Integrability: The Seiberg-Witten and Whitham Equations, Edited together with I.M. Krichever.
Gordon and Breach, 2000.
Obituaries
Victor Enolski, Notices of the American Mathematical Society, December (2020).
Papers
H. W. Braden and Linden Disney-Hogg, Dihedrally Symmetric Monopoles and Affine Toda Equations, J. Phys. A 57, 495207, 2024. [Journal of Physics A] [arXiv:2407.20747]
H. W. Braden, Sergey A. Cherkis and Jason M. Quinones, Construction of exact solutions to Nahm's equations for the multimonopole, Journal of Mathematical Physics, Vol. 64, No. 1 (2023), pp. 011701-1-24. [Journal of Mathematical Physics] [arXiv:2204.07822]
H. W. Braden and V.Z. Enolski, The Charge 2 Monopole via the ADHMN construction (With an Appendix by David E. Braden, Peter Braden, and H. W. Braden), Advances in Theoretical and Mathematical Physic, Vol. 25, No. 4 (2021), pp. 791-956. [Advances in Theoretical and Mathematical Physics] [arXiv:1903.00694]
H. W. Braden and V.Z. Enolski, The Construction of Monopoles, Commun. Math. Phys. 362, 547-570 2018. [Commun. Math. Phys.] [arXiv:1708.09660]
H. W. Braden, G. Aminov, A. Mironov, A. Morozov and A. Zotov, Seiberg-Witten curves and double-elliptic integrable systems JHEP 2015, 033, 2015. [JHEP.2015:33] [arXiv:1410.0698]
H. W. Braden, V. Z. Enolski and Yu. N. Fedorov, Dynamics on strata of trigonal Jacobians and some integrable problems of rigid body motion Nonlinearity 26, 1865-1889 2013. [Nonlinearity] [arXiv:1210.3596]
H. W. Braden and T.P. Northover, Bring's Curve: its Period Matrix and the Vector of Riemann Constants, SIGMA 8, 065, 2012. [SIGMA] [arXiv:1206.6004]
H. W. Braden and V.Z. Enolski, On the Existence of Non-Abelian Monopole: The Algebro-Geometric Approach, Proceedings of the XXIX Workshop on Geometric Methods in Physics, Bialowieza, 2010, American Institute of Physics, AIP Conference Proceedings 1307, 53--67, 2010. [AIP Conference Proceedings] [arXiv:1009.3837]
H. W. Braden, Antonella D'Avanzo and V.Z. Enolski, On Charge-3 Cyclic Monopoles, Nonlinearity 24, 643-675 2011. [Nonlinearity] [arXiv:1006.3408]
H. W. Braden and V.Z. Enolski, Finite gap integration of the SU(2) Bogomolny equations, Glasgow Mathematical Journal 51, 25-41, 2009. [Glasgow Mathematical Journal] [arXiv:0806.1807]
H. W. Braden and V.Z. Enolski, SU(2) Monopoles, Curves with Symmetries and Ramanujan's Heritage, Matem. Sborniki 201, 19-74 2010. [Matematicheskii Sbornik] [arXiv:0704.3939]
H. W. Braden, A. Marshakov, A. Mironov and A. Morozov, WDVV equations for 6d Seiberg-Witten theory and bi-elliptic curves, Acta Applicandae Mathematicae 99, 223-244, 2007. [Acta Applicandae Mathematicae] [hep-th/0606035]
H. W. Braden and V.Z. Enolski, Remarks on the complex geometry of the 3-monopole, Part I appears as "Some remarks on the Ercolani-Sinha construction of monopoles", Theor. Math. Phys. 165, 1567-1597, 2010. [Theoretical and Mathematical Physics] [math-ph/0601040]
H. W. Braden and V.Z. Enolski, A Platonic Monopole, a Riemann surface and an identity of Ramanujan, Ukr. Fiz. Zh. 50, 855-865, 2005. [Ukrainian Journal of Physics]
H. W. Braden, Victor Z. Enolskii and Andrew N.W. Hone, Bilinear recurrences and addition formulae for hyperelliptic sigma functions, J. Nonlinear Math. Phys.12, suppl. 2, 46-62, 2005. [Journal of Nonlinear Mathematical Physics] [math.NT/0501162]
H. W. Braden and J.G.B. Byatt-Smith, An Appendix to A class of equations with peakon and pulson solutions by Andrew N. W. Hone and Darryl D. Holm J. Nonlinear Math. Phys.12 Supplement 1, 380-394, 2005. [Journal of Nonlinear Mathematical Physics] [nlin.SI/0412029]
