Investigations in low dimensional quantum field theory  Page description

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Details of project

  
Identifier
43159
Type K
Principal investigator Vecsernyés, Péter
Title in Hungarian Alacsony dimenziós kvantumtérelméleti modellek vizsgálata
Title in English Investigations in low dimensional quantum field theory
Panel Physics 1
Department or equivalent Theoretical Physics Department (Wigner Research Centre for Physics)
Participants Balog, János
Böhm, Gabriella Eszter
Fehér, László Gyula
Hegedüs, Árpád
Szlachányi, Kornél
Zimborás, Zoltán
Starting date 2003-01-01
Closing date 2006-12-31
Funding (in million HUF) 9.943
FTE (full time equivalent) 0.00
state closed project





 

Final report

  
Results in Hungarian
1. 2d integrálható modellek Termodinamikai Bethe ansatz és integrálegyenlet technikával véges méret spektrumot határoztunk meg. O(N)-modellek kontinuum limesz konstrukciójában megadtuk a rácskorrekciók eltűnésének rácsállandó-függését. O(3)-modellbeli ''hadronikus'' struktúra-függvényre kis Bjorken-x-re egzakt alakot vezettünk le. 2 Szimmetriastruktúrák és Calogero modellek Megadtuk a WZNW-modellek Poisson-Lie szimmetriáit generáló momentum-leképzést, a dinamikai Yang-Baxter egyenlet általánositását, a Calogero modell inekvivalens kvantálásait. Megmutattuk, hogy dinamikai r-mátrix konstrukciói spin Calogero modelleknek Lie csoporton való szabad mozgás hamiltoni redukciói. Negativ görbületű Riemann szimmetrikus téren szabad mozgás hamiltoni redukciója spin Calogero modellre vezet. 3.Spinláncok és rácselméletek Megmutattuk, hogy az XX-láncnál az energiáram, Heisenberg-láncnál a csatolások kváziperiodikus perturbációja az összefonódottságot növeli, s hogy kvantumspinláncok eltolásinvariáns állapotaira vonatkozó nulla entrópia-sűrűség sejtés éles. MC szimulációval azt találtuk, hogy a 4d Ising modell kontinuum limesze triviális, de a konvergencia nagyon lassú. 4.Kvantumgrupoidok 2-es mélységű algebrabővitéseket jellemeztünk bialgebroidokkal, melyek balanszirozott esetben a Galois-csoport analógjai. Bevezettük a Hopf algebroidok fogalmát, tanulmányoztuk szerepüket hasadt algebra-bővitésekben, Hopf-Galois kiterjesztésekben és nem-kommutativ geometrában.
Results in English
1. 2d integrable models Finite volume spectra are given using thermal Bethe ansatz and integral equations. The decay form of lattice artifacts is established in the continuum limit construction of O(N)-models. The exact small (Bjorken) x behaviour of the 'hadronic' structure function in the O(3)-model was derived. 2.Symmetry structures and Calogero models The momentum map, the generator of Poisson-Lie symmetries in WZNW models was given, the dynamical Yang-Baxter equation was generalized. Inequivalent quantizations of Calogero model were given. Dynamical r-matrix construction of spin Calogero model is shown to be the Hamiltonian reduction of free motion on a Lie group. Hamiltonian reduction of free motion on a symmetric Riemann space with negative curvature leads to spin Calogero models. 3.Spin chains and lattice theories The energy current in the XX model and the aperiodic perturbation of couplings in the Heisenberg chain increase the entanglement entropy. The zero-entropy-density conjecture is sharp for translation-invariant states of spin chains. The continuum limit of the 4d Ising model is found to be trivial by MC methods but the convergence is very slow. 4.Quantum groupoids Depth 2 algebra extensions were characterized by bialgebroids, the analogues of Galois groups in the balanced case. The notion of Hopf algebroids was introduced. Their role was determined in cleft algebra extensions, in Hopf-Galois extensions, in non-commutative geometry.
Full text http://real.mtak.hu/954/
Decision
Yes





 

