scholarly journals Reflected entropy for free scalars

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Pablo Bueno ◽  
Horacio Casini
Keyword(s):  
Mutual Information ◽  
Scalar Fields ◽  
Monotonicity Property ◽  
Cross Ratio ◽  
Free Fermion ◽  
Length Scales ◽  
General Inequality ◽  
Fermionic Case ◽  
Free Scalar ◽  
Arbitrary Dimensions

Abstract We continue our study of reflected entropy, R(A, B), for Gaussian systems. In this paper we provide general formulas valid for free scalar fields in arbitrary dimensions. Similarly to the fermionic case, the resulting expressions are fully determined in terms of correlators of the fields, making them amenable to lattice calculations. We apply this to the case of a (1 + 1)-dimensional chiral scalar, whose reflected entropy we compute for two intervals as a function of the cross-ratio, comparing it with previous holographic and free-fermion results. For both types of free theories we find that reflected entropy satisfies the conjectural monotonicity property R(A, BC) ≥ R(A, B). Then, we move to (2 + 1) dimensions and evaluate it for square regions for free scalars, fermions and holography, determining the very-far and very-close regimes and comparing them with their mutual information counterparts. In all cases considered, both for (1 + 1)- and (2 + 1)-dimensional theories, we verify that the general inequality relating both quantities, R(A, B) ≥ I (A, B), is satisfied. Our results suggest that for general regions characterized by length-scales LA ∼ LB ∼ L and separated a distance ℓ, the reflected entropy in the large-separation regime (x ≡ L/ℓ ≪ 1) behaves as R(x) ∼ −I(x) log x for general CFTs in arbitrary dimensions.

scholarly journals Weak cosmic censorship with self-interacting scalar and bound on charge to mass ratio

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Yan Song ◽  
Tong-Tong Hu ◽  
Yong-Qiang Wang
Keyword(s):  
Scalar Field ◽  
Scalar Fields ◽  
Cosmic Censorship ◽  
Mass Ratio ◽  
Quartic Coupling ◽  
Scalar Theory ◽  
Free Scalar ◽  
The One ◽  
Nonzero Scalar ◽  
Large Charge

Abstract We study the model of four-dimensional Einstein-Maxwell-Λ theory minimally coupled to a massive charged self-interacting scalar field, parameterized by the quartic and hexic couplings, labelled by λ and β, respectively. In the absence of scalar field, there is a class of counterexamples to cosmic censorship. Moreover, we investigate the full nonlinear solution with nonzero scalar field included, and argue that these counterexamples can be removed by assuming charged self-interacting scalar field with sufficiently large charge not lower than a certain bound. In particular, this bound on charge required to preserve cosmic censorship is no longer precisely the weak gravity bound for the free scalar theory. For the quartic coupling, for λ < 0 the bound is below the one for the free scalar fields, whereas for λ > 0 it is above. Meanwhile, for the hexic coupling the bound is always above the one for the free scalar fields, irrespective of the sign of β.

CONFORMAL COUPLING AND FOLDY–WOUTHUYSEN TRANSFORMATION

2003 ◽  
Vol 18 (12) ◽  
pp. 867-873 ◽  
Author(s):  
ANTONIO ACCIOLY ◽  
HAROLD BLAS
Keyword(s):  
Scalar Field ◽  
Wide Class ◽  
Mean Square ◽  
Fermionic Case ◽  
Free Scalar ◽  
The Mean

The propagation of a free scalar field ϕ with mass m in a curved background is generally described by the equation (gμν∇μ∇ν + m2 + ξR)ϕ = 0. There exist some arguments in the literature that seem to favor the conformal coupling to the detriment of the minimal one. However, the majority of these claims are inconclusive. Here we show that the exact Foldy–Wouthuysen transformation for spin-0 particle coupled to a wide class of static spacetime metrics exists independently of the value of ξ. Nevertheless, if the coupling is of the conformal type, the gravitational Darwin-like term has an uncomplicated structure and it is proportional to the corresponding term in the fermionic case. In addition, an independent computation of this term, which has its origin in the zitterbewegung fluctuation of the boson's position with the mean square <(δr)2> ≈ 1/m2, gives a result that coincides with that obtained using the aforementioned exact transformation with ξ = 1/6.

scholarly journals Free Scalar Fields in Finite Volume Are Holographic

Universe ◽  
2019 ◽  
Vol 5 (12) ◽  
pp. 223
Author(s):  
Csaba Balázs
Keyword(s):  
Scalar Field ◽  
Surface Area ◽  
Finite Volume ◽  
Degrees Of Freedom ◽  
Scalar Fields ◽  
Flat Space ◽  
Linear Size ◽  
Energy Mode ◽  
Free Scalar ◽  
Quantized Field

This brief note presents a back-of-the-envelope calculation showing that the number of degrees of freedom of a free scalar field in expanding flat space equals the surface area of the Hubble volume in Planck units. The logic of the calculation is the following. The amount of energy in the Hubble volume scales with its linear size, consequently the volume can only contain a finite number of quantized field modes. Since the momentum of the lowest energy mode scales inversely with the linear size of the volume, the maximal number of such modes in the volume scales with its surface area. It is possible to show that when the number of field modes is saturated the modes are confined to the surface of the volume. Gravity only enters this calculation as a regulator, providing a finite volume that contains the field, the entire calculation is done in flat space. While this toy model is bound to be incomplete, it is potentially interesting because it reproduces the defining aspects of holography, and advocates a regularization of the quantum degrees of freedom based on Friedmann’s equation.

Free Scalar Fields

2016 ◽  
pp. 17-39
Author(s):  
Mikko Laine ◽  
Aleksi Vuorinen
Keyword(s):  
Scalar Fields ◽  
Free Scalar

scholarly journals κ-DEFORMED STATISTICS AND CLASSICAL FOUR-MOMENTUM ADDITION LAW

2008 ◽  
Vol 23 (09) ◽  
pp. 653-665 ◽  
Author(s):  
MARCIN DASZKIEWICZ ◽  
JERZY LUKIERSKI ◽  
MARIUSZ WORONOWICZ
Keyword(s):  
Minkowski Space ◽  
Fock Space ◽  
Scalar Fields ◽  
Cross Product ◽  
Creation And Annihilation Operators ◽  
Multiplication Rule ◽  
Symmetry Properties ◽  
Deformed Algebra ◽  
Free Scalar

We consider κ-deformed relativistic symmetries described algebraically by modified Majid–Ruegg bi-cross-product basis and investigate the quantization of field oscillators for the κ-deformed free scalar fields on κ-Minkowski space. By modification of standard multiplication rule, we postulate the κ-deformed algebra of bosonic creation and annihilation operators. Our algebra permits one to define the n-particle states with classical addition law for the four-momentum in a way which is not in contradiction with the nonsymmetric quantum four-momentum co-product. We introduce κ-deformed Fock space generated by our κ-deformed oscillators which satisfy the standard algebraic relations with modified κ-multiplication rule. We show that such a κ-deformed bosonic Fock space is endowed with the conventional bosonic symmetry properties. Finally we discuss the role of κ-deformed algebra of oscillators in field-theoretic noncommutative framework.

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