Complex Path Integrals and the Space of Theories

Ricardo Schiappa, Ricardo Vaz, The Resurgence of Instantons: Multi-Cuts Stokes Phases and the Painleve II Equation , ⟨ arXiv:1302.5138 [hep-th] ⟩. Inês Aniceto, Ricardo Schiappa, Marcel Vonk, The Resurgence of Instantons in String Theory , ⟨ arXiv:1106.5922 [hep-th] ⟩. Marcos Marino, Ricardo Schiappa, Marlene Weiss, Nonperturbative Effects and the Large-Order Behavior of Matrix Models and Topological Strings , ⟨ arXiv:0711.1954 [hep-th] ⟩. Marcos Marino, Ricardo Schiappa, Marlene Weiss, Multi-Instantons and Multi-Cuts , ⟨ arXiv:0809.2619 [hep-th] ⟩. Ricardo Schiappa, Niclas Wyllard, An A r A_{r} threesome: Matrix models, 2 ​ d 2d CFTs and 4 ​ d ​ 𝒩 = 2 4d\,\mathcal{N}=2 gauge theories , ⟨ arXiv:0911.5337 [hep-th] ⟩. Bertrand Eynard, Marcos Marino, A holomorphic and background independent partition function for matrix models and topological strings , ⟨ arXiv:0810.4273 [hep-th] ⟩

Original

1954

Earlier work this paper cites.

Ian Knowles, On J J -Selfadjoint Extensions of J J -Symmetric Operators , ⟨ DOI: 10.1090/S0002-9939-1980-0560580-X ⟩. A. Ibort, Three lectures on global boundary conditions and the theory of self-adjoint extensions of the covariant Laplace–Beltrami and Dirac operators on Riemannian manifolds with boundary , ⟨ arXiv:1205.3579 [math-ph] ⟩

Original

1980

Earlier work this paper cites.

Vladimir Petrov Kostov, The Deligne–Simpson problem — a survey , ⟨ DOI: 10.1016/j.jalgebra.2004.07.013 ⟩, ⟨ arXiv:math/0206298 [math.RA] ⟩. Carlos Simpson, Higgs bundles and local systems , ⟨ Publ. Mathématiques de l’IHÉS 75 (1992), p. 5-95 ⟩. Kevin J. Costello, Notes on supersymmetric and holomorphic field theories in dimensions 2 and 4 , ⟨ arXiv:1111.4234 [math.QA] ⟩

Original

1992

Cited alongside, same era.

N. Südland, G. Baumann, T. F. Nonnenmacher, Open Problem: Who Knows About the ℵ \aleph -Functions? , ⟨ Fract. Calc. Appl. Anal., Vol 1, No 4, (1998) ⟩. N. Südland, G. Baumann, T. F. Nonnenmacher, Fractional Driftless Fokker-Planck Equations with Power Law Diffusion Coefficients , ⟨ The 4th International Workshop on Computer Algebra in Scientific Computing (CASC, Konstanz, Germany, 2001) ⟩. Arjun K. Rathie, A new generalization of generalized hypergeometric functions , ⟨ Le Matematiche, Vol 52, No 2 (1997) ⟩. Ram K. Saxena, Tibor K. Pogány, Mathieu–type Series for the ℵ \aleph -function Occurring in Fokker-Planck Equation , ⟨ EJPAM, Vol 3, No 6 (2010) ⟩

2001

Cited alongside, same era.

S. Garcia, G. S. Guralnik, Z. Guralnik, Theta Vacua and Boundary Conditions of the Schwinger Dyson Equations , ⟨ arXiv:hep-th/9612079 ⟩. D. D. Ferrante, G. S. Guralnik, Mollifying Quantum Field Theory or Lattice QFT in Minkowski Spacetime and Symmetry Breaking , ⟨ arXiv:hep-lat/0602013 ⟩. G. S. Guralnik, Z. Guralnik, Complexified Path Integrals and the Phases of Quantum Field Theory , ⟨ arXiv:0710.1256 [hep-th] ⟩. D. D. Ferrante, G. S. Guralnik, Phase Transitions and Moduli Space Topology , ⟨ arXiv:0809.2778 [hep-th] ⟩. D. D. Ferrante, Symmetry Breaking: A New Paradigm for Non-Perturbative QFT and Topological Transitions , ⟨ arXiv:0904.2205 [hep-th] ⟩

Original

Cited in the paper.

