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Quantum energy inequalities in integrable models with several particle species and bound states (2302.00063v2)
Published 25 Jan 2023 in math-ph, hep-th, and math.MP
Abstract: We investigate lower bounds to the time-smeared energy density, so-called quantum energy inequalities (QEI), in the class of integrable models of quantum field theory. Our main results are a state-independent QEI for models with constant scattering function and a QEI at one-particle level for generic models. In the latter case, we classify the possible form of the stress-energy tensor from first principles and establish a link between the existence of QEIs and the large-rapidity asymptotics of the two-particle form factor of the energy density. Concrete examples include the Bullough-Dodd, the Federbush, and the $O(n)$-nonlinear sigma models.
- Elcio Abdalla, Maria Cristina Batoni Abdalla and Klaus Dieter Rothe “Non-Perturbative Methods in 2 Dimensional Quantum Field Theory.” Singapore: World Scientific Publishing Company, 2001
- P. G. Appleby, B. R. Duffy and R. W. Ogden “On the Classification of Isotropic Tensors” In Glasgow Mathematical Journal 29.2, 1987, pp. 185–196 DOI: 10.1017/S0017089500006832
- A. E. Arinshtein, V. A. Fateyev and A. B. Zamolodchikov “Quantum S-matrix of the (1 + 1)-Dimensional Todd Chain” In Physics Letters B 87.4, 1979, pp. 389–392 DOI: 10.1016/0370-2693(79)90561-6
- “Inverse Scattering and Local Observable Algebras in Integrable Quantum Field Theories” In Communications in Mathematical Physics 354.3, 2017, pp. 913–956 DOI: 10.1007/s00220-017-2891-0
- “Exact Form Factors in Integrable Quantum Field Theories: The Sine-Gordon Model” In Nuclear Physics B 538.3, 1999, pp. 535–586
- “Higher Transcendental Functions - Volume 1” McGraw-Hill Book Company, Inc., 1953
- “Characterization of Local Observables in Integrable Quantum Field Theories” In Communications in Mathematical Physics 337.3 Springer Science and Business Media LLC, 2015, pp. 1199–1240 DOI: 10.1007/s00220-015-2294-z
- “Negative Energy Densities in Integrable Quantum Field Theories at One-Particle Level” In Physical Review D 93.6 American Physical Society (APS), 2016 DOI: 10.1103/physrevd.93.065001
- “Fermionic Integrable Models and Graded Borchers Triples” In arXiv:2112.14686 [math-ph], 2021 arXiv:2112.14686 [math-ph]
- Henning Bostelmann, Daniela Cadamuro and Christopher J. Fewster “Quantum Energy Inequality for the Massive Ising Model” In Physical Review D 88.2 American Physical Society, 2013, pp. 025019 DOI: 10.1103/PhysRevD.88.025019
- Henning Bostelmann and Christopher J. Fewster “Quantum Inequalities from Operator Product Expansions” In Communications in Mathematical Physics 292.3, 2009, pp. 761 DOI: 10.1007/s00220-009-0853-x
- H. Babujian, A. Foerster and M. Karowski “Exact Form Factors in Integrable Quantum Field Theories: The Scaling Z(N)-Ising Model” In Nuclear Physics B 736.3, 2006, pp. 169–198 DOI: 10.1016/j.nuclphysb.2005.12.001
- H. M. Babujian, A. Foerster and M. Karowski “The Form Factor Program: A Review and New Results, the Nested SU(N) off-Shell Bethe Ansatz and the 1/N Expansion” In Theoretical and Mathematical Physics 155.1, 2008, pp. 512–522 DOI: 10.1007/s11232-008-0042-7
- Hrachya M. Babujian, Angela Foerster and Michael Karowski “Exact Form Factors of the SU(N) Gross–Neveu Model and 1/N Expansion” In Nuclear Physics B 825.3, 2010, pp. 396–425 DOI: 10.1016/j.nuclphysb.2009.09.023
