scholarly journals Topological surprises in de Sitter QFT in two-dimensions

2018 ◽  
Vol 33 (34) ◽  
pp. 1845009 ◽  
Author(s):  
Henri Epstein ◽  
Ugo Moschella
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Thermal State ◽  
Two Dimensions ◽  
Quantum Field ◽  
De Sitter ◽  
Sitter Spacetime ◽  
Klein Gordon ◽  
New Type ◽  
Two Universes

Motivated by the study of soluble models of quantum field theory, we illustrate a new type of topological effect by comparing the constructions of canonical Klein–Gordon quantum fields on the two-dimensional de Sitter spacetime as opposed to its double covering. We show that while the commutators of the two fields coincide locally, the global topological differences make the theories drastically different. Many of the well-known features of de Sitter quantum field theory disappear. In particular, there is nothing like a Bunch–Davies vacuum. Correspondingly, even though the local horizon structure is the same for the two universes, there is no Hawking–Gibbons thermal state. Finally, there is no complementary series of fields.

Quantization and topology: SL(2,R)-de Sitter invariant fields in two dimensions

2020 ◽  
Vol 35 (02n03) ◽  
pp. 2040018
Author(s):  
Henri Epstein ◽  
Ugo Moschella
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Two Dimensions ◽  
Quantum Field ◽  
Two Dimensional ◽  
De Sitter ◽  
Cosmological Background ◽  
Local Commutativity ◽  
And Topology ◽  
The Many

We explore the interplay between quantization, local commutativity and the analyticity properties of the two-point functions of a quantum field in a non trivial topological cosmological background in the example of the two-dimensional de Sitter manifold and its double covering. The global topological differences make the many of the well-known features of de Sitter quantum field theory disappear. In particular there is nothing like a Bunch-Davies vacuum and there are no [Formula: see text]-invariant fields whose mass is less than 1/2.

scholarly journals Finite lifespan of solutions of the semilinear wave equation in the Einstein–de Sitter spacetime

2019 ◽  
Vol 32 (07) ◽  
pp. 2050018 ◽  
Author(s):  
Anahit Galstian ◽  
Karen Yagdjian
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Wave Equation ◽  
De Sitter Spacetime ◽  
Quantum Field ◽  
De Sitter ◽  
Semilinear Wave Equation ◽  
Sitter Spacetime ◽  
Text Model ◽  
De Sitter Universe

We examine the solutions of the semilinear wave equation, and, in particular, of the [Formula: see text] model of quantum field theory in the curved spacetime. More exactly, for [Formula: see text] we prove that the solution of the massless self-interacting scalar field equation in the Einstein–de Sitter universe has finite lifespan.

scholarly journals Classical Simulations of Quantum Field Theory in Curved Spacetime I: Fermionic Hawking-Hartle Vacua from a Staggered Lattice Scheme

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 351
Author(s):  
Adam G. M. Lewis ◽  
Guifré Vidal
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Unruh Effect ◽  
Dirac Fermions ◽  
Quantum Field ◽  
De Sitter ◽  
Curved Spacetime ◽  
Expectation Values ◽  
Sitter Spacetime ◽  
The Continuum

We numerically compute renormalized expectation values of quadratic operators in a quantum field theory (QFT) of free Dirac fermions in curved two-dimensional (Lorentzian) spacetime. First, we use a staggered-fermion discretization to generate a sequence of lattice theories yielding the desired QFT in the continuum limit. Numerically-computed lattice correlators are then used to approximate, through extrapolation, those in the continuum. Finally, we use so-called point-splitting regularization and Hadamard renormalization to remove divergences, and thus obtain finite, renormalized expectation values of quadratic operators in the continuum. As illustrative applications, we show how to recover the Unruh effect in flat spacetime and how to compute renormalized expectation values in the Hawking-Hartle vacuum of a Schwarzschild black hole and in the Bunch-Davies vacuum of an expanding universe described by de Sitter spacetime. Although here we address a non-interacting QFT using free fermion techniques, the framework described in this paper lays the groundwork for a series of subsequent studies involving simulation of interacting QFTs in curved spacetime by tensor network techniques.

scholarly journals How low can vacuum energy go when your fields are finite-dimensional?

2019 ◽  
Vol 28 (14) ◽  
pp. 1944006
Author(s):  
ChunJun Cao ◽  
Aidan Chatwin-Davies ◽  
Ashmeet Singh
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Degrees Of Freedom ◽  
Vacuum Energy ◽  
Quantum Field ◽  
Locally Finite ◽  
Finite Dimensional ◽  
Finite Dimensionality ◽  
Klein Gordon ◽  
Dimensional Version

According to the holographic bound, there is only a finite density of degrees of freedom in space when gravity is taken into account. Conventional quantum field theory does not conform to this bound, since in this framework, infinitely many degrees of freedom may be localized to any given region of space. In this paper, we explore the viewpoint that quantum field theory may emerge from an underlying theory that is locally finite-dimensional, and we construct a locally finite-dimensional version of a Klein–Gordon scalar field using generalized Clifford algebras. Demanding that the finite-dimensional field operators obey a suitable version of the canonical commutation relations makes this construction essentially unique. We then find that enforcing local finite dimensionality in a holographically consistent way leads to a huge suppression of the quantum contribution to vacuum energy, to the point that the theoretical prediction becomes plausibly consistent with observations.

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