scholarly journals QUANTIZATION OF FIELDS BASED ON GENERALIZED UNCERTAINTY PRINCIPLE

2006 ◽  
Vol 21 (16) ◽  
pp. 1285-1296 ◽  
Author(s):  
TOSHIHIRO MATSUO ◽  
YUUICHIROU SHIBUSA
Keyword(s):  
Quantum Theory ◽  
Scalar Field ◽  
Path Integral ◽  
Uncertainty Principle ◽  
Deformation Parameter ◽  
Generalized Uncertainty Principle ◽  
Heisenberg Algebra ◽  
Integral Formalism ◽  
Higher Dimensional ◽  
Free Scalar

We construct a quantum theory of free scalar field in (1+1) dimensions based on the deformed Heisenberg algebra [Formula: see text] where β is a deformation parameter. Both canonical and path integral formalisms are employed. A higher dimensional extension is easily performed in the path integral formalism.

scholarly journals Quantization of Free Scalar Fields in the Presence of Natural Cutoffs

2012 ◽  
Vol 2012 ◽  
pp. 1-19
Author(s):  
K. Nozari ◽  
F. Moafi ◽  
F. Rezaee Balef
Keyword(s):  
Quantum Theory ◽  
Path Integral ◽  
Deformation Parameter ◽  
Heisenberg Algebra ◽  
Scalar Fields ◽  
Integral Formalism ◽  
Path Integral Formalism ◽  
Higher Dimensional ◽  
Free Scalar ◽  
Maximal Momentum

We construct a quantum theory of free scalar fields in (1+1)-dimensions based on the deformed Heisenberg algebrax^,p^=iħ1-βp+2β2p2, that admits the existence of both a minimal measurable length and a maximal momentum, whereβis a deformation parameter. We consider both canonical and path integral formalisms of the scenario. Finally a higher dimensional extension is easily performed in the path integral formalism.

scholarly journals SUPERSYMMETRIC FIELD THEORY BASED ON GENERALIZED UNCERTAINTY PRINCIPLE

2007 ◽  
Vol 22 (29) ◽  
pp. 5279-5286 ◽  
Author(s):  
YUUICHIROU SHIBUSA
Keyword(s):  
Field Theory ◽  
Quantum Theory ◽  
Deformation Parameter ◽  
Generalized Uncertainty Principle ◽  
Heisenberg Algebra ◽  
Majorana Fermion ◽  
Fermion Field ◽  
Free Fermion ◽  
Supersymmetry Algebra ◽  
Guiding Principle

We construct a quantum theory of free fermion field based on the deformed Heisenberg algebra [Formula: see text] where β is a deformation parameter using supersymmetry as a guiding principle. A supersymmetric field theory with a real scalar field and a Majorana fermion field is given explicitly and we also find that the supersymmetry algebra is deformed from an usual one.

scholarly journals Heisenberg Algebra in the Bargmann-Fock Space with Natural Cutoffs

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Maryam Roushan ◽  
Kourosh Nozari
Keyword(s):  
Uncertainty Principle ◽  
Fock Space ◽  
Generalized Uncertainty Principle ◽  
Heisenberg Algebra ◽  
Minimal Length ◽  
Maximal Momentum

We construct a Heisenberg algebra in Bargmann-Fock space in the presence of natural cutoffs encoded as minimal length, minimal momentum, and maximal momentum through a generalized uncertainty principle.

COVARIANT DEFORMATION OF THE POINCARÉ–HEISENBERG ALGEBRA

1998 ◽  
Vol 13 (20) ◽  
pp. 1587-1595
Author(s):  
CLEMENS HEUSON
Keyword(s):  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Heisenberg Algebra ◽  
Lorentz Transformations ◽  
Deformation Function

Starting from deformed coordinates a covariant deformation of the Poincaré and Heisenberg algebra is derived. The deformation function is determined uniquely by the Jacobi identities leading to noncommutative coordinates, a generalized uncertainty principle and deformed Lorentz transformations.

scholarly journals Scalar field cosmology modified by the generalized uncertainty principle

2015 ◽  
Vol 32 (24) ◽  
pp. 245006 ◽  
Author(s):  
Andronikos Paliathanasis ◽  
Supriya Pan ◽  
Souvik Pramanik
Keyword(s):  
Scalar Field ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Scalar Field Cosmology

scholarly journals LCE Violation for the Relational to Quantum Transition

2021 ◽  
Author(s):  
Chitradeep Gupta
Keyword(s):  
Quantum Theory ◽  
Path Integral ◽  
Uncertainty Principle ◽  
Quantum Transition ◽  
Arrow Of Time ◽  
Local Conservation ◽  
Conservation Of Energy ◽  
Space And Time

Abstract Quantization historically was never as much a problem as it was a solution to a problem and the problem was the failure of the classical material evolution statement. Under the axiomatic assumption that quantum theory is founded in Heisenberg’s principle and Feynman’s evolution we show that the QM path integral exists at the negation of the evolution of local conservation of energy(LCE) which in its presence fails with arbitrarily many interference terms. Along with LCE violation we uncover another GR-QM contradiction between the local arrow of time and the uncertainty principle. Every contradiction ∼ (p)∩(q) is also a transition in p changing to q. The problem is GR is also caught up in an implication trail and cannot go through multiple parallel changes for LCE violation in presence of the QM path integral. To improve the recovery we go to an alternate projection of GR that has a set of independent frame invariant statements with a Lorentz invariant distinction of space and time.

scholarly journals Primordial big bang nucleosynthesis and generalized uncertainty principle

2021 ◽  
Vol 81 (12) ◽  
Author(s):  
Giuseppe Gaetano Luciano
Keyword(s):  
Uncertainty Principle ◽  
Deformation Parameter ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Big Bang ◽  
Minimal Length ◽  
Gravity Models ◽  
Light Elements ◽  
Semiclassical Approach ◽  
Big Bang Nucleosynthesis

AbstractThe Generalized Uncertainty Principle (GUP) naturally emerges in several quantum gravity models, predicting the existence of a minimal length at Planck scale. Here, we consider the quadratic GUP as a semiclassical approach to thermodynamic gravity and constrain the deformation parameter by using observational bounds from Big Bang Nucleosynthesis and primordial abundances of the light elements $${}^4 He, D, {}^7 Li$$ 4 H e , D , 7 L i . We show that our result fits with most of existing bounds on $$\beta $$ β derived from other cosmological studies.

scholarly journals Scale-dependent Hayward black hole and the generalized uncertainty principle

2018 ◽  
Vol 33 (32) ◽  
pp. 1850184 ◽  
Author(s):  
E. Contreras ◽  
P. Bargueño
Keyword(s):  
Black Hole ◽  
Uncertainty Principle ◽  
Deformation Parameter ◽  
Generalized Uncertainty Principle ◽  
Schwarzschild Solution ◽  
Hilbert Action

In this work, we present a technique to obtain bounds on the generalized uncertainty principle deformation parameter by using an improved Schwarzschild solution represented by the Hayward metric in the context of scale-dependent gravity. Specifically, this deformation parameter can be interpreted in terms of a running parameter which controls the deviation from the standard Einstein–Hilbert action in the scale-dependent scenario.

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