- H. M. Babujian, A. Foerster and M. Karowski “Exact Form Factors of the O(N) Sigma-Model” In Journal of High Energy Physics, 2013, pp. 89–143 DOI: 10.1007/JHEP11(2013)089
- Hrachya M. Babujian, Angela Foerster and Michael Karowski “Asymptotic Factorization of N-Particle SU(N) Form Factors” In Journal of High Energy Physics 2021.6, 2021, pp. 32 DOI: 10.1007/JHEP06(2021)032
- “Exact Form Factors in Integrable Quantum Field Theories: The Sine-Gordon Model (II)” In Nuclear Physics B 620.3, 2002, pp. 407–455 DOI: 10.1016/S0550-3213(01)00551-X
- Henning Bostelmann, Gandalf Lechner and Gerardo Morsella “Scaling Limits of Integrable Quantum Field Theories” In Reviews in Mathematical Physics 23.10 World Scientific Publishing Co., 2011, pp. 1115–1156 DOI: 10.1142/S0129055X11004539
- L. Castillejo, R. H. Dalitz and F. J. Dyson “Low’s Scattering Equation for the Charged and Neutral Scalar Theories” In Physical Review 101.1 American Physical Society, 1956, pp. 453–458 DOI: 10.1103/PhysRev.101.453
- “Form Factors from Free Fermionic Fock Fields, the Federbush Model” In Nuclear Physics B 618.3, 2001, pp. 437–464 DOI: 10.1016/S0550-3213(01)00462-X
- “Wedge-Local Fields in Integrable Models with Bound States” In Communications in Mathematical Physics 340.2, 2015, pp. 661–697 DOI: 10.1007/s00220-015-2448-z
- S. P. Dawson “A Quantum Weak Energy Inequality for the Dirac Field in Two-Dimensional Flat Spacetime” In Classical and Quantum Gravity 23.1, 2006, pp. 287–293 DOI: 10.1088/0264-9381/23/1/014
- G. Delfino, P. Simonetti and J. L. Cardy “Asymptotic Factorisation of Form Factors in Two-Dimensional Quantum Field Theory” In Physics Letters B 387.2, 1996, pp. 327–333 DOI: 10.1016/0370-2693(96)01035-0
- C. J. Fewster and S. P. Eveson “Bounds on Negative Energy Densities in Flat Spacetime” In Physical Review D 58.8, 1998 DOI: 10.1103/PhysRevD.58.084010
- P. Federbush “A Two-Dimensional Relativistic Field Theory” In Physical Review 121.4, 1961, pp. 1247–1249 DOI: 10.1103/PhysRev.121.1247
- Christopher J. Fewster “Lectures on Quantum Energy Inequalities” In arXiv:1208.5399 [gr-qc, math-ph], 2012 arXiv:1208.5399 [gr-qc, math-ph]
- Christopher J. Fewster and Stefan Hollands “Quantum Energy Inequalities in Two-Dimensional Conformal Field Theory” In Reviews in Mathematical Physics 17.05 World Scientific Pub Co Pte Lt, 2005, pp. 577–612 DOI: 10.1142/s0129055x05002406
- A. Fring, G. Mussardo and P. Simonetti “Form Factors for Integrable Lagrangian Field Theories, the Sinh-Gordon Model” In Nuclear Physics B 393, 1993, pp. 413–441 DOI: 10.1016/0550-3213(93)90252-k
- L. H. Ford “Quantum Coherence Effects and the Second Law of Thermodynamics” In Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 364.1717 Royal Society, 1978, pp. 227–236 DOI: 10.1098/rspa.1978.0197
- Th. Jolicoeur and J. C. Niel “An Analytical Evaluation for the Mass Gap of the Non-Linear Sigma Model” In Nuclear Physics B 300, 1988, pp. 517–530 DOI: 10.1016/0550-3213(88)90610-4
- “On the Uniqueness of a Purely Elastic S-matrix in (1+1) Dimensions” In Physics Letters B 67.3, 1977, pp. 321–322 DOI: 10.1016/0370-2693(77)90382-3
- Tosio Kato “Perturbation Theory for Linear Operators”, Classics in Mathematics Springer, 1995
- “On the Operator Content of the Sinh-Gordon Model” In Physics Letters B 311.1, 1993, pp. 193–201 DOI: 10.1016/0370-2693(93)90554-U
