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.

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 Infinite dimensional Langevin equation and Fokker-Planck equation

1981 ◽  
Vol 81 ◽  
pp. 177-223 ◽  
Author(s):  
Yoshio Miyahara
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Hilbert Space ◽  
Partial Differential Equations ◽  
Langevin Equation ◽  
Planck Equation ◽  
Theory Theory ◽  
Quantum Field ◽  
Filtering Theory ◽  
Infinite Dimensional

Stochastic processes on a Hilbert space have been discussed in connection with quantum field theory, theory of partial differential equations involving random terms, filtering theory in electrical engineering and so forth, and the theory of those processes has greatly developed recently by many authors (A. B. Balakrishnan [1, 2], Yu. L. Daletskii [7], D. A. Dawson [8, 9], Z. Haba [12], R. Marcus [18], M. Yor [26]).

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 Area-Dependent Quantum Field Theory

2020 ◽  
Author(s):  
Ingo Runkel ◽  
Lóránt Szegedy
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
Two Dimensional ◽  
Positive Real ◽  
Yang Mills ◽  
Infinite Dimensional ◽  
Frobenius Algebras ◽  
Topological Quantum ◽  
Topological Theories

AbstractArea-dependent quantum field theory is a modification of two-dimensional topological quantum field theory, where one equips each connected component of a bordism with a positive real number—interpreted as area—which behaves additively under glueing. As opposed to topological theories, in area-dependent theories the state spaces can be infinite-dimensional. We introduce the notion of regularised Frobenius algebras in Hilbert spaces and show that area-dependent theories are in one-to-one correspondence to commutative regularised Frobenius algebras. We also provide a state sum construction for area-dependent theories. Our main example is two-dimensional Yang–Mills theory with compact gauge group, which we treat in detail.

ASYMPTOTICS OF INFINITE-DIMENSIONAL INTEGRALS WITH RESPECT TO SMOOTH MEASURES I

1999 ◽  
Vol 02 (04) ◽  
pp. 529-556 ◽  
Author(s):  
S. ALBEVERIO ◽  
V. STEBLOVSKAYA
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Probability Measures ◽  
Quantum Field ◽  
Laplace Method ◽  
Large Parameter ◽  
Infinite Dimensions ◽  
Infinite Dimensional ◽  
Smooth Measures ◽  
Minimum Points

This is the first part of a work on Laplace method for the asymptotics of integrals with respect to smooth measures and a large parameter developed in infinite dimensions. Here the case of finitely many (nondegenerate) minimum points is studied in details. Applications to large parameters behavior of expectations with respect to probability measures occurring in the study of systems of statistical mechanics and quantum field theory are mentioned.

scholarly journals Infinite-dimensional Lie algebras in 4D conformal quantum field theory

2008 ◽  
Vol 41 (19) ◽  
pp. 194002 ◽  
Author(s):  
Bojko Bakalov ◽  
Nikolay M Nikolov ◽  
Karl-Henning Rehren ◽  
Ivan Todorov
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Lie Algebras ◽  
Quantum Field ◽  
Infinite Dimensional
Sign in / Sign up

Export Citation Format

Share Document