Semiclassical quantization of circular strings in de Sitter and anti-de Sitter spacetimes
Identifieur interne : 000090 ( PascalFrancis/Corpus ); précédent : 000089; suivant : 000091Semiclassical quantization of circular strings in de Sitter and anti-de Sitter spacetimes
Auteurs : H. J. De Vega ; A. L. Larsen ; N. SánchezSource :
- Physical Review D (Particles and Fields) [ 0556-2821 ] ; 1995-06-15.
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Abstract
We compute the exact equation of state of circular strings in the (2+1)-dimensional de Sitter (dS) and anti-de Sitter (AdS) spacetimes, and analyze its properties for the different (oscillating, contracting, and expanding) strings. The string equation of state has the perfect fluid form P = (γ-1)E, with the pressure and energy expressed closely and completely in terms of elliptic functions, the instantaneous coefficient γ depending on the elliptic modulus. We semiclassically quantize the oscillating circular strings. The string mass is m = * root *C /(πHα′), C being the Casimir operator, C = -LμνLμν, of the O(3,1)-dS [O(2,2)-AdS] group, and H is the Hubble constant. We find α′mdS2* roughly-equal *4n-5H2α′n2 (n* is-an-element-of *N0), and a finite number of states NdS* roughly-equal *0.34/(H2α′) in de Sitter spacetime; mAdS2* roughly-equal *H2n2 (large n* is-an-element-of *N0) and NAdS = ∞ in anti-de Sitter spacetime. The level spacing grows with n in AdS spacetime, while it is approximately constant (although smaller than in Minkowski spacetime and slightly decreasing) in dS spacetime. The massive states in dS spacetime decay through the tunnel effect and the semiclassical decay probability is computed. The semiclassical quantization of exact (circular) strings and the canonical quantization of generic string perturbations around the string center of mass qualitatively agree.
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| NO : | PASCAL 95-0291912 AIP |
|---|---|
| ET : | Semiclassical quantization of circular strings in de Sitter and anti-de Sitter spacetimes |
| AU : | DE VEGA (H. J.); LARSEN (A. L.); SÁNCHEZ (N.) |
| AF : | Laboratoire de Physique Théorique et Hautes Energies, Université de Paris VI et VII, Tour 16, 1er étage, 4, Place Jussieu, 75252 Paris cedex 05, France (1 aut.); Isaac Newton Institute, Cambridge, CB3 0EH, United Kingdom (1 aut.); Observatoire de Paris, DEMIRM, Observatoire de Paris et École Normale Supérieure, 61, Avenue de l'Observatoire, 75014 Paris, France (2 aut., 3 aut.) |
| DT : | Publication en série; Niveau analytique |
| SO : | Physical Review D (Particles and Fields); ISSN 0556-2821; Coden PRVDAQ; Etats-Unis; Da. 1995-06-15; Vol. 51; No. 12; Pp. 6917-6928 |
| LA : | Anglais |
| EA : | We compute the exact equation of state of circular strings in the (2+1)-dimensional de Sitter (dS) and anti-de Sitter (AdS) spacetimes, and analyze its properties for the different (oscillating, contracting, and expanding) strings. The string equation of state has the perfect fluid form P = (γ-1)E, with the pressure and energy expressed closely and completely in terms of elliptic functions, the instantaneous coefficient γ depending on the elliptic modulus. We semiclassically quantize the oscillating circular strings. The string mass is m = * root *C /(πHα′), C being the Casimir operator, C = -LμνLμν, of the O(3,1)-dS [O(2,2)-AdS] group, and H is the Hubble constant. We find α′mdS2* roughly-equal *4n-5H2α′n2 (n* is-an-element-of *N0), and a finite number of states NdS* roughly-equal *0.34/(H2α′) in de Sitter spacetime; mAdS2* roughly-equal *H2n2 (large n* is-an-element-of *N0) and NAdS = ∞ in anti-de Sitter spacetime. The level spacing grows with n in AdS spacetime, while it is approximately constant (although smaller than in Minkowski spacetime and slightly decreasing) in dS spacetime. The massive states in dS spacetime decay through the tunnel effect and the semiclassical decay probability is computed. The semiclassical quantization of exact (circular) strings and the canonical quantization of generic string perturbations around the string center of mass qualitatively agree. |
| CC : | 001B10A27; 001B10A25M |
| FD : | Etude théorique; 1127; 1125M; Modèle corde; Calcul 3 dimensions; Espace temps; Equation état; Energie; Masse; Quantification; Approximation semiclassique; Opérateur Casimir; Système centre masse; Espace Minkowski |
| ED : | Theoretical study; String models; Three-dimensional calculations; Space-time; Equations of state; Energy; Mass; Quantization; Semiclassical approximation; Casimir operators; Center-of-mass system; Minkowski space |
| LO : | INIST-144D |
| ID : | 95-0291912 |
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Larsen</name><affiliation><inist:fA14 i1="03"><s1>Observatoire de Paris, DEMIRM, Observatoire de Paris et École Normale Supérieure, 61, Avenue de l'Observatoire, 75014 Paris, France</s1><sZ>2 aut.</sZ><sZ>3 aut.</sZ></inist:fA14></affiliation></author><author><name sortKey="Sanchez, N" sort="Sanchez, N" uniqKey="Sanchez N" first="N." last="Sánchez">N. Sánchez</name><affiliation><inist:fA14 i1="03"><s1>Observatoire de Paris, DEMIRM, Observatoire de Paris et École Normale Supérieure, 61, Avenue de l'Observatoire, 75014 Paris, France</s1><sZ>2 aut.</sZ><sZ>3 aut.</sZ></inist:fA14></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">INIST</idno><idno type="inist">95-0291912</idno><date when="1995-06-15">1995-06-15</date><idno type="stanalyst">PASCAL 95-0291912 AIP</idno><idno type="RBID">Pascal:95-0291912</idno><idno type="wicri:Area/PascalFrancis/Corpus">000090</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a">Semiclassical quantization of circular strings in de Sitter and anti-de Sitter spacetimes</title><author><name sortKey="De Vega, H J" sort="De Vega, H J" uniqKey="De Vega H" first="H. J." last="De Vega">H. J. De Vega</name><affiliation><inist:fA14 i1="01"><s1>Laboratoire de Physique Théorique et Hautes Energies, Université de Paris VI et VII, Tour 16, 1er étage, 4, Place Jussieu, 75252 Paris cedex 05, France</s1><sZ>1 aut.</sZ></inist:fA14></affiliation><affiliation><inist:fA14 i1="02"><s1>Isaac Newton Institute, Cambridge, CB3 0EH, United Kingdom</s1><sZ>1 aut.</sZ></inist:fA14></affiliation></author><author><name sortKey="Larsen, A L" sort="Larsen, A L" uniqKey="Larsen A" first="A. L." last="Larsen">A. L. Larsen</name><affiliation><inist:fA14 i1="03"><s1>Observatoire de Paris, DEMIRM, Observatoire de Paris et École Normale Supérieure, 61, Avenue de l'Observatoire, 75014 Paris, France</s1><sZ>2 aut.</sZ><sZ>3 aut.</sZ></inist:fA14></affiliation></author><author><name sortKey="Sanchez, N" sort="Sanchez, N" uniqKey="Sanchez N" first="N." last="Sánchez">N. Sánchez</name><affiliation><inist:fA14 i1="03"><s1>Observatoire de Paris, DEMIRM, Observatoire de Paris et École Normale Supérieure, 61, Avenue de l'Observatoire, 75014 Paris, France</s1><sZ>2 aut.</sZ><sZ>3 aut.