Nikolai Laskin, Fractional quantum mechanics and Lévy path integrals , ⟨ DOI: 10.1016/S0375-9601(00)00201-2 ⟩. Nick Laskin, Fractional Schrodinger equation , ⟨ arXiv:quant-ph/0206098 ⟩. Nick Laskin, Lévy Flights over Quantum Paths , ⟨ arXiv:quant-ph/0504106 ⟩. Nick Laskin, Fractional Quantum Mechanics , ⟨ arXiv:0811.1769 [math-ph] ⟩. Nick Laskin, Principles of Fractional Quantum Mechanics , ⟨ arXiv:1009.5533 [math-ph] ⟩. Francesco Mainardia, Gianni Pagninib, R. K. Saxena, Fox H H -functions in fractional diffusion , ⟨ DOI: 10.1016/j.cam.2004.08.006 ⟩. Selcuk S. Bayin, Fox’s H H -Functions and the Time Fractional Schrödinger Equation , ⟨ arXiv:1103.3295 [math-ph] ⟩. Yakubovich, S. B. and Luchko, Y. F., The Hypergeometric Approach to Integral Transforms and Convolutions , ⟨ ISBN: 978-0-7923-2856-8 ⟩

Original

Cited in the paper.

Kurt Bernardo Wolf, Integral transforms in science and engineering , ⟨ ISBN: 0306392518, 9780306392511 ⟩

Cited in the paper.

Lev A. Borisov, R. Paul Horja, Mellin–Barnes integrals as Fourier–Mukai transforms , ⟨ arXiv:math/0510486 [math.AG] ⟩. A. M. Mathai, R. K. Saxena, H. J. Haubold, The H H -Function: Theory and Applications , ⟨ ISBN: 978-1-4419-0915-2 ⟩

Cited in the paper.

Petr Hořava, Quantum Gravity at a Lifshitz Point , ⟨ arXiv:0901.3775 [hep-th] ⟩

Original

Cited in the paper.

M. Reed, B. Simon, Methods of Modern Mathematical Physics, Vol. 2: Fourier Analysis, Self-Adjointness , ⟨ ISBN: 978-0-1258-5002-5 ⟩

Cited in the paper.

John P. Boyd, The Devil’s Invention: Asymptotic, Superasymptotic and Hyperasymptotic Series , ⟨ DOI: 10.1023/A:1006145903624 ⟩

Cited in the paper.

W. R. Schneider, Stable distributions: Fox function representation and generalization , ⟨ DOI: 10.1007/3540171665_92 ⟩. Vladimir V. Uchaikin, V. M. Zolotarev, Chance and stability: stable distributions and their applications , ⟨ ISBN: 9067643017, 9789067643016 ⟩. Francesco Mainardi, Yuri Luchko, Gianni Pagnini, The fundamental solution of the space-time fractional diffusion equation , ⟨ arXiv:cond-mat/0702419 [cond-mat.stat-mech] ⟩

Cited in the paper.

Tom Bridgeland, Valerio Toledano-Laredo, Stability conditions and Stokes factors , ⟨ arXiv:0801.3974 [math.AG] ⟩

Original

Cited in the paper.

Carl M. Bender, Dorje C. Brody, Hugh F. Jones, Complex Extension of Quantum Mechanics , ⟨ arXiv:quant-ph/0208076 ⟩

Cited in the paper.

Yakov Eliashberg, Alexander Givental, Helmut Hofer, Introduction to Symplectic Field Theory , ⟨ arXiv:math/0010059 [math.SG] ⟩. Yakov Eliashberg, Symplectic field theory and its applications , ⟨ Proceedings of the International Congress of Mathematicians: Madrid, August 22--30, 2006, Vol. 1, ISBN 978-3-03719-022-7, 217--246 ⟩

2006

Later among the works it cites.

Robert P. Langlands, Beyond endoscopy , ⟨ Shalika volume, Johns Hopkins University Press. (2004) ⟩. P. Edward Herman, The Functional Equation and Beyond Endoscopy , ⟨ arXiv:1208.5783 [math.NT] ⟩. Robert P. Langlands, Functoriality and Reciprocity , ⟨ Lectures at IAS, March, 2011 ⟩. Daniel Sternheimer, Quantization: Deformation and/or Functor? , ⟨ DOI: 10.1007/ s11005-005-0028-4 ⟩. N. P. Landsman, Quantization as a functor , ⟨ arXiv:math-ph/0107023 ⟩

Original

2011

Later among the works it cites.