- “Energy Conditions in General Relativity and Quantum Field Theory” In Classical and Quantum Gravity 37.19, 2020, pp. 193001 DOI: 10.1088/1361-6382/ab8fcf
- “Exact Form Factors in (1 + 1)-Dimensional Field Theoretic Models with Soliton Behaviour” In Nuclear Physics B 139.4, 1978, pp. 455–476 DOI: 10.1016/0550-3213(78)90362-0
- M. Yu Lashkevich “Sectors of Mutually Local Fields in Integrable Models of Quantum Field Theory” In arXiv:hep-th/9406118, 1994 arXiv:hep-th/9406118
- Gandalf Lechner “Algebraic Constructive Quantum Field Theory: Integrable Models and Deformation Techniques” arXiv, 2015 DOI: 10.48550/arXiv.1503.03822
- “Fock Representations of Quantum Fields with Generalized Statistic” In Communications in Mathematical Physics 169.3, 1995, pp. 635–652 DOI: 10.1007/BF02099316
- “Towards an Operator-Algebraic Construction of Integrable Global Gauge Theories” In Annales Henri Poincaré 15.4, 2014, pp. 645–678 DOI: 10.1007/s00023-013-0260-x
- Jan Mandrysch “Energy Inequalities in Integrable Quantum Field Theory”, 2023 URL: nbn-resolving.org/urn:nbn:de:bsz:15-qucosa2-873564
- Jan Mandrysch “Numerical Results on Quantum Energy Inequalities in Integrable Models at the Two-Particle Level” arXiv, 2023 arXiv:2312.14960 [gr-qc, physics:hep-th]
- “NIST Digital Library of Mathematical Functions”, http://dlmf.nist.gov/, Release 1.1.7 of 2022-10-15
- K. R. Parthasarathy “Eigenvalues of Matrix-Valued Analytic Maps” In Journal of the Australian Mathematical Society 26.2, 1978, pp. 179–197 DOI: 10.1017/S144678870001168X
- “Methods of Modern Mathematical Physics II: Fourier Analysis, Self-Adjointness” Elsevier Science, 1975
- S. N. M. Ruijsenaars “Integrable Quantum Field Theories and Bogoliubov Transformations” In Annals of Physics 132.2, 1981, pp. 328–382 DOI: 10.1016/0003-4916(81)90071-3
- S. N. M. Ruijsenaars “Scattering Theory for the Federbush, Massless Thirring and Continuum Ising Models” In Journal of Functional Analysis 48.2, 1982, pp. 135–171 DOI: 10.1016/0022-1236(82)90065-9
- “Current Definition and a Generalized Federbush Model” In Annals of Physics 115.1, 1978, pp. 136–152 DOI: 10.1016/0003-4916(78)90178-1
- F. A. Smirnov “Form Factors In Completely Integrable Models Of Quantum Field Theory” World Scientific, 1992
- B. Schroer, T.T. Truong and P. Weisz “Towards an Explicit Construction of the Sine-Gordon Field Theory” In Physics Letters B 63.4, 1976, pp. 422–424 DOI: 10.1016/0370-2693(76)90386-5
- Yoh Tanimoto “Construction of Two-Dimensional Quantum Field Models through Longo-Witten Endomorphisms” In Forum of Mathematics, Sigma 2.e7 Cambridge University Press, 2014 DOI: 10.1017/fms.2014.3
- A. B. Zamolodchikov “Irreversibility of the Flux of the Renormalization Group in a 2D Field Theory” In Journal of Experimental and Theoretical Physics Letters 43, 1986, pp. 730–732
- Alexander B. Zamolodchikov and Alexey B. Zamolodchikov “Relativistic Factorized S-matrix in Two Dimensions Having O(N) Isotopic Symmetry” In Nuclear Physics B 133.3, 1978, pp. 525–535 DOI: 10.1016/0550-3213(78)90239-0
- Alexander B. Zamolodchikov and Alexey B. Zamolodchikov “Factorized S-matrices in Two Dimensions as the Exact Solutions of Certain Relativistic Quantum Field Theory Models” In Annals of Physics 120.2, 1979, pp. 253–291 DOI: 10.1016/0003-4916(79)90391-9
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