Covariant quantum fields on noncommutative spacetimes

Novel quantum concepts acquire content not by representing new beables but through material-inferential relations between claims about them and other claims. Acceptance of quantum theory modifies other concepts in accordance with a pragmatist inferentialist account of how claims acquire content. Quantum theory itself introduces no new beables, but accepting it affects the content of claims about classical magnitudes and other beables unknown to classical physics: the content of a magnitude claim about a physical object is a function of its physical context in a way that eludes standard pragmatics but may be modeled by decoherence. Leggett’s proposed test of macro-realism illustrates this mutation of conceptual content. Quantum fields are not beables but assumables of a quantum theory we use to make claims about particles and non-quantum fields whose denotational content may also be certified by models of decoherence.

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A path integral formulation for particle detectors: the Unruh-DeWitt model as a line defect

Journal of High Energy Physics ◽

10.1007/jhep03(2021)076 ◽

2021 ◽

Vol 2021 (3) ◽

Author(s):

Ivan M. Burbano ◽

T. Rick Perche ◽

Bruno de S. L. Torres

Keyword(s):

Path Integral ◽

Degrees Of Freedom ◽

Wilson Line ◽

Transition Probability ◽

Relativistic Quantum ◽

Quantum Fields ◽

Line Defect ◽

Particle Detectors ◽

Nonlocal Operators ◽

Detector Model

Abstract Particle detectors are an ubiquitous tool for probing quantum fields in the context of relativistic quantum information (RQI). We formulate the Unruh-DeWitt (UDW) particle detector model in terms of the path integral formalism. The formulation is able to recover the results of the model in general globally hyperbolic spacetimes and for arbitrary detector trajectories. Integrating out the detector’s degrees of freedom yields a line defect that allows one to express the transition probability in terms of Feynman diagrams. Inspired by the light-matter interaction, we propose a gauge invariant detector model whose associated line defect is related to the derivative of a Wilson line. This is another instance where nonlocal operators in gauge theories can be interpreted as physical probes for quantum fields.

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Gårding Domains and Analytic Vectors for Quantum Fields

Journal of Mathematical Physics ◽

10.1063/1.1666057 ◽

1972 ◽

Vol 13 (6) ◽

pp. 821-827 ◽

Cited By ~ 15

Author(s):

Gerhard C. Hegerfeldt

Keyword(s):

Quantum Fields

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Palatial Twistors from Quantum Inhomogeneous Conformal Symmetries and Twistorial DSR Algebras

Symmetry ◽

10.3390/sym13081309 ◽

2021 ◽

Vol 13 (8) ◽

pp. 1309

Author(s):

Jerzy Lukierski

Keyword(s):

Phase Space ◽

Hopf Algebras ◽

Deformation Parameter ◽

Heisenberg Algebra ◽

Planck Length ◽

Covariant Quantum ◽

Drinfeld Twist ◽

Quantum Deformations ◽

Heisenberg Double ◽

Conformal Symmetries

We construct recently introduced palatial NC twistors by considering the pair of conjugated (Born-dual) twist-deformed D=4 quantum inhomogeneous conformal Hopf algebras Uθ(su(2,2)⋉T4) and Uθ¯(su(2,2)⋉T¯4), where T4 describes complex twistor coordinates and T¯4 the conjugated dual twistor momenta. The palatial twistors are suitably chosen as the quantum-covariant modules (NC representations) of the introduced Born-dual Hopf algebras. Subsequently, we introduce the quantum deformations of D=4 Heisenberg-conformal algebra (HCA) su(2,2)⋉Hℏ4,4 (Hℏ4,4=T¯4⋉ℏT4 is the Heisenberg algebra of twistorial oscillators) providing in twistorial framework the basic covariant quantum elementary system. The class of algebras describing deformation of HCA with dimensionfull deformation parameter, linked with Planck length λp, is called the twistorial DSR (TDSR) algebra, following the terminology of DSR algebra in space-time framework. We describe the examples of TDSR algebra linked with Palatial twistors which are introduced by the Drinfeld twist and the quantization map in Hℏ4,4. We also introduce generalized quantum twistorial phase space by considering the Heisenberg double of Hopf algebra Uθ(su(2,2)⋉T4).

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