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Jedrzej Sniatycki

  • Professor Emeritus of Mathematics & Statistics
  • Applied Mathematics
  • Mathematics

Currently Teaching

Not currently teaching any courses.
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List of Graduate Students

Ph.D. Students:

  • 2000-2002. Andrej Bona. Thesis: The Dirac equation in geometric quantization.
  • 2000-2001. Mohammadreza Simchi. Thesis: Decomposition of prequantization representation for Sl(2;R).
  • 1994-2000. David Kemppainen, Thesis: Bargmann, Michel, and Telegdis equation from the reduction of a Hamiltonian system.
  • 1994-1997, Creighton MacDonnell (co-supervised).Thesis: A family of nonholonomic systems with symmetry.
  • 1986-1966, Larry Bates. Thesis: Singular co-adjoint orbits.

M.Sc. Students:

  • 2004-2006, Jordan Watts: Thesis: Calculus on subcartesian spaces.
  • 2003-2005, Mathew Emmet: Thesis: Mechanics of a pseudo-rigid disc rolling.
  • 1992-1994, David Kemppainen. Thesis: The geometry of the rolling disk.
  • 1983-1985, George Patrick. Thesis: Degenerate dynamics.
  • 1974-1976, S. Toporowski. Thesis: Representation spaces in geometric quantization.

 

Publications

RESEARCH MONOGRAPHS

J. Sniatycki, Differential Geometry of Singular Spaces and Reduction of Symmetries, Cambridge University Press, Cambridge, 2013.

R. Cushman, J.J. Duistermaat and J. Sniatycki, Geometry of Nonholonomic Constraints, World Scientific, Singapore, 2010.

E. Binz, J. Sniatycki and H. Fischer, Geometry of Classical Fields, Elseviere Science Publishers, Amsterdam, 1988. Reprinted by Dover Publications, Inc., Mineola, N.Y., 2006.

J. Sniatycki, Geometric Quantization and Quantum Mechanics, Applied Mathematical Science, Vol. 30, Springer Verlag, New York, 1980.

REFEREED PUBLICATIONS IN SCIENTIFIC JOURNALS

R.Segev and J. Sniatycki, Hyper-stresses in k-jet field theories, Journal of Elasticity, 113, (2018).

R. Segev and J. Sniatycki, On jets, almost symmetric tensors and traction hyper-stresses, Mathematics and Mechanics of Complex Systems, 6 (2018). 

R. Cushman and J. Sniatycki, Lie algebra actions, Discrete and Continuous Dynamical Systems, in press. 

R. Cushman and J. Sniatycki, A globalization of a theorem of Horozow, Indagationes Mathematicae, 27 (2016) 1030-1041.

L. Bates, R. Chhabra and J. Sniatycki, Elastica as a dynamical system, Journal of Geometry and Physics, 110 (2016) 348-381.

F. Diacu, S. Ibrahim, and J. Sniatycki, The continuous transition of Hamiltonian vector fields through manifolds of constant curvature, Journal of Mathematical Physics, 57 (2016) doi: 10.1063/1.4953371.

J. Sniatycki, Lectures on geometric quantization, Seventeenth International Conference on Geometry, Integrability and Quantization, June 5-10, (2015), Varna, Bulgaria. I.M. Mladenov, G. Meng and A. Yoshioka (Editors), Anangard Prima, Sofia (2016) 95-129.

L. Bates and J. Sniatycki, Polite actions of non-compact Lie groups, Geometry Mechanics and Dynamics: the Legacy of Jerry Marsden, Fields Institute Communications, 73 (2015) 427-433.

T. Lusala and J. Sniatycki, Slice theorem for differential spaces and reduction by stages, Demonstratio Mathematics, 47 (2014) 192-210.

L. Bates and J. Sniatycki, An extension of the Dirac theory of constraints, J. Fixed Point Theory Appl., 14 (2013) 527-554.

