Operator ordering in quantum field theory. Nonlinear Lagrangian of scalar fields

1986 ◽  
Vol 94 (2) ◽  
pp. 176-195
Author(s):  
Y. Yamashita ◽  
T. Fukuda ◽  
M. Monda ◽  
M. Takeda
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scalar Fields ◽  
Quantum Field ◽  
Operator Ordering ◽  
Nonlinear Lagrangian

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.

scholarly journals The Role of Operator Ordering in Quantum Field Theory

1980 ◽  
Vol 63 (1) ◽  
pp. 287-302 ◽  
Author(s):  
T. Suzuki ◽  
A. C. Hirshfeld ◽  
H. Leschke
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
Operator Ordering

scholarly journals Exploring the thermodynamics of noncommutative scalar fields

2016 ◽  
Vol 31 (11) ◽  
pp. 1650057 ◽  
Author(s):  
Francisco A. Brito ◽  
Elisama E. M. Lima
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Thermodynamic Properties ◽  
Scalar Fields ◽  
Einstein Condensate ◽  
Target Space ◽  
Quantum Field ◽  
Condensate Fraction ◽  
Bose Einstein Condensate ◽  
Bose Einstein

We study the thermodynamic properties of the Bose–Einstein condensate (BEC) in the context of the quantum field theory with noncommutative target space. Our main goal is to investigate in which temperature and/or energy regimes the noncommutativity can characterize some influence on the BEC properties described by a relativistic massive noncommutative boson gas. The noncommutativity parameters play a key role in the modified dispersion relations of the noncommutative fields, leading to a new phenomenology. We have obtained the condensate fraction, internal energy, pressure and specific heat of the system and taken ultrarelativistic (UR) and nonrelativistic (NR) limits. The noncommutative effects on the thermodynamic properties of the system are discussed. We found that there appear interesting signatures around the critical temperature.

scholarly journals Quantum Fields and Local Measurements

2020 ◽  
Vol 378 (2) ◽  
pp. 851-889
Author(s):  
Christopher J. Fewster ◽  
Rainer Verch
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Specific Interaction ◽  
Scalar Fields ◽  
Quantum Field ◽  
Initial State ◽  
Actual Measurement ◽  
Quadratic Interaction ◽  
Scattering Map ◽  
Coupled Theory

Abstract The process of quantum measurement is considered in the algebraic framework of quantum field theory on curved spacetimes. Measurements are carried out on one quantum field theory, the “system”, using another, the “probe”. The measurement process involves a dynamical coupling of “system” and “probe” within a bounded spacetime region. The resulting “coupled theory” determines a scattering map on the uncoupled combination of the “system” and “probe” by reference to natural “in” and “out” spacetime regions. No specific interaction is assumed and all constructions are local and covariant. Given any initial state of the probe in the “in” region, the scattering map determines a completely positive map from “probe” observables in the “out” region to “induced system observables”, thus providing a measurement scheme for the latter. It is shown that the induced system observables may be localized in the causal hull of the interaction coupling region and are typically less sharp than the probe observable, but more sharp than the actual measurement on the coupled theory. Post-selected states conditioned on measurement outcomes are obtained using Davies–Lewis instruments that depend on the initial probe state. Composite measurements involving causally ordered coupling regions are also considered. Provided that the scattering map obeys a causal factorization property, the causally ordered composition of the individual instruments coincides with the composite instrument; in particular, the instruments may be combined in either order if the coupling regions are causally disjoint. This is the central consistency property of the proposed framework. The general concepts and results are illustrated by an example in which both “system” and “probe” are quantized linear scalar fields, coupled by a quadratic interaction term with compact spacetime support. System observables induced by simple probe observables are calculated exactly, for sufficiently weak coupling, and compared with first order perturbation theory.

scholarly journals Entanglement transfer from quantum matter to classical geometry in an emergent holographic dual description of a scalar field theory

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Ki-Seok Kim ◽  
Shinsei Ryu
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Renormalization Group ◽  
Scalar Field ◽  
Scalar Fields ◽  
Quantum Field ◽  
Group Transformation ◽  
Renormalization Group Transformation ◽  
Quantum Matter ◽  
Entanglement Transfer