</sZ></inist:fA14></affiliation></author></analytic><series><title level="j" type="main">Physical Review D (Particles and Fields)</title><title level="j" type="abbreviated">Phys. Rev. D</title><idno type="ISSN">0556-2821</idno><imprint><date when="1995-06-15">1995-06-15</date></imprint></series></biblStruct></sourceDesc><seriesStmt><title level="j" type="main">Physical Review D (Particles and Fields)</title><title level="j" type="abbreviated">Phys. Rev. D</title><idno type="ISSN">0556-2821</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Casimir operators</term><term>Center-of-mass system</term><term>Energy</term><term>Equations of state</term><term>Mass</term><term>Minkowski space</term><term>Quantization</term><term>Semiclassical approximation</term><term>Space-time</term><term>String models</term><term>Theoretical study</term><term>Three-dimensional calculations</term></keywords><keywords scheme="Pascal" xml:lang="fr"><term>Etude théorique</term><term>1127</term><term>1125M</term><term>Modèle corde</term><term>Calcul 3 dimensions</term><term>Espace temps</term><term>Equation état</term><term>Energie</term><term>Masse</term><term>Quantification</term><term>Approximation semiclassique</term><term>Opérateur Casimir</term><term>Système centre masse</term><term>Espace Minkowski</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">We compute the exact equation of state of circular strings in the (2+1)-dimensional de Sitter (dS) and anti-de Sitter (AdS) spacetimes, and analyze its properties for the different (oscillating, contracting, and expanding) strings. The string equation of state has the perfect fluid form P = (γ-1)E, with the pressure and energy expressed closely and completely in terms of elliptic functions, the instantaneous coefficient γ depending on the elliptic modulus. We semiclassically quantize the oscillating circular strings. The string mass is m = * root *C /(πHα′), C being the Casimir operator, C = -L<sub>μν</sub>L<sup>μν</sup>, of the O(3,1)-dS [O(2,2)-AdS] group, and H is the Hubble constant. We find α′m<sub>dS</sub><sup>2</sup>* roughly-equal *4n-5H<sup>2</sup>α′n<sup>2</sup> (n* is-an-element-of *N<sub>0</sub>), and a finite number of states N<sub>dS</sub>* roughly-equal *0.34/(H<sup>2</sup>α′) in de Sitter spacetime; m<sub>AdS</sub><sup>2</sup>* roughly-equal *H<sup>2</sup>n<sup>2</sup> (large n* is-an-element-of *N<sub>0</sub>) and N<sub>AdS</sub> = ∞ in anti-de Sitter spacetime. The level spacing grows with n in AdS spacetime, while it is approximately constant (although smaller than in Minkowski spacetime and slightly decreasing) in dS spacetime. The massive states in dS spacetime decay through the tunnel effect and the semiclassical decay probability is computed. The semiclassical quantization of exact (circular) strings and the canonical quantization of generic string perturbations around the string center of mass qualitatively agree.</div></front></TEI><inist><standard h6="B"><pA><fA01 i1="01" i2="1"><s0>0556-2821</s0></fA01><fA02 i1="01"><s0>PRVDAQ</s0></fA02><fA03 i2="1"><s0>Phys. Rev. D</s0></fA03><fA05><s2>51</s2></fA05><fA06><s2>12</s2></fA06><fA08 i1="01" i2="1" l="ENG"><s1>Semiclassical quantization of circular strings in de Sitter and anti-de Sitter spacetimes</s1></fA08><fA11 i1="01" i2="1"><s1>DE VEGA (H. J.)</s1></fA11><fA11 i1="02" i2="1"><s1>LARSEN (A. L.)</s1></fA11><fA11 i1="03" i2="1"><s1>SÁNCHEZ (N.)</s1></fA11><fA14 i1="01"><s1>Laboratoire de Physique Théorique et Hautes Energies, Université de Paris VI et VII, Tour 16, 1er étage, 4, Place Jussieu, 75252 Paris cedex 05, France</s1><sZ>1 aut.