R. Cushman and J. Sniatycki, Bohr-Sommerfeld-Heisenberg theory in geometric quantization, J. Fixed Point Theory Appl., 13 (2013) 3-24.

J. Sniatycki, Commutation of quantization and algebraic reduction, Mathematical Aspects of Quantization, Contemprary Mathematics 583 (2012) 295-308.

J.Sniatycki, Reduction of symmetries of Dirac structures, J. Fixed Point Theory Appl., 10, (2011), 339-358.

M. Jotz, T. Ratiu and J. Sniatycki, Singular reduction of Dirac structures, Trans. Am. Math. Soc. 363 (2011) 2967-3013.

T. Lusala and J. Sniatycki, Stratiffed subcartesian spaces, Canadian Math. Bull. 54 (2011)

T. Lusala, J. Sniatycki and J. Watts, Regular points of a subcartesian space, Canadian Math. Bull. 53 (2010) 340-346.

L. Bates, R.Cushman, M. Hamilton and J. Sniatycki, Quantization of singular reduction, Reviews of Mathematical Physics, 21 (2009) 315-371.

J. Sniatycki, Geometric quantization, reduction and decomposition of group representationî, J. Fixed Point Theory Appl. 3 (2008) 307-315

J. Sniatycki, Singular reduction of symmetries in mechanics and control theory, Mekhanika tverdogo tela, ISSN 0321-1975, 37 (2007) pp. 152-162.

M. Epstein and J. Sniatycki, The Koch curve as a smooth manifold, Chaos, Solitons and Fractals, 38 (2008) 334-338.

J. Sniatycki and R. Cushman, Non-holonomic reduction of symmetries, con-straints and integrability, Regular and Chaotic Dynamics, 12 (2007) 485-491.

J. Sniatycki, Generalizations of Frobenius' theorem on manifolds and subcartesian spaces, Can. Math. Bull., 50 (2007) 447-459.

M. Epstein and J. Sniatycki, Fractal Mechanics, Physica D, 220 (2006), 54-68.

J. Sniatycki, Singular reduction for nonlinear control systems, Rep. Math. Phys, 57 (2006) 163-178.

M. Epstein and J. Sniatycki, Nonlocal inhomogeneity and Eshelby entities, Philosophical Magazine, 85 (2005) 3939-3955.

J. Sniatycki, Poisson algebras in reduction of symmetries, Rep. Math. Phys., 56 (2005) 53-73.

J. Sniatycki, Multisymplectic reduction for proper actions, Canad. J. Math. 56 (2004) 638-654.

J. Sniatycki, Orbits of families of vector fields on subcartesian spaces, Ann. Inst. Fourier (Grenoble), 53 (2003) 2257-2296.

R. Cushman and J. Sniatycki, A nonholonomic oscillator, Rep. Math. Phys., 50 (2002) 85-98.

R. Cushman and J. Sniatycki, Nonholonomic reduction for free and proper actions, Reg. Chaotic Dyn., 7 (2002) 61-72.

J. Sniatycki, The momentum equation and the second order differential equation condition, Rep. Math. Phys. 49 (2002) 371-394.

J. Sniatycki, Almost Poisson spaces and non-holonomic singular reduction, Rep. Math. Phys., 48 (2001) 235-248.

R. Cushman and J. Sniatycki, Differential structure of orbit spaces, Canad. J. Math. 53 (2001) 235-248.

J. Sniatycki, Gauge momentum map and spatial control of extended objects, Technische Mechanik, 20 (2000) 121-128.

J. Sniatycki, A Hamiltonian analysis of Yang-Mills equations, Rep. Math. Phys., 44 (1999) 205-214.

R. Cushman and J. Sniatycki, Hamiltonian mechanics on principal bundles, C.R. Math. Rep. Acad. Sci. Canada, 21 (1999) 60-64.

J. Sniatycki, Geometry of the constraint sets for Yang-Mills-Dirac equations with inhomogeneous boundary conditions, Commun. Math. Phys., 203 (1999) 707-712.