Abstract Applying recursive renormalization group transformations to a scalar field theory, we obtain an effective quantum gravity theory with an emergent extra dimension, described by a dual holographic Einstein-Klein-Gordon type action. Here, the dynamics of both the dual order-parameter field and the metric tensor field originate from density-density and energy-momentum tensor-tensor effective interactions, respectively, in the recursive renormalization group transformation, performed approximately in the Gaussian level. This linear approximation in the recursive renormalization group transformation for the gravity sector gives rise to a linearized quantum Einstein-scalar theory along the z-directional emergent space. In the large N limit, where N is the flavor number of the original scalar fields, quantum fluctuations of both dynamical metric and dual scalar fields are suppressed, leading to a classical field theory of the Einstein-scalar type in (D+1)-spacetime dimensions. We show that this emergent background gravity describes the renormalization group flows of coupling functions in the UV quantum field theory through the extra dimension. More precisely, the IR boundary conditions of the gravity equations correspond to the renormalization group β-functions of the quantum field theory, where the infinitesimal distance in the extra-dimensional space is identified with an energy scale for the renormalization group transformation. Finally, we also show that this dual holographic formulation describes quantum entanglement in a geometrical way, encoding the transfer of quantum entanglement from quantum matter to classical gravity in the large N limit. We claim that this entanglement transfer serves as a microscopic foundation for the emergent holographic duality description.

Functional Quantum Theory of Free Relativistic Scalar Fields

1971 ◽  
Vol 26 (9) ◽  
pp. 1553-1558 ◽  
Author(s):  
W. Bauhoff
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Theory ◽  
Functional Equations ◽  
Scalar Product ◽  
Functional Space ◽  
Scalar Fields ◽  
Quantum Field ◽  
Isometric Mapping ◽  
Free Scalar

Abstract Dynamics of quantum field theory can be formulated by functional equations. Starting with the Schwinger functionals of the free scalar field, functional equations and corresponding many particle functionals are derived. To establish a complete functional quantum theory, a scalar product in functional space has to be defined as an isometric mapping of physical Hilbert space into the functional space.

scholarly journals The Entropic Dynamics of Quantum Scalar Fields Coupled to Gravity

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1324
Author(s):  
Selman Ipek ◽  
Ariel Caticha
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Relativistic Quantum ◽  
Superposition Principle ◽  
Hamiltonian Formalism ◽  
Scalar Fields ◽  
Space Time ◽  
Relativistic Quantum Mechanics ◽  
Quantum Field ◽  
Entropic Dynamics

Entropic dynamics (ED) are a general framework for constructing indeterministic dynamical models based on entropic methods. ED have been used to derive or reconstruct both non-relativistic quantum mechanics and quantum field theory in curved space-time. Here we propose a model for a quantum scalar field propagating in dynamical space-time. The approach rests on a few key ingredients: (1) Rather than modelling the dynamics of the fields, ED models the dynamics of their probabilities. (2) In accordance with the standard entropic methods of inference, the dynamics are dictated by information encoded in constraints. (3) The choice of the physically relevant constraints is dictated by principles of symmetry and invariance. The first of such principle imposes the preservation of a symplectic structure which leads to a Hamiltonian formalism with its attendant Poisson brackets and action principle. The second symmetry principle is foliation invariance, which, following earlier work by Hojman, Kuchař, and Teitelboim, is implemented as a requirement of path independence. The result is a hybrid ED model that approaches quantum field theory in one limit and classical general relativity in another, but is not fully described by either. A particularly significant prediction of this ED model is that the coupling of quantum fields to gravity implies violations of the quantum superposition principle.

scholarly journals Acausal quantum theory for non-Archimedean scalar fields

2019 ◽  
Vol 31 (04) ◽  
pp. 1950011 ◽  
Author(s):  
M. L. Mendoza-Martínez ◽  
J. A. Vallejo ◽  
W. A. Zúñiga-Galindo
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Theory ◽  
Scalar Fields ◽  
Background Field ◽  
Quantum Field ◽  
Second Quantization ◽  
Klein Gordon ◽  
Free Fields ◽  
Wightman Axioms

We construct a family of quantum scalar fields over a [Formula: see text]-adic spacetime which satisfy [Formula: see text]-adic analogues of the Gårding–Wightman axioms. Most of the axioms can be formulated in the same way for both the Archimedean and non-Archimedean frameworks; however, the axioms depending on the ordering of the background field must be reformulated, reflecting the acausality of [Formula: see text]-adic spacetime. The [Formula: see text]-adic scalar fields satisfy certain [Formula: see text]-adic Klein–Gordon pseudo-differential equations. The second quantization of the solutions of these Klein–Gordon equations corresponds exactly to the scalar fields introduced here. The main conclusion is that there seems to be no obstruction to the existence of a mathematically rigorous quantum field theory (QFT) for free fields in the [Formula: see text]-adic framework, based on an acausal spacetime.

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