scholarly journals Spacetime granularity from finite-dimensionality of local observable algebras

2020 ◽  
Vol 37 (4) ◽  
pp. 045014
Author(s):  
Matti Raasakka
Keyword(s):  
Local Observable ◽  
Finite Dimensionality

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.

scholarly journals Entanglement quantification through local observable correlations

2007 ◽  
Vol 75 (1) ◽  
Author(s):  
Christian Kothe ◽  
Gunnar Björk
Keyword(s):  
Local Observable

On the time periodic thermistor problem

2004 ◽  
Vol 15 (1) ◽  
pp. 55-77 ◽  
Author(s):  
WALTER ALLEGRETTO ◽  
YANPING LIN ◽  
SHUQING MA
Keyword(s):  
Periodic Solutions ◽  
Degree Theory ◽  
Time Behaviour ◽  
Uniform Attractor ◽  
Long Time Behaviour ◽  
Galerkin Approximations ◽  
Long Time ◽  
Finite Dimensionality ◽  
Time Periodic Solutions ◽  
Time Periodic

In this paper we study a nonlocal parabolic/elliptic system which models thermistor behaviour in cases where heat losses to the surrounding gas play a significant role. The existence of time periodic solutions for the system is established through Faedo-Galerkin approximations and the Leray–Schauder degree theory. We show that for the small gas pressure case, the temperature of the time periodic solutions is positive. Moreover we consider the long time behaviour of the system and prove the existence of a uniform attractor. Finally, the finite dimensionality of the attractor is discussed.

scholarly journals Homological characterizations of the approximation property for Banach spaces

1992 ◽  
Vol 34 (2) ◽  
pp. 229-239 ◽  
Author(s):  
Yu. V. Selivanov
Keyword(s):  
Banach Space ◽  
Banach Algebra ◽  
Banach Spaces ◽  
Cohomology Group ◽  
Approximation Property ◽  
Three Dimensional ◽  
Nuclear Operators ◽  
Finite Dimensionality

Let E be a Banach space, and let N(E) be the Banach algebra of all nuclear operators on E. In this work, we shall study the homological properties of this algebra. Some of these properties turn out to be equivalent to the (Grothendieck) approximation property for E. These include:(i) biprojectivity of N(E);(ii) biflatness of N(E);(iii) homological finite-dimensionality of N(E);(iv) vanishing of the three-dimensional cohomology group, H3(N(E), N(E)).

SYMMETRIES IN THEORY OF LOCAL OBSERVABLES AND THE CHOICE OF THE NET OF LOCAL ALGEBRAS

1992 ◽  
Vol 04 (spec01) ◽  
pp. 1-14 ◽  
Author(s):  
HUZIHIRO ARAKI
Keyword(s):  
Scattering Theory ◽  
Local Observable ◽  
Particle Spectrum ◽  
Massive Scalar ◽  
Local Algebras ◽  
Local Observables ◽  
Physical Consequences ◽  
Sector Theory ◽  
Internal Symmetries

For a given net of algebras of local observables, satisfying standard assumptions, we propose the problem of classifying a net of subalgebras which provides the same physical consequences (possibly via Doplicher-Haag-Roberts sector theory) such as particle spectrum and scattering theory. The notion of symmetry of the net of local algebras are introduced and its geometrical aspects are analyzed, with the conclusion that the net reproduces the geometry of supporting regions to some extent. The internal symmetries provides a possible net of subalgebras, as is discussed by Doplicher, Haag and Roberts. We discuss other possibilities by generating subalgebras from a local observable. Results and problems for the simple case of a neutral massive scalar free Held are summarized.

scholarly journals Bounds on Mixed State Entanglement

Entropy ◽  
2020 ◽  
Vol 22 (1) ◽  
pp. 62 ◽  
Author(s):  
Bruno Leggio ◽  
Anna Napoli ◽  
Hiromichi Nakazato ◽  
Antonino Messina
Keyword(s):  
Mixed State ◽  
General Framework ◽  
Quantum Correlations ◽  
Thermal Entanglement ◽  
Mixed States ◽  
Clear Explanation ◽  
Finite Dimensionality ◽  
Partial Transpose ◽  
The Subject

In the general framework of d 1 × d 2 mixed states, we derive an explicit bound for bipartite negative partial transpose (NPT) entanglement based on the mixedness characterization of the physical system. The derived result is very general, being based only on the assumption of finite dimensionality. In addition, it turns out to be of experimental interest since some purity-measuring protocols are known. Exploiting the bound in the particular case of thermal entanglement, a way to connect thermodynamic features to the monogamy of quantum correlations is suggested, and some recent results on the subject are given a physically clear explanation.

The finite-dimensionality problem for Busemann G-spaces

1977 ◽  
Vol 18 (1) ◽  
pp. 159-161 ◽  
Author(s):  
V. N. Berestovskii
Keyword(s):  
Finite Dimensionality
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