J. Sniatycki, Regularity of constraints and reduction in the Minkowski space Yang-Mills-Dirac theory, Ann. Inst. H. Poincare, 70 (1999) 277-293.

J. Sniatycki, Non-holonomic Noether Theorem and Reduction of Symmetries, Rep. Math. Phys., 42 (1998) 5-23.

R. Cushman, D. Kempainnen and J. Sniatycki, A classical particle with spin realized by reduction of a nonlinear nonholonomic constraint, Rep. Math. Phys., 41 (1998) 133-142.

G. Schwarz, J. Sniatycki, and J. Tafel: Yang-Mills and Dirac fields with inhomogeneous boundary conditions, Commun. Math. Phys., 188 (1997) 439-448.

J. Tafel and J. Sniatycki: Non-linear semigroups and the Yang-Mills equations with the metallic boundary conditions, Commun. Partial Diff. Eqns., 22 (1997) 46- 69.

G. Schwarz and J. Sniatycki, Gauge symmetries of an extended phase space for Yang-Mills and Dirac fields, Ann. Inst. Henri Poincare, 66 (1997) 109-136.

J. Sniatycki: What can we learn from the classical theory of Yang-Mills and Dirac fields, Acta Phys. Polon., 27B, (1996) 2497-2505.

G. Schwarz and J. Sniatycki, The Hamiltonian evolution of Yang-Mills fields in bounded domains, Acta Phys. Polon., 27B (1996) 881-892.

R. Cushman, D. Kemppainen, J. Sniatycki and L. Bates, Geometry of non-holonomic constraints, Rep. Math. Phys. 36 (1995) 275-286.

R. Cushman and J. Sniatycki, Local Integrability of the mixmaster model, Rep. Math. Phys., 36 (1995) 75-89.

J. Sniatycki, G. Schwarz and L. Bates, Yang-Mills and Dirac fields in a bag, constraints and reduction, Commun. Math. Phys., 176 (1996) 95-115.

G. Schwarz and J. Sniatycki, Yang-Mills and Dirac fields in a bag, existence and uniqueness theorems, Commun. Math. Phys., 168 (1995) 441-453.

 J. Sniatycki and G. Schwarz, An Invariance Argument for Confinement, Rep. Math. Phys., 34 (1994) 311-324.

J. Sniatycki and G. Schwarz, The existence and uniqueness of solutions of Yang- Mills equations with bag boundary conditions, Commun. Math. Phys., 159 (1994) 593-304.

L. Bates and J. Sniatycki, Non-holonomic Reduction, Rep. Math. Phys., 32 (1993), pp. 99-115.

L. Bates and J. Sniatycki, On Action Angle Variables, Arch. Rat. Mech. Anal., Vol. 120 (1992), pp. 337-343.

Y. Kerbrat, H. Kerbrat-Lunc and J. Sniatycki, Geometry of Minisuperspace in Examples, Rep. Math. Phys., Vol. 31 (1992), pp. 205-215.

L.Bates and J. Sniatycki, On the Period-Energy Relation, Proc. A.M.S., Vol. 114 (1992), pp. 877-878.

M. Epstein and J. Sniatycki, Fermat Principle in Elastodynamics, J. Elasticity, 27 (1992), pp. 45 -56.

J. Sniatycki, Regularity of Constraints in the Minkowski Space Yang-Mills Theory, Commun. Math. Phys., Vol. 141 (1991), pp. 593-597.

Y. Kerbrat, H. Kerbrat-Lunc and J. Sniatycki, Generalized Gauge Fields, J. Math. Phys., Vol. 32 (1991), pp. 1750-1754.

C. Duval, J. Elhadad, M.J. Gotay, J. Sniatycki and G.M. Tuynman, Quantization and bosonic BRST theory, Ann. Phys., Vol. 206 (1991), pp. 1-26.

Y. Kerbrat, H. Kerbrat-Lunc and J. Sniatycki, A Geometric Interpretation of Symmetry Breaking in Electroweak Interactions, Rep. Math. Phys., Vol. 28 (1989), pp. 201-212.

