scholarly journals Some Aspects of Supersymmetric Field Theories with Minimal Length and Maximal Momentum

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Kourosh Nozari ◽  
F. Moafi ◽  
F. Rezaee Balef
Keyword(s):  
Deformation Parameter ◽  
Heisenberg Algebra ◽  
Minimal Length ◽  
Field Theories ◽  
Majorana Fermion ◽  
Fermion Field ◽  
Free Fermion ◽  
Supersymmetric Field Theories ◽  
Fermion Fields ◽  
Maximal Momentum

We consider a real scalar field and a Majorana fermion field to construct a supersymmetric quantum theory of free fermion fields based on the deformed Heisenberg algebra[x,p] = iℏ(1−βp+2β2p2), whereβis a deformation parameter. We present a deformed supersymmetric algebra in the presence of minimal length and maximal momentum.

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.

scholarly journals RECENT DEVELOPMENTS IN D=2 STRING FIELD THEORY

1994 ◽  
Vol 09 (18) ◽  
pp. 3103-3141 ◽  
Author(s):  
MICHIO KAKU
Keyword(s):  
Field Theory ◽  
String Field Theory ◽  
Correlation Functions ◽  
Two Dimensions ◽  
Field Theories ◽  
Fermion Field ◽  
Free Fermion ◽  
Temporal Gauge ◽  
Recent Developments ◽  
The Relationship

We review the recent developments in the construction of string field theory in two dimensions. We analyze the bewildering number of string field theories that have been proposed, all of which correctly reproduce the correlation functions of two-dimensional string theory. These include (1) free fermion field theory, (2) collective string field theory, (3) temporal gauge string field theory and (4) nonpolynomial string field theory. We will analyze discrete states, the ω(∞) symmetry, and correlation functions in terms of these different string field theories. We will also comment on the relationship between these field theories, which is still not well understood.

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.

On the Heisenberg algebra in Bargmann–Fock space with natural cutoffs

2016 ◽  
Vol 13 (05) ◽  
pp. 1650054 ◽  
Author(s):  
K. Nozari ◽  
M. Roushan
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
General Framework ◽  
Fock Space ◽  
Heisenberg Algebra ◽  
Minimal Length ◽  
Space Representation ◽  
Maximal Momentum

We construct a generalized Hilbert space representation of quantum mechanics in [Formula: see text]-dimensions based on Bargmann–Fock space with natural cutoffs as a minimal length, minimal momentum and maximal momentum in order to have a general framework for Heisenberg algebra in Bargmann–Fock space.

scholarly journals Palatial Twistors from Quantum Inhomogeneous Conformal Symmetries and Twistorial DSR Algebras

Symmetry ◽  
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).

scholarly journals LAGRANGIAN FORMULATION OF A MAGNETOSTATIC FIELD IN THE PRESENCE OF A MINIMAL LENGTH SCALE BASED ON THE KEMPF ALGEBRA

2013 ◽  
Vol 28 (30) ◽  
pp. 1350142 ◽  
Author(s):  
S. K. MOAYEDI ◽  
M. R. SETARE ◽  
B. KHOSROPOUR
Keyword(s):  
Integral Form ◽  
Heisenberg Algebra ◽  
Minimal Length ◽  
Lagrangian Formulation ◽  
Length Scale ◽  
Magnetostatic Field ◽  
Classical Level ◽  
Spatial Dimensions ◽  
Minimal Length Scale ◽  
The Relationship

In the 1990s, Kempf and his collaborators Mangano and Mann introduced a D-dimensional (β, β′)-two-parameter deformed Heisenberg algebra which leads to an isotropic minimal length [Formula: see text]. In this work, the Lagrangian formulation of a magnetostatic field in three spatial dimensions (D = 3) described by Kempf algebra is presented in the special case of β′ = 2β up to the first-order over β. We show that at the classical level there is a similarity between magnetostatics in the presence of a minimal length scale (modified magnetostatics) and the magnetostatic sector of the Abelian Lee–Wick model in three spatial dimensions. The integral form of Ampere's law and the energy density of a magnetostatic field in the modified magnetostatics are obtained. Also, the Biot–Savart law in the modified magnetostatics is found. By studying the effect of minimal length corrections to the gyromagnetic moment of the muon, we conclude that the upper bound on the isotropic minimal length scale in three spatial dimensions is 4.42×10-19m. The relationship between magnetostatics with a minimal length and the Gaete–Spallucci nonlocal magnetostatics [J. Phys. A: Math. Theor. 45, 065401 (2012)] is investigated.

scholarly journals The (2+1) dimensional metric f (R) gravity non-minimally coupled with fermion field

2021 ◽  
Vol 2090 (1) ◽  
pp. 012065
Author(s):  
Nurgissa Myrzakulov ◽  
Gulnur Tursumbayeva ◽  
Shamshyrak Myrzakulova
Keyword(s):  
Gravitational Theory ◽  
Noether Symmetry ◽  
Fermion Field ◽  
Field Equations ◽  
Friedmann Equations ◽  
Fermion Fields ◽  
Cosmological Solutions

Abstract In this article, we examine a gravitational theory including a fermion field that is non-minimally coupled to metric f (R) gravity in (2+1) dimensions. We give the field equations for fermion fields and Friedmann equations. In this context, we study cosmological solutions of the field equations using these forms obtained by the existent of Noether symmetry.

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