H. W. Braden and Timothy J. Hollowood, The Curve of Compactified 6D Gauge Theories and Integrable Systems, JHEP 12, 023, 2003. [JHEP.12(2003)023] [hep-th/0311024]
H. W. Braden, V.A. Dolgushev, M.A. Olshanetsky and A.V. Zotov, Classical R-Matrices and the Feigin-Odesskii Algebra via Hamiltonian and Poisson Reductions, J. Phys. A 36, 6979-7000, 2003. [J. Phys. A] [hep-th/0301121]
H. W. Braden and A. Marshakov, WDVV Equations as Functional Relations, Phys.Lett. B541, 376-383,2002. [Physics Letters B.] [hep-th/0205308]
J.G.B. Byatt-Smith and H. W. Braden, On a Functional Equation of Ruijsenaars, Teoreticheskaya i Mathematicheskaya Fizika, 133, 353-366, 2002; (Translated) Theoretical and Mathematical Physics, 133, 1619-1630, 2002. [Theoretical and Mathematical Physics] [nlin.SI/0201014]
H. W. Braden, A. Gorsky, A. Odesskii and V. Rubtsov, Double Elliptic Dynamical Systems From Generalized Mukai - Sklyanin Algebras, Nucl. Phys. B633, 414-442, 2002. [Nuclear Physics B.] [hep-th/0111066]
H. W. Braden and J.G.B. Byatt-Smith, Mechanical Systems with Poincare Invariance, Phys.Lett. A295, 208-216, 2002. [Physics Letters A.] [nlin.SI/0110014]
J.G.B. Byatt-Smith and H. W. Braden, Functional Equations and Poincare Invariant Mechanical Systems, Siam. J. Math. Anal. 34, 736-758, 2003. [Siam. J. Math. Anal.] [math-ph/0110012]
H. W. Braden, A. Mironov and A. Morozov, QCD, Wick's Theorem for KdV $\tau$-functions and the String Equation, Phys.Lett. B514, 293-298, 2001. [Phys.Lett. B] [hep-th/0105169]
H. W. Braden and N. A. Nekrasov, Instantons, Hilbert Schemes and Integrability, in Integrable Structures of Exactly Solvable Two-Dimensional Models of Quantum Field Theory, S. Pakuliak and G. von Gehlen Eds., Kluwer 2001. [Kluwer] [hep-th/0103204]
H. W. Braden and A. Marshakov, Singular Phases of Seiberg-Witten Integrable Systems: Weak and Strong Coupling, Nucl. Phys. B595, 417-466, 2001. [Nucl. Phys. B] [hep-th/0009060]
H. W. Braden, Rigidity, Functional Equations and the Calogero-Moser Model, J. Phys. A34, 2197-2204, 2001. [J. Phys. A] [nlin.SI/0005046]
H. W. Braden and Nikita A. Nekrasov, Space-time Foam from Noncommutative Instantons, Commun. Math. Phys. 249, 431-448, 2004. [Commun. Math. Phys.] [hep-th/9912019]
H. W. Braden, A. Marshakov, A. Mironov and A. Morozov, On Double-Elliptic Integrable Systems. 1. A Duality Argument for the case of SU(2), Nucl. Phys. B573, 553-572, 2000. [Nucl. Phys. B] [hep-th/9906240]
H. W. Braden, A. Marshakov, A. Mironov and A. Morozov, The Ruijsenaars-Schneider Model in the Context of Seiberg-Witten Theory, Nucl. Phys. B558, 371-390, 1999. [Nucl. Phys. B] [hep-th/9902205]
H. W. Braden, A. Marshakov, A. Mironov and A. Morozov, Seiberg-Witten Theory for a Nontrivial Compactification from Five-Dimensions to Four-Dimensions, Phys. Lett. B448, 195-202, 1999. [Phys. Lett. B] [hep-th/9812078]
H. W. Braden and V. Varela, The Bogomolny Equations and Solutions for Einstein-Yang-Mills-Dilaton- $\sigma$ Models, Phys. Rev. D58, 124020, 1998. [Phys. Rev. D] [hep-th/9804204]
H. W. Braden and J. G. B. Byatt-Smith, On a Functional Differential Equation of Determinantal Type, Bull. London Math. Soc. 31, 463-470, 1999. [Bull. London Math. Soc.] [math/9804082]
H. W. Braden, R-matrices and Generalized Inverses, J. Phys. A30, L485-L493, 1997. [J. Phys. A] [solv-int/9706001]
H. W. Braden, The Equation $A\sp{T}X-X\sp{T}A=B$, Siam J. Matrix Anal. Appl. 20, 395-402, 1998. [Siam J. Matrix Anal. Appl.]