List of publications

  
Á. Hegedus: Finite size effects in the SS-model: two component nonlinear integral equations, Nucl. Phys. B679, 545-567, 2004
G. Böhm, K. Szlachányi: Hopf algebroids with bijective antipodes: axioms, integrals and duals, J. Algebra 274, 708-750, 2004
G. Böhm: Internal bialgebroids, entwining structures and corings, AMS Contemp. Math. 376, 207-226, 2005
J. Balog, P. Weisz: Test of asymptotic freedom and scaling hypothesis in the 2d O(3) sigma model, Nucl. Phys. B668, 506-516, 2003
J. Balog, F. Knechtli, T. Korzec, U. Wolff: Numerical confirmation of analytic predictions for the finite volume mass gap of the XY model, Nucl. Phys. B675, 555-566, 2003
L. Fehér, B.G. Pusztai: Explicit description of twisted Wakimoto realizations of affine Lie algebras, Nucl. Phys. B674, 509-532, 2003
L. Kadison, K. Szlachányi: Dual bialgebroids for depth two ring extensions, Adv. Math. 179, 75-121, 2003
K. Szlachányi: The monoidal Eilenberg-Moore construction and bialgebroids, J. Pure Appl. Algebra 182, 287-315, 2003
P. Vecsernyés: Larson-Sweedler theorem and the role of grouplike elements in weak Hopf algebras, J. Algebra 270, 471-520, 2003
K. Szlachányi: Galois actions by finite quantum groupoids, Locally compact quantum groups and groupoids, Proc. of the meeting of theor.phys. and math., Strasbourg, 2002; IRMA Lect. in Math. and Theor.Phys., de Gruyter, 2003
J. Balog, P. Weisz: Structure functions of the 2d O(N) non-linear sigma models, Nucl. Phys. B709, 329-380, 2005
J. Balog, A. Duncan, R. Willey, F. Niedermayer, P. Weisz: The 4d one component lattice phi^4 model in the broken phase revisited, Nucl. Phys. B714, 256-268, 2005
G. Böhm: Galois theory for Hopf algebroids, Annali dell'Universita di Ferrara, Sezione VII, Scienze Matematiche, Vol.LI, 233-262, 2005
G. Böhm: Integral theory for Hopf algebroids, Algebras and Rep. Theory 8, 563-599, 2005
L. Fehér, B.G. Pusztai: Spin Calogero models obtained from dynamical r-matrices and geodesic motion, Nucl.Phys. B734, 304-325, 2006
Á. Hegedus: Nonlinear integral equations for finite volume excited state energies of the O(3) and O(4) sigma models, J.Phys. A38, 5345-5358, 2005
V. Eisler, Z. Zimborás: Entaglement in the XX spin chain with energy current, Phys. Rev. A71, 042318, 2005
J. Balog, Á. Hegedus: TBA equations for excited states in the O(3) and O(4) nonlinear sigma-model, J. of Phys. A37, 1881-1902, 2004
J. Balog, Á. Hegedus: TBA equations for excited states in the sine-Gordon model, J. of Phys. A37, 1903-1923, 2004
J. Balog, P. Weisz: Structure functions of 2d integrable asymptotically free models, Phys. Lett. B594, 141-152, 2004
G. Böhm, K. Szlachányi: Hopf algebroid symmetry of abstract Frobenius extensions of depth 2, Commun. Algebra 32, 4433-4464, 2004
Z. Bajnok, G. Böhm, G. Takács: On perturbative quantum field theory with boundary, Nucl. Phys. B682, 585-617, 2004
K. Szlachányi: The double algebraic view of finite quantum groupoids, J. Algebra 280, 249-294, 2004
J. Balog, F. Knechtli, , T. Korzer, U. Wolff: Comparison of analytic and numerical results in the XY model, Nucl. Phys. Proc. Suppl. 129, 777-779, 2004
G. Böhm: An alternative notion of Hopf algebroid, Lect. Notes in Pure and Appl. Math. 239, 31-54, Marcel Dekker, 2004
U. Wolff, F. Knechtli, B. Leder, J. Balog: Cutoff effects in the O(N) sigma model at large N, PoS LAT2005, 253, 2006
J. Balog, A. Hegedus: TBA equations for the mass gap in the O(2N) non-linear sigma models, Nucl. Phys. B725, 531-553, 2005
Á. Hegedus: Nonlinear integral equations for the finite size effects of RSOS and vertex-models and related quantum field theories, Nucl.Phys. B732, 463-486, 2005
L. Fehér, B.G. Pusztai: Spin Calogero models and dynamical r-matrices, Bulgarian J. of Phys. 33, 2006
G. Böhm, T. Brzezinski: Strong connections and the relative Chern-Galois character for corings, Int. Math. Res. Notices 42, 2579-2625, 2005
G. Böhm, T. Brzezinski: Cleft extensions of Hopf algebroids, Appl.Cat.Str. 14, 431-469, 2006
I. Balint, K. Szlachanyi: Finitary Galois extensions over noncommutative bases, J.Algebra 296, 520-560, 2006
S. Farkas, Z. Zimborás: On the sharpness of the zero-entropy-density conjecture, J. Math. Phys. 46, 123301, 2005
Z. Zimborás: What can one reconstruct from the representation ring of a compact group?, Bulgarian J. of Phys. 33, 2006
J. Balog, F. Niedermayer, P. Weisz: Repairing Stevenson's step in the 4-D Ising model, Nucl. Phys. B741, 390-403, 2006
G. Böhm, J. Vercruysse: Morita theory for coring extensions and cleft bicomodules, Adv. Math. 209, 611-648, 2007
A. Ardizzoni, G. Böhm, C. Menini: A Schneider type theorem for Hopf algebroids, arXiv:math.QA/0612633, 2006
G. Böhm, T. Brzezinski: Pre-torsors and equivalences, arXiv:math.QA/0607529, 2006
G. Böhm: Galois extensions over commutative and non-commutative base, arXiv:math.QA/0701064, 2007
L. Fehér, B.G. Pusztai: A class of Calogero type reductions of free motions on a simple Lie group, arXiv:math-ph/0609085, 2006
L. Fehér, B.G. Pusztai: Spin Calogero models associated with Riemannian symmetric spaces of negative curvature, Nucl.Phys. B751, 436-458, 2006
L. Fehér, I. Tsutsui, I. Fulop: Inequivalent quantizations of the three-particle Calogero model constructed by separation of variables, Nucl.Phys. B715, 713-757, 2005
L. Fehér: Poisson-Lie dynamical r-matrices from Dirac reduction, Czech.J.Phys. 54, 1265-1274, 2004
L. Fehér, I. Marshall: The non-Abelian momentum map for Poisson-Lie symmetries on the chiral WZNW phase space, Int.Math.Res.Not. 49, 2611-2636, 2004
Á. Hegedus, F. Ravanini, J. Suzuki: Exact finite size spectrum in super sine-Gordon model, Nucl.Phys. B763, 330-353, 2007
K. Szlachányi: Monoidal Morita equivalence, Contemp.Math. 391, 353-369, 2005
F. Igloi, R. Juhasz, Z. Zimborás: Entaglement entropy of aperiodic quantum spin chains, arXiv:cond-mat/0701527, 2007



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