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 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.

scholarly journals Kinetic energy properties and weak equivalence principle in a space with generalized uncertainty principle

2020 ◽  
Vol 35 (13) ◽  
pp. 2050096
Author(s):  
Kh. P. Gnatenko ◽  
V. M. Tkachuk
Keyword(s):  
Kinetic Energy ◽  
Energy Dependence ◽  
Uncertainty Principle ◽  
Equivalence Principle ◽  
Generalized Uncertainty Principle ◽  
Weak Equivalence ◽  
Weak Equivalence Principle ◽  
Deformation Function ◽  
Commutation Relations ◽  
Deformed Commutation Relations

A space with deformed commutation relations for coordinates and momenta leading to generalized uncertainty principle (GUP) is studied. We show that GUP causes great violation of the weak equivalence principle for macroscopic bodies, violation of additivity property of the kinetic energy, dependence of the kinetic energy on composition, great corrections to the kinetic energy of macroscopic bodies. We find that all these problems can be solved in the case of arbitrary deformation function depending on momentum if parameter of deformation is proportional inversely to squared mass.

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 The most general form of deformation of the Heisenberg algebra from the generalized uncertainty principle

2016 ◽  
Vol 763 ◽  
pp. 218-227 ◽  
Author(s):  
Syed Masood ◽  
Mir Faizal ◽  
Zaid Zaz ◽  
Ahmed Farag Ali ◽  
Jamil Raza ◽  
...  
Keyword(s):  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Heisenberg Algebra

scholarly journals On the origin of generalized uncertainty principle from compactified M5-brane

2017 ◽  
Vol 32 (24) ◽  
pp. 1750123
Author(s):  
Alireza Sepehri ◽  
Anirudh Pradhan ◽  
A. Beesham
Keyword(s):  
Field Theory ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Heisenberg Algebra ◽  
Higher Derivative ◽  
M Theory ◽  
Brane Action ◽  
Matter Fields

In this paper, we demonstrate that compactification in M-theory can lead to a deformation of field theory consistent with the generalized uncertainty principle (GUP). We observe that the matter fields in the M3-brane action contain higher derivative terms. We demonstrate that such terms can also be constructed from a reformulation of the field theory by the GUP. In fact, we will construct the Heisenberg algebra consistent with this deformation, and explicitly demonstrate it to be the Heisenberg algebra obtained from the GUP. Thus, we use compactification in M-theory to motivate for the existence of the GUP.

scholarly journals Generalized uncertainty principle: from the harmonic oscillator to a QFT toy model

2021 ◽  
Vol 81 (11) ◽  
Author(s):  
Pasquale Bosso ◽  
Giuseppe Gaetano Luciano
Keyword(s):  
Harmonic Oscillator ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Heisenberg Algebra ◽  
Quantum Field ◽  
Exact Form ◽  
Ladder Operators ◽  
Heisenberg Uncertainty Principle ◽  
Heisenberg Uncertainty

AbstractSeveral models of quantum gravity predict the emergence of a minimal length at Planck scale. This is commonly taken into consideration by modifying the Heisenberg uncertainty principle into the generalized uncertainty principle. In this work, we study the implications of a polynomial generalized uncertainty principle on the harmonic oscillator. We revisit both the analytic and algebraic methods, deriving the exact form of the generalized Heisenberg algebra in terms of the new position and momentum operators. We show that the energy spectrum and eigenfunctions are affected in a non-trivial way. Furthermore, a new set of ladder operators is derived which factorize the Hamiltonian exactly. The above formalism is finally exploited to construct a quantum field theoretic toy model based on the generalized uncertainty principle.

scholarly journals A Solution to the Soccer Ball Problem for Generalized Uncertainty Relations

2019 ◽  
Vol 64 (11) ◽  
pp. 1036 ◽  
Author(s):  
M. J. Lake
Keyword(s):  
Uncertainty Principle ◽  
Equivalence Principle ◽  
Generalized Uncertainty Principle ◽  
Heisenberg Algebra ◽  
Total Momentum ◽  
Uncertainty Relations ◽  
Relativistic Limit ◽  
Soccer Ball ◽  
Ball Problem ◽  
Extended Uncertainty

We propose a new method for generating generalized uncertainty relations (GURs) including the generalized uncertainty principle (GUP), extended uncertainty principle (EUP), and extended generalized uncertainty principle (EGUP), previously proposed in the quantum gravity literature, without modifying the Heisenberg algebra. Our approach is compatible with the equivalence principle, and with local Poincar´e invariance in the relativistic limit, thus circumventing many of the problems associated with GURs derived from modified commutation relations. In particular, it does not require the existence of a nonlinear additional law for momenta. This allows sensible multi-particle states to be constructed in which the total momentum is macroscopic, even if the momentum of an individual particle is bounded by the Planck momentum, thus providing a resolution of the “soccer ball problem” that plagues current approaches to GURs.

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