H. W. Braden, R-Matrices, Generalized Inverses and Calogero-Moser-Sutherland Models, in ``Calogero-Moser-Sutherland Models '', CRM Series in Mathematical Physics, Springer-Verlag 2000. [CRM Series in Mathematical Physics]
H. W. Braden and Ryu Sasaki, The Ruijsenaars-Schneider Model, Prog. Theor. Phys. 97, 1003-1018, 1997. [Prog. Theor. Phys.] [hep-th/9702182]
H. W. Braden and P.M. Sutcliffe, A Monopole Metric, Phys. Lett. B391, 366-373, 1997. [Phys. Lett. B] [hep-th/9610141]
H. W. Braden and Andrew N.W. Hone, Affine Toda Solitons and Systems of Calogero-Moser Type, Phys. Lett. B380, 296-302, 1996. [Phys. Lett. B] [hep-th/9603178]
H. W. Braden and V. M. Buchstaber, The General Analytic Solution of a Functional Equation of Addition type, Siam. J. Math. Anal. 28, 903-923, 1997. [Siam. J. Math. Anal.][funct-an/9508002]
H. W. Braden and V. M. Buchstaber, Integrable Systems with Pairwise Interactions and Functional Equations, Reviews in Mathematics and Mathematical Physics 10, 121-166, 1997. [hep-th/9411240]
H. W. Braden, Problem 94-4. Solution acknowledged in Siam Review 37, 106 (1995). [Siam Review]
H. W. Braden and Chris Smyth, Sums Given By Zeta Functions, James Cook Mathematics Notes 66, 7010 – 7014 (1995). [James Cook Math. Notices]
H. W. Braden and Takashi Suzuki, R-matrices for the n=2,3 elliptic Calogero-Moser Models, Phys. Lett. 192A, 17 – 21 (1994). [Phys. Lett. A] [hep-th/9312031]
H. W. Braden and Takashi Suzuki, R-matrices for Elliptic Calogero-Moser Models, Lett. Math. Phys. 30, 147 – 158 (1994). [Lett. Math. Phys.] [hep-th/9309033]
H. W. Braden, H.S.Cho, J.D.Kim, I.G.Koh and R.Sasaki, Singularity Analysis in An Affine Toda Theories, Progress of Theoretical Physics 88, 1205 (1992). [Prog. Theor. Phys.] [hep-th/9207025]
H. W. Braden and R.Sasaki, Affine Toda Perturbation Theory, Nucl. Phys. B379, 377 - 428 (1992). [Nucl. Phys. B]
H. W. Braden, A Note on Affine Toda Couplings, J. Phys. A25, L15 – 20 (1992). [J. Phys. A]
H. W. Braden, E.Corrigan, P.E.Dorey and R.Sasaki, Affine Toda Field Theory; S-Matrix vs Perturbation, Kulish P.P. (Ed), Proc. “Euler Inter. Math. Inst. on Quantum Groups." Lect. Notes Math. 151 Springer, Berlin (1992) 210-220. [Springer]
H. W. Braden, E.Corrigan, P.E.Dorey and R.Sasaki, Multiple Poles and Other Features of affine Toda field theory, Nucl. Phys. B356, 469 – 498 (1991). [Nucl. Phys. B]
H. W. Braden and R.Sasaki, The S-Matrix Coupling Dependence for a,d,e Affine Toda Field Theory, Phys. Lett. 255B, 343 - 352 (1991). [Phys. Lett. B]
H. W. Braden, E.Corrigan, P.E.Dorey and R.Sasaki, Aspects of affine Toda field theory, in the Proceedings of the Winter School on Geometry and Physics, Snri, Czechoslovakia; Integrable systems and Quantum Groups, Pavia, Italy; and 'Quantum Groups', p275-305, World Scientific (Singapore) 1991.
