Minimum physical length and the generalized uncertainty principle in string theory

Konishi, Kenichi; Paffuti, Giampiero; Provero, Paolo

doi:10.1016/0370-2693(90)91927-4

Cited by 724 publications

(544 citation statements)

References 15 publications

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“…A general predictions of any quantum theory of gravity is that there exists a minimal length below which no other length can be observed [1]- [6]. From perturbative string theory point of view [1,2], such a minimal observable length is due to the fact that strings cannot probe distances smaller than the sting size.…”

Section: Introductionmentioning

confidence: 99%

Generalized uncertainty principle in Bianchi type I quantum cosmology

Vakili

Sepangi

2007

Physics Letters B

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We study a quantum Bianchi type I model in which the dynamical variables of the corresponding minisuperspace obey the generalized Heisenberg algebra. Such a generalized uncertainty principle has its origin in the existence of a minimal length suggested by quantum gravity and sting theory. We present approximate analytical solutions to the corresponding Wheeler-DeWitt equation in the limit where the scale factor of the universe is small and compare the results with the standard commutative and noncommutative quantum cosmology. Similarities and differences of these solutions are also discussed.

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Section: Introductionmentioning

confidence: 99%

Generalized uncertainty principle in Bianchi type I quantum cosmology

Vakili

Sepangi

2007

Physics Letters B

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“…The GUP can be thought of as arising from the studies of string scattering at very high energies [6,7] or from worldsheet renormalization group considerations [8].…”

Section: Jhep04(2009)005mentioning

confidence: 99%

“…(3.6) is the term involving time derivatives. 8 Notice additionally, that here p −1 denotes a comoving wavelength whereas ρ −1 = a(τ )p −1 corresponds to a physical wavelength. As we shall see in section 4, this reformulation simplifies greatly the treatment of a scalar field on a de Sitter background which respects the GUP, as it allows to solve exactly for the mode functions in such a way that continuously deforms known results in terms of β.…”

Section: Jhep04(2009)005mentioning

confidence: 99%

Inflation with a stringy minimal length, reworked

Palma

Patil

2009

J. High Energy Phys.

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In this paper we revisit the formulation of scalar field theories on de Sitter backgrounds subject to the generalized uncertainty principle (GUP). The GUP arises in several contexts in string theory, but is most readily thought of as resulting from using strings as effective probes of geometry, which suggests an uncertainty relation incorporating the string scale l s . After reviewing the string theoretic case for the GUP, which implies a minimum length scale l s , we follow in the footsteps of Kempf and concern ourselves with how one might write down field theories which respect the GUP. We uncover a new representation of the GUP, which unlike previous studies, readily permits exact analytical solutions for the mode functions of a scalar field on de Sitter backgrounds. We find that scalar fields cannot be quantized on inflationary backgrounds with a Hubble radius H −1 smaller than the string scale, implying a sensibly stringy (as opposed to Planckian) cutoff on the scale of inflation resulting from the GUP. We also compute (Hl s ) 2 corrections to the two point correlation function analytically and comment on the future prospects of observing such corrections in the fortunate circumstance our universe is described by a very weakly coupled string theory.

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“…The conventional method to resolve the above singular behavior of the Hawking temperature for the Schwarzschild black hole is to introduce the Planck mass as a cutoff M P in the regime of the generalized uncertainty principle (GUP) [26][27][28][29][30][31][32], and then the GUP temperature is obtained as…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic phase transition based on the nonsingular temperature

2015

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The Hawking temperature for the Schwarzschild black hole is divergent when the mass of the black hole vanishes; however, the corresponding geometry becomes the Minkowski spacetime whose intrinsic temperature is zero. In connection with this issue, we construct a nonsingular temperature which follows the Hawking temperature for the large black hole, while it vanishes when the black hole is completely evaporated. For the thermodynamic significances of this modified temperature, we calculate thermodynamic quantities and study phase transitions. It turns out that even the small black hole can be stable below a certain temperature, and the hot flat space is always metastable so that it decays into the stable small black hole or the stable large black hole.

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Minimum physical length and the generalized uncertainty principle in string theory

Cited by 724 publications

References 15 publications

Generalized uncertainty principle in Bianchi type I quantum cosmology

Generalized uncertainty principle in Bianchi type I quantum cosmology

Inflation with a stringy minimal length, reworked

Thermodynamic phase transition based on the nonsingular temperature

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