M. Elzanowski, M. Epstein and J. Sniatycki, Integrability of G-structures vs. homogeneity of uniform materials, J. Elasticity, Vol. 23 (1990), pp. 167-180.

Y. Kerbrat, H. Kerbrat-Lunc and J. Sniatycki, How to Get Masses from Kaluza Klein Theory, J. Geom. Phys., Vol. 6 (1989), pp. 311-329.

 J. Sniatycki, Gauge Invariance, Boundary Conditions, and Charges, Rep. Math. Phys., Vol. 25 (1988), pp. 291-303.

J. Sniatycki, Conservation laws in asymptotically áat space-times revisited, Rep. Math. Phys., Vol. 25 (1988), pp. 127-140.

E. Binz and J. Sniatycki, Conservation laws in space time with boundary, Class. Quant. Grav., Vol. 3 (1986), 1191-1197.

J. Sniatycki, Geometric quantization and constraints in field theory, J. Geom. Phys., Vol. 2 (1985), 1-21.

J. Sniatycki, The Cauchy data space formulation of classical field theory, Rep. Math. Phys., Vol. 19 (1984), 407-422.

J. Sniatycki, On gauge invariance and confinement, Hadronic J., Vol. 6 (1983), 1509-1517.

M. Gotay, R. Lashof, J. Sniatycki and A. Weinstein, Closed forms on symplectic fibre bundles, Comment. Math. Helv., Vol. 52 (1983), 497-509.

J. Sniatycki and A. Weinstein, Reduction and quantization for singular momentum mappings, Lett. Math. Phys., Vol. 7 (1983), 155-161.

M. Gotay and J. Sniatycki, On the quantization of presymplectic systems via coisotropic imbeddings, Comm. Math. Phys., Vol. 82 (1981), 377-389.

J. Sniatycki, On particles with gauge degrees of freedom, Hadronic J. Vol. 4 (1981), 844-878.

J. Sniatycki, Kinematics of particles with isotopic spin, Hadronic J., Vol. 3 (1980), 743-764.

J. Sniatycki, On Hamiltonian dynamics of particles with gauge degrees of freedom, Hadronic J., Vol. 2 (1979), 642-656.

J. Sniatycki and S. Toporowski, On representation spaces in geometric quantiza- tion, Int. J. Theor. Phys., Vol. 16 (1977), 615-633.

J. Sniatycki, Wave functions relative to a real polarization, Int. J. Theor. Phys., Vol. 14 (1975), 277-288.

J. Sniatycki, Bohr-Sommerfeld conditions in geometric quantization, Rep. Math. Phys., Vol. 7 (1975), 303-311.

J. Sniatycki, J., Dirac brackets in geometric dynamics, Ann. Inst. Henri PoincarÈ, Vol. 20 (1974), 365-372.

B. Lawruk, J. Sniatycki and W.M. Tulczyjew, Special symplectic spaces, J. Dif- ferential Equations, Vol. 17 (1974), 477-479.

J. Sniatycki, Prequantization of charge, J. Math. Phys., Vol. 15 (1974), 619-620.

J. Sniatycki and W.M. Tulczyjew, Canonical formulation of Newtonian dynamics, Ann. Inst. Henri PoincarÈ, Vol. 16 (1972), 23-27.

J. Sniatycki and W.M. Tulczyjew, Generating forms of Lagrangian submanifolds, Indiana Univ. Math. J., 22 (1972), 267-275.

J. Sniatycki and W.M. Tulczyjew, Canonical dynamics of relativistic charged par- ticles, Ann. Inst. Henri Poincare, Vol. 15 (1971), 177-187.

J. Sniatycki, On the geometric structure of classical field theory in Lagrangian formulation, Proc. Camb. Phil. Soc., Vol. 68 (1970), 475-483.