H. W. Braden, E.Corrigan, P.E.Dorey and R.Sasaki, Affine Toda Field Theory and Exact S-Matrices, Nucl. Phys. B338, 689 - 746 (1990). [Nucl. Phys. B]
H. W. Braden, E.Corrigan, P.E.Dorey and R.Sasaki, Aspects of Perturbed Conformal Field Theory, Affine Toda Field Theory and Exact S-Matrices, in the Proceedings of the XVIII International Conference on Differential Geometric Methods in Theoretical Physics: Physics and Geometry, Lake Tahoe, USA 2-8 July 1989 (Plenum 1990). [Plenum]
H. W. Braden, E.Corrigan, P.E.Dorey and R.Sasaki, Extended Toda Field Theory and Exact S-Matrices, Phys. Lett. 227B, 411 – 416 (1989). [Phys. Lett. B]
H. W. Braden, Integral Pairings and Dynkin Indices, J. London Math. Soc. (2) 43, 313-323 (1991). [J. Lond. Math. Soc.]
H. W. Braden, J.D.Brown, B. Whiting and J.W.York, Charged Black Hole in a Grand Canonical Ensemble, Phys. Rev. D42, 3376 – 3385 (1990). [Phys. Rev. D]
H. W. Braden and D.K.Siegwart, SU(n) Anomaly Generating Functionals, J. Phys. A23, 665-675 (1990). [J. Phys. A]
H. W. Braden, Anomalous Congruences, J. Math. Phys. 29, 2494 – 2498 (1988). [J. Math. Phys.]
H. W. Braden, Anomaly Coefficients: Their Calculation and Congruences, J. Math. Phys. 29, 727-741 (1988). [J. Math. Phys.]
H. W. Braden, On the Absence of Global Anomalies, Phys. Lett. 200B, 91 – 94 (1988). [Phys. Lett. B]
H. W. Braden, L.C.Biedenharn, P.Truini and H.Van Dam, Relativistic Wave Functions on Spinor Spaces, J. Phys. A21, 3593 – 3610 (1988). [J. Phys. A]
H. W. Braden, B.Whiting and J.W.York, Density of States for a Blackhole in a Box, Phys. Rev. D36, 3614 – 3625 (1987). [Phys. Rev. D]
H. W. Braden, Extending N=1/2 Supersymmetries, Nucl. Phys. B291, 516-534 (1987). [Nucl. Phys. B]
H. W. Braden and D.R.T. Jones, N=2 Supersymmetric $\sigma$-Models and Infra-red Divergences, Phys. Rev. D35, 1519 – 1521 (1987). [Phys. Rev. D]
H. W. Braden and P.H.Frampton, Worldsheet Supersymmetry, Phys. Rev. Lett. 57, 2112-2114 (1986). [Phys. Rev. Lett.]
H. W. Braden, N=1/2 Hidden Symmetries, Phys. Rev. D37, 3019-3023 (1988). [Phys. Rev. D].
H. W. Braden, P.H. Frampton, T.W. Kephart and A.K.Kshirsagar, Limitations of Heterotic String Phenomenology, Phys. Rev. Lett. 56, 2668-2671 (1986). [Phys. Rev. Lett.]
H. W. Braden, Sigma Models with Torsion, Ann. Phys. (N.Y.) 171, 433 - 462 (1986). [Ann. Phys.]
H. W. Braden, Parallelizing Torsion and Anomalies, Phys. Rev. D33, 2411 – 2145 (1986); D3, 1938E (1986). [Phys. Rev. D] [Phys. Rev. D]
H. W. Braden, Supersymmetry with Torsion, Phys. Lett. 163B, 171 – 175 (1985); 167B, 485E (1986). [Phys. Lett. B] [Phys. Lett. B]
H. W. Braden, Anomaly Calculations, DAMTP 84/20.
H. W. Braden, Mass Corrections to Periodic Solitons, J. Math. Phys. 28, 929-934 (1987). [J. Math. Phys.]
H. W. Braden and A.J.Macfarlane, Supersymmetric Quantum Mechanical Models with Continuous Spectrum and the Witten Index, J. Phys. A18, 3151 – 3156 (1985). [J. Phys. A]
H. W. Braden, Periodic Functional Determinants, J. Phys. A18, 2127 – 2140 (1985). [J. Phys. A]
H. W. Braden, A New Expression for the D-Dimensional Fierz Coefficients, J. Phys. A17, 2927-2934 (1984). [J. Phys. A]
H. W. Braden, A Completely Integrable Mechanical System, Lett. Math. Phys. 6, 449-452 (1982). [Lett. Math. Phys.]
H. W. Braden, N-Dimensional Spinors: Their Properties in Terms of Finite Groups, J. Math. Phys. 26, 613 – 620 (1985). [J. Math. Phys.]
H. W. Braden, Expansions for Field Theories on S¹ × Σ, Phys. Rev. D25, 1028-1038 (1982). [Phys. Rev. D]