Supersymmetric Field Theory Based on Generalized Uncertainty Principle

Shibusa, Yuuichirou

doi:10.1142/s0217751x07037913

Cited by 9 publications

(15 citation statements)

References 19 publications

(17 reference statements)

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“…This effectively chooses a special frame of reference, bringing back the notion of an aether. Because of this difficulty, GUP models so far have been mainly considered in non-relativistic theories with few attempts in relativistic theories and quantum field theory [18][19][20][21][22][23][24][25][26][27][28]. In the present work, we study this aspect and propose a Lorentz covariant GUP which reduces to its familiar non-relativistic versions at low energies, and incorporates a minimum length.…”

Section: Introductionmentioning

confidence: 99%

Relativistic generalized uncertainty principle

2019

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The Generalized Uncertainty Principle and the related minimum length are normally considered in non-relativistic Quantum Mechanics. Extending it to relativistic theories is important for having a Lorentz invariant minimum length and for testing the modified Heisenberg principle at high energies.In this paper, we formulate a relativistic Generalized Uncertainty Principle. We then use this to write the modified Klein-Gordon, Schrödinger and Dirac equations, and compute quantum gravity corrections to the relativistic hydrogen atom, particle in a box, and the linear harmonic oscillator.1 The parameters used in [11] and [29] are related to the ones used here as follows: β 1 = (α + ε)γ 2 and β 2 = (β + 2ε)γ 2 .

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Section: Introductionmentioning

confidence: 99%

Relativistic generalized uncertainty principle

2019

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“…The Lagrangian of the gauge gauge field sector is a special manifestation of the general case of the generalized Yang-Mills Lagrangian (18) with (17), (19), (20), (21), (22) and (23). In the special case of the generalized electroweak theory there are four generators.…”

Section: Gauge Field Sector Of the Generalized Electroweak Theorymentioning

confidence: 99%

“…This Lagrangian contains the generalized uncertainty principle and is invariant under local gauge transformations of the form The Lagrangian of quantum chromodynamics itself under incorporation of a generalized uncertainty principle can obviously be obtained very easily, if there is known the above consideration of the general case of Yang-Mills theories. One has just to consider the special case of the SU (3) c in the above consideration of general Yang-Mills theories and then the corresponding special Lagrangians (13) and (18) describe the theory, if as generators T a the eight Gell-Mann matrices are used and the f abc are accordingly identified with their structure constants. However, things become more intricate, if there is explored the combination of the electroweak theory and quantum chromodynamics which means that there is considered the full gauge group of the standard model,…”

Section: Gauge Field Sector Of the Generalized Electroweak Theorymentioning

confidence: 99%

“…Inserting the modified momentum operator to quantum theoretical field equations leads to a corresponding modification of the dynamics they describe and in this sense to an extended formulation of these quantum field theories. There have been explored many aspects of quantum mechanics and quantum field theory [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22] as well as many issues concerning gravity [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38], [39], [40], [41], [42], [43], [44], [45], [46], [47], [48] under incorporation of a generalized uncertainty p...…”

Section: Introductionmentioning

confidence: 99%

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Electroweak Theory With a Minimal Length

Kober

2011

Int. J. Mod. Phys. A

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According to the introduction of a minimal length to quantum field theory which is directly related to a generalized uncertainty principle the implementation of the gauge principle becomes much more intricated. It has been shown in another paper how gauge theories have to be extended in general, if there is assumed the existence of a minimal length. In this paper this generalization of the description of gauge theories is applied to the case of Yang-Mills theories with gauge group SU (N ) to consider especially the application to the electroweak theory as it appears in the standard model. The modifications of the lepton-, Higgs-and gauge field sector of the extended Lagrangian of the electroweak theory maintaining local gauge invariance under SU (2)L ⊗ U (1)Y transformations are investigated. There appear additional interaction terms between the leptons or the Higgs particle respectively with the photon and the W-and Z-bosons as well as additional self-interaction terms of these gauge bosons themselves. It is remarkable that in the quark sector where the full gauge group of the standard model, SU (3)c ⊗ SU (2)L ⊗ U (1)Y , has to be considered there arise coupling terms between the gluons und the W-and Z-bosons which means that the electroweak theory is not separated from quantum chromodynamics anymore.

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“…If the generalized momentum operator represented in position space is inserted to quantum theoretical field equations, this leads to a modification of the dynamics depending on the scale, which is directly related to the corresponding parameter introduced by the modification of the uncertainty principle. There have already been considered various implications of such a generalized description of nature to certain aspects of quantum mechanics and quantum field theory as they are investigated in [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12] [13], [14], [15], [16] as well as to many topics related to gravity as they are treated in [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38], [39]. A very important topic with respect to the formulation of quantum field theories with a generalized uncertainty principle is the implication concerning the gauge principle on which all interaction theories of the standard model as well as gravity, which can be considered to be the gauge theory of local translations or Lorentz rotations, are based on.…”

Section: Introductionmentioning

confidence: 99%

Gauge theories under incorporation of a generalized uncertainty principle

Kober

2010

Phys. Rev. D

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There is considered an extension of gauge theories according to the assumption of a generalized uncertainty principle which implies a minimal length scale. A modification of the usual uncertainty principle implies an extended shape of matter field equations like the Dirac equation. If there is postulated invariance of such a generalized field equation under local gauge transformations, the usual covariant derivative containing the gauge potential has to be replaced by a generalized covariant derivative. This leads to a generalized interaction between the matter field and the gauge field as well as to an additional self-interaction of the gauge field. Since the existence of a minimal length scale seems to be a necessary assumption of any consistent quantum theory of gravity, the gauge principle is a constitutive ingredient of the standard model, and even gravity can be described as gauge theory of local translations or Lorentz transformations, the presented extension of gauge theories appears as a very important consideration.

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Supersymmetric Field Theory Based on Generalized Uncertainty Principle

Cited by 9 publications

References 19 publications

Relativistic generalized uncertainty principle

Relativistic generalized uncertainty principle

Electroweak Theory With a Minimal Length

Gauge theories under incorporation of a generalized uncertainty principle

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