On the generalized function calculus for infrared and ultraviolet singular quantum fields

2004 ◽  
Vol 45 (5) ◽  
pp. 1944-1958 ◽  
Author(s):  
M. A. Soloviev
Keyword(s):  
Generalized Function ◽  
Quantum Fields ◽  
Function Calculus

Meaning

2017 ◽  
Author(s):  
Richard Healey
Keyword(s):  
Quantum Theory ◽  
Physical Object ◽  
Quantum Fields ◽  
Conceptual Content ◽  
Classical Physics ◽  
Physical Context

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.

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

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.

scholarly journals Partial sums and inclusion relations for analytic functions involving (p, q)-differential operator

2021 ◽  
Vol 19 (1) ◽  
pp. 329-337
Author(s):  
Huo Tang ◽  
Kaliappan Vijaya ◽  
Gangadharan Murugusundaramoorthy ◽  
Srikandan Sivasubramanian
Keyword(s):  
Analytic Function ◽  
Differential Operator ◽  
Lower Bounds ◽  
Analytic Functions ◽  
Function Class ◽  
Partial Sums ◽  
Generalized Function ◽  
Inclusion Relations ◽  
Alpha Beta

Abstract Let f k ( z ) = z + ∑ n = 2 k a n z n {f}_{k}\left(z)=z+{\sum }_{n=2}^{k}{a}_{n}{z}^{n} be the sequence of partial sums of the analytic function f ( z ) = z + ∑ n = 2 ∞ a n z n f\left(z)=z+{\sum }_{n=2}^{\infty }{a}_{n}{z}^{n} . In this paper, we determine sharp lower bounds for Re { f ( z ) / f k ( z ) } {\rm{Re}}\{f\left(z)\hspace{-0.08em}\text{/}\hspace{-0.08em}{f}_{k}\left(z)\} , Re { f k ( z ) / f ( z ) } {\rm{Re}}\{{f}_{k}\left(z)\hspace{-0.08em}\text{/}\hspace{-0.08em}f\left(z)\} , Re { f ′ ( z ) / f k ′ ( z ) } {\rm{Re}}\{{f}^{^{\prime} }\left(z)\hspace{-0.08em}\text{/}\hspace{-0.08em}{f}_{k}^{^{\prime} }\left(z)\} and Re { f k ′ ( z ) / f ′ ( z ) } {\rm{Re}}\{{f}_{k}^{^{\prime} }\left(z)\hspace{-0.08em}\text{/}\hspace{-0.08em}{f}^{^{\prime} }\left(z)\} , where f ( z ) f\left(z) belongs to the subclass J p , q m ( μ , α , β ) {{\mathcal{J}}}_{p,q}^{m}\left(\mu ,\alpha ,\beta ) of analytic functions, defined by Sălăgean ( p , q ) \left(p,q) -differential operator. In addition, the inclusion relations involving N δ ( e ) {N}_{\delta }\left(e) of this generalized function class are considered.

Gårding Domains and Analytic Vectors for Quantum Fields

1972 ◽  
Vol 13 (6) ◽  
pp. 821-827 ◽  
Author(s):  
Gerhard C. Hegerfeldt
Keyword(s):  
Quantum Fields

scholarly journals Interacting quantum fields in various charts of anti–de Sitter spacetime

2021 ◽  
Vol 103 (4) ◽  
Author(s):  
E. T. Akhmedov ◽  
A. A. Artemev ◽  
I. V. Kochergin
Keyword(s):  
De Sitter Spacetime ◽  
Quantum Fields ◽  
De Sitter ◽  
Sitter Spacetime

Design and research of a novel type of mechanical presses driven by three servo motors in parallel

2012 ◽  
Vol 227 (3) ◽  
pp. 580-591 ◽  
Author(s):  
Xun Huang ◽  
Chunxiang Ma ◽  
Suxing Wu ◽  
Qian Wang ◽  
Zhibo Wang ◽  
...  
Keyword(s):  
Probability Theory ◽  
Forward Kinematics ◽  
Generalized Function ◽  
Engineering Practice ◽  
Drawing Process ◽  
Fuzzy Probability ◽  
Fuzzy Reliability ◽  
Deep Drawing Process ◽  
Computing Method ◽  
Fuzzy Probability Theory

A novel type of mechanical presses design driven by three servo motors in parallel is proposed to develop high stamping capacity based on the theory of generalized function sets, and then is improved to enhance its practicability in engineering practice. The inverse and forward kinematics analyses are conducted later. Based on the fuzzy probability theory, the computing method of fuzzy reliability of kinematic accuracy of slider is then obtained. Finally, with a set of optimized length parameters of the presses given, the fuzzy reliability is calculated, on the basis of which a typical deep-drawing process is simulated.

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