J. Sniatycki, On commutation relations for the energy-momentum tensor, Bull. Acad. Polon. Sci., Ser. Sci. Astr., Math. et Phys., Vol. 16 (1968), 249-251.

J. Sniatycki, On Utiyama identities in quantum electrodynamics, Bull. Acad. Polon. Sci., Ser. Sci. Astr., Math. et Phys., Vol. 15 (1967), 627-629.

J. Sniatycki, The classical motion of spin-1 particles, Nuovo Cimento, Vol. 35 (1965), 664-665.

J. Sniatycki, On the motion of spin-1/2 particles, Bull. Acad. Polon. Sci., Ser. Sci. Astr., Math. et Phys., Vol. 14 (1966), 37-39.

I. Bialynicki-Birula, J. Sniatycki and S. Tatur, Functional methods in the Thirring model, Bull. Acad. Polon. Sci., Ser. Sci. Astr., Math. et Phys., Vol. 11 (1963), 479-481.

REFEREED CONFERENCE REPORTS:

Larry Bates, Richard Cushman, Mark Hamilton and Jeædrzej Sniatycki, Decomposition of the quantization representation of an SU(2) action, Proceedings of XXVII Workshop on Geometrical Methods in Physics, P. Kielanowski, A. Odzijewicz, M. Schlichenmaier and Th. Voronov (editors). AIP Conference Proceedings 1079, Melville, New York, 2008.

J. Sniatycki, Geometric quantization of algebraic reduction, Proceedings of XXVI Workshop on Geometrical Methods in Physics, Bialowieza, Poland, 1-7 July, 2007, P. Kielanowski, A. Odzijewicz, M. Schlichenmaier and Th. Voronov (editors), AIP Conference Proceedings 956, Melville, New York, 2007.

J. Sniatycki, Integral curves of derivations on locally semi-algebraic differential spaces, Dynamical Systems and Differential Equations, (Proceedings of the Fourth International Conference on Dynamical Systems and Di§erential Equations, May 24- 27, 2002, Wilmington, NC, USA), W. Feng, S. Hu and X. Lu (Editors), American Institute of Mathematical Sciences Press, Springfield MO. 2003, pp. 825-831.

J. Sniatycki: Orbit spaces for Hamiltonian actions, in the Proceedings of the Conference Od podstaw do zastosowan -edukacyjna funkcja Internetu, Wyzsza Szkola Informatyki i Ekonomii TWP, Olsztyn 2001, pp. 169-174.

J. Sniatycki: Quantization of Yang-Mills fields commutes with reduction,  Proceedings of the International Symposium Quantum Theory and Symmetries, H.- D Doebner, K.V. Dobrev, J.-D. Henning and W. Lucke (editors), World Scientific, Singapore, 2000, pp. 68-75.

J. Sniatycki: Geometry of solutions spaces of Yang-Mills equations, Proceedings of Conference Leray 99, University of Karlskrona-Ronneby, August 30 - September 3, 1999.

J. Sniatycki: Ghostbuster's approach to constraints, Quantization and Coherent States Methods, S.T. Ali, I.M. Mladenov and A. Odzijewicz, (eds.), World ScientiÖc, Singapore 1993, pp. 36-44.

J. Sniatycki: Geometry of minisuperspace, Gravitation, A Banff Summer Institute, R. Mann and P. Wesson, (eds.), World Scientific, Singapore, 1991, pp. 91- 97.

J. Sniatycki: îHamiltonian constraints, the Jacobi principle and gravity, Symplectic Geometry and Mathematical Physics, P. Donato, C. Duval, J. Elhadad and G.M. Tuynman (eds.), Birkhauser, Boston, 1991, pp. 433-441.

J. Sniatycki: On reduction of almost regular momentum maps, Hamiltonian Systems, Transformation Groups and Spectral Transform Methods, J. Harnad and J.E. Marsden (eds.), Centre de Recherches MathÈmatiques, Universitee de Montreal, Montreal, 1990, 229 ó 233.

