scholarly journals Momentum-space entanglement in scalar field theory on fuzzy spheres

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Shoichi Kawamoto ◽  
Tsunehide Kuroki
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Momentum Space ◽  
Degrees Of Freedom ◽  
Entanglement Entropy ◽  
Noncommutative Space ◽  
Quantum Field ◽  
Fuzzy Sphere ◽  
Scalar Field Theory ◽  
Different Characteristics

Abstract Quantum field theory defined on a noncommutative space is a useful toy model of quantum gravity and is known to have several intriguing properties, such as nonlocality and UV/IR mixing. They suggest novel types of correlation among the degrees of freedom of different energy scales. In this paper, we investigate such correlations by the use of entanglement entropy in the momentum space. We explicitly evaluate the entanglement entropy of scalar field theory on a fuzzy sphere and find that it exhibits different behaviors from that on the usual continuous sphere. We argue that these differences would originate in different characteristics; non-planar contributions and matrix regularizations. It is also found that the mutual information between the low and the high momentum modes shows different scaling behaviors when the effect of a cutoff becomes important.

scholarly journals Entanglement entropy in scalar field theory on the fuzzy sphere

2016 ◽  
Vol 2016 (2) ◽  
pp. 023B03 ◽  
Author(s):  
Shizuka Okuno ◽  
Mariko Suzuki ◽  
Asato Tsuchiya
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Entanglement Entropy ◽  
Fuzzy Sphere ◽  
Scalar Field Theory

scholarly journals SHORT DISTANCE PROPERTIES FROM LARGE DISTANCE BEHAVIOR

1998 ◽  
Vol 13 (23) ◽  
pp. 4101-4122 ◽  
Author(s):  
PAUL MANSFIELD ◽  
MARCOS SAMPAIO ◽  
JIANNIS PACHOS
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scalar Field ◽  
Large Distance ◽  
Short Distance ◽  
Quantum Field ◽  
Scalar Field Theory ◽  
Expansion Coefficients ◽  
Distance Behavior ◽  
Distance Properties

For slowly varying fields the vacuum functional of a quantum field theory may be expanded in terms of local functionals. This expansion satisfies its own form of the Schrödinger equation from which the expansion coefficients can be found. For scalar field theory in 1+1 dimensions we show that this approach correctly reproduces the short-distance properties as contained in the counterterms. We also describe an approximate simplification that occurs for the sine–Gordon and sinh–Gordon vacuum functionals.

scholarly journals THE BOLTZMANN EQUATION IN SCALAR FIELD THEORY

1998 ◽  
Vol 13 (24) ◽  
pp. 4281-4288 ◽  
Author(s):  
F. T. BRANDT ◽  
J. FRENKEL ◽  
A. GUERRA
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Temperature Limit ◽  
Equation Of Motion ◽  
Green Functions ◽  
Static Case ◽  
Quantum Field ◽  
Scalar Field Theory ◽  
High Temperature Limit ◽  
Classical Transport

We derive the classical transport equation, in scalar field theory with a g2V(ϕ) interaction, from the equation of motion for the quantum field. We obtain a very simple, but iterative, expression for the effective action Γ which generates all the n-point Green functions in the high-temperature limit. An explicit and closed form is given for Γ in the static case.

scholarly journals On the renormalization of entanglement entropy

2021 ◽  
Vol 31 (1) ◽  
Author(s):  
Jin-Yi Pang ◽  
Jiunn-Wei Chen
Keyword(s):  
Field Theory ◽  
Black Hole ◽  
Scalar Field ◽  
Entanglement Entropy ◽  
Black Hole Entropy ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Replica Trick ◽  
Dimensional Spacetime

AbstractThe renormalization of entanglement entropy of quantum field theories is investigated in the simplest setting with a λϕ4 scalar field theory. The 3+1 dimensional spacetime is separated into two regions by an infinitely flat 2-dimensional interface. The entanglement entropy of the system across the interface has an elegant geometrical interpretation using the replica trick, which requires putting the field theory on a curved spacetime background. We demonstrate that the theory, and hence the entanglement entropy, is renormalizable at order λ once all the relevant operators up to dimension 4 are included in the action. This exercise has a one-to-one correspondence to entanglement entropy interpretation of the black hole entropy which suggests that our treatment is sensible. Our study suggests that entanglement entropy is renormalizable and is a physical quantity.

scholarly journals A short introduction to κ-deformation

2017 ◽  
Vol 32 (35) ◽  
pp. 1730026 ◽  
Author(s):  
J. Kowalski-Glikman
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Minkowski Space ◽  
Momentum Space ◽  
Short Review ◽  
Short Introduction ◽  
Scalar Field Theory ◽  
Poincaré Algebra ◽  
Free Scalar

In this short review we describe some aspects of [Formula: see text]-deformation. After discussing the algebraic and geometric approaches to [Formula: see text]-Poincaré algebra we construct the free scalar field theory, both on noncommutative [Formula: see text]-Minkowski space and on curved momentum space. Finally, we make a few remarks concerning the interacting scalar field.

scholarly journals Renormalization in open quantum field theory. Part I. Scalar field theory

2017 ◽  
Vol 2017 (11) ◽  
Author(s):  
Avinash Baidya ◽  
Chandan Jana ◽  
R. Loganayagam ◽  
Arnab Rudra
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scalar Field ◽  
Quantum Field ◽  
Scalar Field Theory ◽  
Open Quantum
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