</sZ></fA14><fA14 i1="02"><s1>Isaac Newton Institute, Cambridge, CB3 0EH, United Kingdom</s1><sZ>1 aut.</sZ></fA14><fA14 i1="03"><s1>Observatoire de Paris, DEMIRM, Observatoire de Paris et École Normale Supérieure, 61, Avenue de l'Observatoire, 75014 Paris, France</s1><sZ>2 aut.</sZ><sZ>3 aut.</sZ></fA14><fA20><s1>6917-6928</s1></fA20><fA21><s1>1995-06-15</s1></fA21><fA23 i1="01"><s0>ENG</s0></fA23><fA43 i1="01"><s1>INIST</s1><s2>144D</s2></fA43><fA44><s0>8100</s0><s1>© AIP</s1></fA44><fA47 i1="01" i2="1"><s0>95-0291912</s0></fA47><fA60><s1>P</s1></fA60><fA61><s0>A</s0></fA61><fA64 i1="01" i2="1"><s0>Physical Review D (Particles and Fields)</s0></fA64><fA66 i1="01"><s0>USA</s0></fA66><fC01 i1="01" l="ENG"><s0>We compute the exact equation of state of circular strings in the (2+1)-dimensional de Sitter (dS) and anti-de Sitter (AdS) spacetimes, and analyze its properties for the different (oscillating, contracting, and expanding) strings. The string equation of state has the perfect fluid form P = (γ-1)E, with the pressure and energy expressed closely and completely in terms of elliptic functions, the instantaneous coefficient γ depending on the elliptic modulus. We semiclassically quantize the oscillating circular strings. The string mass is m = * root *C /(πHα′), C being the Casimir operator, C = -L<sub>μν</sub>L<sup>μν</sup>, of the O(3,1)-dS [O(2,2)-AdS] group, and H is the Hubble constant. We find α′m<sub>dS</sub><sup>2</sup>* roughly-equal *4n-5H<sup>2</sup>α′n<sup>2</sup> (n* is-an-element-of *N<sub>0</sub>), and a finite number of states N<sub>dS</sub>* roughly-equal *0.34/(H<sup>2</sup>α′) in de Sitter spacetime; m<sub>AdS</sub><sup>2</sup>* roughly-equal *H<sup>2</sup>n<sup>2</sup> (large n* is-an-element-of *N<sub>0</sub>) and N<sub>AdS</sub> = ∞ in anti-de Sitter spacetime. The level spacing grows with n in AdS spacetime, while it is approximately constant (although smaller than in Minkowski spacetime and slightly decreasing) in dS spacetime. The massive states in dS spacetime decay through the tunnel effect and the semiclassical decay probability is computed. The semiclassical quantization of exact (circular) strings and the canonical quantization of generic string perturbations around the string center of mass qualitatively agree.</s0></fC01><fC02 i1="01" i2="3"><s0>001B10A27</s0></fC02><fC02 i1="02" i2="3"><s0>001B10A25M</s0></fC02><fC03 i1="01" i2="3" l="FRE"><s0>Etude théorique</s0></fC03><fC03 i1="01" i2="3" l="ENG"><s0>Theoretical study</s0></fC03><fC03 i1="02" i2="3" l="FRE"><s0>1127</s0><s2>PAC</s2><s4>INC</s4></fC03><fC03 i1="03" i2="3" l="FRE"><s0>1125M</s0><s2>PAC</s2><s4>INC</s4></fC03><fC03 i1="04" i2="3" l="FRE"><s0>Modèle corde</s0></fC03><fC03 i1="04" i2="3" l="ENG"><s0>String models</s0></fC03><fC03 i1="05" i2="3" l="FRE"><s0>Calcul 3 dimensions</s0></fC03><fC03 i1="05" i2="3" l="ENG"><s0>Three-dimensional calculations</s0></fC03><fC03 i1="06" i2="3" l="FRE"><s0>Espace temps</s0></fC03><fC03 i1="06" i2="3" l="ENG"><s0>Space-time</s0></fC03><fC03 i1="07" i2="3" l="FRE"><s0>Equation état</s0></fC03><fC03 i1="07" i2="3" l="ENG"><s0>Equations of state</s0></fC03><fC03 i1="08" i2="3" l="FRE"><s0>Energie</s0></fC03><fC03 i1="08" i2="3" l="ENG"><s0>Energy</s0></fC03><fC03 i1="09" i2="3" l="FRE"><s0>Masse</s0></fC03><fC03 i1="09" i2="3" l="ENG"><s0>Mass</s0></fC03><fC03 i1="10" i2="3" l="FRE"><s0>Quantification</s0></fC03><fC03 i1="10" i2="3" l="ENG"><s0>Quantization</s0></fC03><fC03 i1="11" i2="3" l="FRE"><s0>Approximation semiclassique</s0></fC03><fC03 