered product for field theories on globally hyperbolic spacetimes. In particular, we prove the existence of the E-product and we discuss both its properties and the renormalization ambiguities in the underlying procedure. As the last step, we extend the whole analysis to observables admitting derivatives of the field configurations and we discuss the quantum Møller operator which is used to investigate interacting models at a perturbative level
Strict Deformation Quantization and Local Spin Interactions
No full textWe define a strict deformation quantization which is compatible with any Hamiltonian with local spin interaction (e.g. the Heisenberg Hamiltonian) for a spin chain. This is a generalization of previous results known for mean-field theories. The main idea is to study the asymptotic properties of a suitably defined algebra of sequences invariant under the group generated by a cyclic permutation. Our point of view is similar to the one adopted by Landsman, Moretti and van de Ven (Rev Math Phys 32(10):2050031, 2020, https://doi.org/10.1142/S0129055X20500312), who considered a strict deformation quantization for the case of mean-field theories. However, the methods for a local spin interaction are considerably more involved, due to the presence of a strictly smaller symmetry group
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
- …