J. Sniatycki: Does symmetry breaking mean less symmetry?, New Theories in Physics, Z. Ajduk, S. Pokorski and A. Trautman, (eds.), World Scientific Publishers, Singapore, 1989, pp. 66-72.

M. Epstein, M. Elzanowski and J. Sniatycki: Locality and uniformity in global elasticity, Lecture Notes in Mathematics, Vol. 1139, Springer Verlag, Berlin, 1985, pp. 300-310.

J. Sniatycki: On quantization of systems with constraintsî, Mathematical Physics Studies, Vol. 6, D. Reidel Publishing Company, Dordrecht, 1984, pp. 207- 211.

J. Sniatycki: Constraints and quantization, Lecture Notes in Mathematics, Vol. 1037, Springer Verlag, Berlin, 1983, pp. 301-334.

J. Sniatycki: Applications of geometric quantization in quantum mechanics, Lecture Notes in Mathematics, Vol. 676, Springer Verlag, Berlin, 1978, pp. 357-367.

J. Sniatycki: On geometric quantization of classical systems, Mathematical Foundations of Quantum Theory, edited by A.E. Marlow, Academic Pres, New York, 1978, pp. 287-297.

J . Sniatycki: On cohomology groups appearing in geometric quantization, Lecture Notes in Mathematics, Vol. 570, Springer Berlag, Berlin, 1977, pp. 46-65.

J. Sniatycki: On wave functions in geometric quantization, Lecture Notes in Physics, Vol. 50, Springer Verlag, Berlin, 1976, pp. 194-198.

J. Sniatycki: Bohr-Sommerfeld quantum systems, Proceedings of the 3rd International Colloquium on Group Theoretical Methods in Physics, Marseille, France, 1974. Vol. 1, pp. 42-51.

J. Sniatycki: Lagrangian systems, canonical systems and Legendre transformation, Proceedings of 13th Biennial Seminar of the Canadian Mathematical Congress, Halifax, Nova Scotia, 1971. Proceedings, Vol. 2, pp. 125-143.

 J. Sniatycki: On the canonical formulation of general relativity, Proceedings of Journees relativistes 1970, Caen, France, pp. 127-135.

J. Sniatycki: Geometric theory of constraints, Proceedings of Journees relativistes 1970, Caen, France, pp. 119-126.

J. Sniatycki: Some remarks on canonical formulation of field theory and its geometric structure,  Acta Universitatis Wratislaviensis, No. 113, Wroclaw, 1969, pp. 259-267.

J. Sniatycki: On the motion of spin1/2 particles, Universitas Iagiellonica Acta Scientarum Litterarumque CLXXVI, Schedae Physicae, Fasc. V,  pp. 361-368. Krakow, 1967.

REFEREED CHAPTERS

 J. Sniatycki: Yang-Mills Ffields in spatially bounded domains, Differential Geometry, Group Representation and Quantization,  J.D. Hennig, W. Lucke, and J. Tolar, (eds.), Springer, Berlin, 1991, pp. 43 ó 53.

M. Elzanowski, M. Epstein and J. Sniatycki, Geometry of uniform bodies, Geometry and Topology, G.M. Stratopoulos and G.M. Rassias, (eds), pp. 134-151, World Scientific Publishers, Singapore, 1989.

 J. Sniatycki, On quantization of Yang-Mills fields, Di§erential Geometry Topology and Related Fields and their Applications to the Physical Sciences and Engineering, G. M. Rassias, (ed.), Taubner Verlag, Leipzig, 1985.

CONFERENCE PROCEEDINGS EDITED

R. Cushman and J. Sniatycki (eds.). Workshop on Nonholonomic Constraints in Dynamics, Reports on Mathematical Physics, vol. 42 (1998) No 1/2.

REVIEWS

J. Sniatycki, Review of Momentum Maps and Hamiltonian Reduction by J.-P. Ortega and T.S. Ratiu, Bull. A.M.S., vol. 42 (2004).215-223.

 
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