i1="11" i2="3" l="ENG"><s0>Semiclassical approximation</s0></fC03><fC03 i1="12" i2="3" l="FRE"><s0>Opérateur Casimir</s0></fC03><fC03 i1="12" i2="3" l="ENG"><s0>Casimir operators</s0></fC03><fC03 i1="13" i2="3" l="FRE"><s0>Système centre masse</s0></fC03><fC03 i1="13" i2="3" l="ENG"><s0>Center-of-mass system</s0></fC03><fC03 i1="14" i2="3" l="FRE"><s0>Espace Minkowski</s0></fC03><fC03 i1="14" i2="3" l="ENG"><s0>Minkowski space</s0></fC03><fN21><s1>171</s1></fN21><fN47 i1="01" i2="1"><s0>9511M2248</s0></fN47></pA></standard><server><NO>PASCAL 95-0291912 AIP</NO><ET>Semiclassical quantization of circular strings in de Sitter and anti-de Sitter spacetimes</ET><AU>DE VEGA (H. J.); LARSEN (A. L.); SÁNCHEZ (N.)</AU><AF>Laboratoire de Physique Théorique et Hautes Energies, Université de Paris VI et VII, Tour 16, 1er étage, 4, Place Jussieu, 75252 Paris cedex 05, France (1 aut.); Isaac Newton Institute, Cambridge, CB3 0EH, United Kingdom (1 aut.); Observatoire de Paris, DEMIRM, Observatoire de Paris et École Normale Supérieure, 61, Avenue de l'Observatoire, 75014 Paris, France (2 aut., 3 aut.)</AF><DT>Publication en série; Niveau analytique</DT><SO>Physical Review D (Particles and Fields); ISSN 0556-2821; Coden PRVDAQ; Etats-Unis; Da. 1995-06-15; Vol. 51; No. 12; Pp. 6917-6928</SO><LA>Anglais</LA><EA>We compute the exact equation of state of circular strings in the (2+1)-dimensional de Sitter (dS) and anti-de Sitter (AdS) spacetimes, and analyze its properties for the different (oscillating, contracting, and expanding) strings. The string equation of state has the perfect fluid form P = (γ-1)E, with the pressure and energy expressed closely and completely in terms of elliptic functions, the instantaneous coefficient γ depending on the elliptic modulus. We semiclassically quantize the oscillating circular strings. The string mass is m = * root *C /(πHα′), C being the Casimir operator, C = -L<sub>μν</sub>L<sup>μν</sup>, of the O(3,1)-dS [O(2,2)-AdS] group, and H is the Hubble constant. We find α′m<sub>dS</sub><sup>2</sup>* roughly-equal *4n-5H<sup>2</sup>α′n<sup>2</sup> (n* is-an-element-of *N<sub>0</sub>), and a finite number of states N<sub>dS</sub>* roughly-equal *0.34/(H<sup>2</sup>α′) in de Sitter spacetime; m<sub>AdS</sub><sup>2</sup>* roughly-equal *H<sup>2</sup>n<sup>2</sup> (large n* is-an-element-of *N<sub>0</sub>) and N<sub>AdS</sub> = ∞ in anti-de Sitter spacetime. The level spacing grows with n in AdS spacetime, while it is approximately constant (although smaller than in Minkowski spacetime and slightly decreasing) in dS spacetime. The massive states in dS spacetime decay through the tunnel effect and the semiclassical decay probability is computed. The semiclassical quantization of exact (circular) strings and the canonical quantization of generic string perturbations around the string center of mass qualitatively agree.</EA><CC>001B10A27; 001B10A25M</CC><FD>Etude théorique; 1127; 1125M; Modèle corde; Calcul 3 dimensions; Espace temps; Equation état; Energie; Masse; Quantification; Approximation semiclassique; Opérateur Casimir; Système centre masse; Espace Minkowski</FD><ED>Theoretical study; String models; Three-dimensional calculations; Space-time; Equations of state; Energy; Mass; Quantization; Semiclassical approximation; Casimir operators; Center-of-mass system; Minkowski space</ED><LO>INIST-144D</LO><ID>95-0291912</ID></server></inist></record>Pour manipuler ce document sous Unix (Dilib)
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