Field operators and their spectral properties in finite-dimensional quantum field theory

1985 ◽  
Vol 15 (3) ◽  
pp. 319-331
Author(s):  
Vladimir Naroditsky
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Spectral Properties ◽  
Quantum Field ◽  
Finite Dimensional

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 Some remarks on representations up to homotopy

2016 ◽  
Vol 13 (03) ◽  
pp. 1650024
Author(s):  
Giorgio Trentinaglia ◽  
Chenchang Zhu
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Compact Group ◽  
Compact Groups ◽  
Quantum Field ◽  
Algebraic Quantum Field Theory ◽  
Trivial Bundle ◽  
Finite Dimensional ◽  
Algebraic Quantum

Motivated by the study of the interrelation between functorial and algebraic quantum field theory (AQFT), we point out that on any locally trivial bundle of compact groups, representations up to homotopy are enough to separate points by means of the associated representations in cohomology. Furthermore, we observe that the derived representation category of any compact group is equivalent to the category of ordinary (finite-dimensional) representations of the group.

scholarly journals The Hilbert space of quantum gravity is locally finite-dimensional

2017 ◽  
Vol 26 (12) ◽  
pp. 1743013 ◽  
Author(s):  
Ning Bao ◽  
Sean M. Carroll ◽  
Ashmeet Singh
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Hilbert Space ◽  
Quantum Gravity ◽  
Density Operator ◽  
Small Region ◽  
Quantum Field ◽  
Locally Finite ◽  
Finite Dimensional ◽  
Model Independent

We argue in a model-independent way that the Hilbert space of quantum gravity is locally finite-dimensional. In other words, the density operator describing the state corresponding to a small region of space, when such a notion makes sense, is defined on a finite-dimensional factor of a larger Hilbert space. Because quantum gravity potentially describes superpositions of different geometries, it is crucial that we associate Hilbert-space factors with spatial regions only on individual decohered branches of the universal wave function. We discuss some implications of this claim, including the fact that quantum-field theory cannot be a fundamental description of nature.

scholarly journals MODULAR THEORY AND GEOMETRY

2000 ◽  
Vol 12 (01) ◽  
pp. 139-158 ◽  
Author(s):  
B. SCHROER ◽  
H.-W. WIESBROCK
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
Hidden Symmetries ◽  
Modular Theory ◽  
Infinite Dimensional ◽  
Finite Dimensional

In this communication we present some new results on modular theory in the context of quantum field theory. In doing this we develop some new proposals how to generalize concepts of finite dimensional geometrical actions to infinite dimensional "hidden" symmetries. The latter are of a purely modular origin and remain hidden in any quantization approach. The spirit of this work is more on a programmatic side, with many details remaining to be elaborated.

ON THE REPRESENTATION INDEPENDENCE OF TOPOLOGICAL EFFECTS IN QUANTUM FIELD THEORY

1989 ◽  
Vol 04 (17) ◽  
pp. 4627-4642
Author(s):  
MATTHIAS BLAU
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Configuration Space ◽  
Homogeneous Spaces ◽  
Geometric Quantization ◽  
Line Bundles ◽  
Quantum Field ◽  
Momentum Representation ◽  
Formal Representation ◽  
Finite Dimensional

The formal representation-independence of topological effects in quantum field theory like those associated with monopole line bundles on the configuration space or vacuum angles is established within the framework of geometric quantization by studying simple finite-dimensional examples. Some deficiencies of the ordinary momentum representation are pointed out and an alternative generalization of the momentum representation to homogeneous spaces is suggested.

scholarly journals EXACT FORMFACTORS IN THE ONE-LOOP CURVED-SPACE QED AND THE NONLOCAL MULTIPLICATIVE ANOMALY

2010 ◽  
Vol 25 (11) ◽  
pp. 2382-2390 ◽  
Author(s):  
BRUNO GonÇALVES ◽  
GUILHERME DE BERREDO-PEIXOTO ◽  
ILYA L. SHAPIRO
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Differential Operators ◽  
Quantum Field ◽  
Curved Space ◽  
Finite Dimensional ◽  
Qualitative Level ◽  
The Difference ◽  
The One ◽  
Considerable Work

The well-known formula det (A · B) = det A · det B can be easily proved for finite dimensional matrices but it may be incorrect for the functional determinants of differential operators, including the ones which are relevant for Quantum Field Theory applications. Considerable work has been done to prove that this equality can be violated, but in all previously known cases the difference could be reduced to renormalization ambiguity. We present the first example, where the difference between the two functional determinants is a nonlocal expression and therefore can not be explained by the renormalization ambiguity. Moreover, through the use of other even dimensions we explain the origin of this difference at qualitative level.

Sign in / Sign up

Export Citation Format

Share Document