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 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.

Renormalization Group

2020 ◽  
pp. 289-318
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Renormalization Group ◽  
Critical Phenomena ◽  
Degrees Of Freedom ◽  
Gaussian Model ◽  
Coupling Constants ◽  
Quantum Field ◽  
Important Notion ◽  
Effective Hamiltonians

Chapter 8 introduces the key ideas of the renormalization group, including how they provide a theoretical scheme and a proper language to face critical phenomena. It covers the scaling transformations of a system and their implementations in the space of the coupling constants and reducing the degrees of freedom. From this analysis, the reader is led to the important notion of relevant, irrelevant and marginal operators and then to the universality of the critical phenomena. Furthermore, the chapter also covers (as regards the RG) transformation laws, effective Hamiltonians, the Gaussian model, the Ising model, operators of quantum field theory, universal ratios, critical exponents and β‎-functions.

scholarly journals QUANTUM FIELD THEORY ON CURVED BACKGROUNDS — A PRIMER

2013 ◽  
Vol 28 (17) ◽  
pp. 1330023 ◽  
Author(s):  
MARCO BENINI ◽  
CLAUDIO DAPPIAGGI ◽  
THOMAS-PAUL HACK
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Hilbert Space ◽  
Degrees Of Freedom ◽  
Algebraic Approach ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
System A ◽  
Step Procedure ◽  
Free Fields

Goal of this paper is to introduce the algebraic approach to quantum field theory on curved backgrounds. Based on a set of axioms, first written down by Haag and Kastler, this method consists of a two-step procedure. In the first one, it is assigned to a physical system a suitable algebra of observables, which is meant to encode all algebraic relations among observables, such as commutation relations. In the second step, one must select an algebraic state in order to recover the standard Hilbert space interpretation of a quantum system. As quantum field theories possess infinitely many degrees of freedom, many unitarily inequivalent Hilbert space representations exist and the power of such approach is the ability to treat them all in a coherent manner. We will discuss in detail the algebraic approach for free fields in order to give the reader all necessary information to deal with the recent literature, which focuses on the applications to specific problems, mostly in cosmology.

MESON-DIQUARK LOOP EXPANSION

1993 ◽  
Vol 08 (02) ◽  
pp. 277-300 ◽  
Author(s):  
M. LUTZ ◽  
J. PRASCHIFKA
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Effective Action ◽  
Degrees Of Freedom ◽  
Auxiliary Field ◽  
Quantum Field ◽  
Field Approach ◽  
Loop Expansion ◽  
Quark Models

We consider a general (nonlocal) four-fermion quantum field theory and show how the Cornwall-Jackiw-Tomboulis effective action can be systematically expanded in the number, η, of composite, bose loops. This is achieved by the introduction of auxiliary, bilocal fields which describe fermion-fermion and fermion-antifermion correlations. The η expansion can be understood as a generalization of the [Formula: see text] expansion and is of particular interest in quark models, for example, where the bilocal fields can be identified with meson and diquark degrees of freedom. Comparison with the usual loop (ħ) expansion reveals some unusual characteristics of the η expansion and throws light on recent studies of diquark degrees of freedom in which the auxiliary field approach is used.

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 ISSUES WITH VACUUM ENERGY AS THE ORIGIN OF DARK ENERGY

2012 ◽  
Vol 27 (27) ◽  
pp. 1250154 ◽  
Author(s):  
HOURI ZIAEEPOUR
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Dark Energy ◽  
Particle Physics ◽  
Vacuum Energy ◽  
A Priori ◽  
Higgs Field ◽  
Scalar Fields ◽  
Vacuum Energy Density ◽  
Quantum Field

In this paper, we address some of the issues raised in the literature about the conflict between a large vacuum energy density, a priori predicted by quantum field theory, and the observed dark energy which must be the energy of vacuum or include it. We present a number of arguments against this claim and in favor of a null vacuum energy. They are based on the following arguments: A new definition for the vacuum in quantum field theory as a frame-independent coherent state; results from a detailed study of condensation of scalar fields in Friedmann–Lemaître–Robertson–Walker (FLRW) background performed in a previous work; and our present knowledge about the Standard Model of particle physics. One of the predictions of these arguments is the confinement of nonzero expectation value of Higgs field to scales roughly comparable with the width of electroweak gauge bosons or shorter. If the observation of Higgs by the LHC is confirmed, accumulation of relevant events and their energy dependence in near future should allow us to measure the spatial extend of the Higgs condensate.

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