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Jedrzej Sniatycki

photograph of Jedrzej Sniatycki

Job Title:

  • Professor

Phone:

  • +1 (403) 220-3957

Office:

  • MS 320

Email:

Web site:

Degrees:

Research Interests:

  • Symplectic geometry
  • Differential spaces
  • Hamiltonian mechanics
  • Non-holonomic constraints
  • Geometric quantization
  • Multisymplectic systems
  • Yang-Mills theory

Masters Students:

  • Jordan Watts (2006)
  • Mathew Emmett (2005)

Ph. D. Student:

  • Andrej Bona (2002)

Teaching:

Past Courses:

  • AMAT311 - DIFFERENTIAL EQUATIONS I
  • AMAT411 - DIFFERENTIAL EQUATIONS II
  • AMAT505 - CALCULUS ON MANIFOLDS
  • AMAT509 - ANALYTICAL DYNAMICS
  • MATH211 - Linear Methods I
  • MATH221 - Linear Algebra For Science & Engg
  • MATH253 - CALCULUS II
  • MATH331 - MULTIVARIATE CALCULUS
  • PMAT435 - ANALYSIS I
  • PMAT445 - Analysis II
Representative Publications:
Journal Paper
Sniatycki, Jedrzej. "Multisymplectic reduction for proper actions" Canadian Journal of Mathematics. Journal Canadien de Math\'ematiques 56.3 (2004): 638-654
Sniatycki, Jedrzej. "Integral curves of derivations on locally semi-algebraic differential spaces" Discrete and Continuous Dynamical Systemssuppl. (2003): 827-833
Cushman, Richard and Sniatycki, Jedrzej. "Erratum: ``{D}ifferential structure of orbit spaces'' [{C}anad. {J}. {M}ath. {\bf 53} (2001), no. 4, 715-755; \refmr {MR}1848504 (2002j:53109)\endrefmr]" Canadian Journal of Mathematics. Journal Canadien de Math\'ematiques 55.2 (2003): 247
Sniatycki, Jedrzej. Geometry of solution spaces of spaces of {Y}ang-{M}ills equations 24 (2003): 249-265
Sniatycki, Jedrzej. "Orbits of families of vector fields on subcartesian spaces" Universit\'e de Grenoble. Annales de l'Institut Fourier 53.7 (2003): 2257-2296
Cushman, Richard and Sniatycki, Jedrzej. "Erratum: ``{D}ifferential structure of orbit spaces'' [{C}anad. {J}. {M}ath. {\bf 53} (2001), no. 4, 715-755; {MR}1848504 (2002j:53109)]" Canadian Journal of Mathematics. Journal Canadien de Math\'ematiques 55.2 (2003): 247
Cushman, Richard and Sniatycki, Jedrzej. "A nonholonomic oscillator" Rep. Math. Phys. 50.1 (2002): 85-98
Sniatycki, Jedrzej. "The momentum equation and the second order differential equation condition" Rep. Math. Phys. 49.2-3 (2002): 371-394
Cushman, Richard and Sniatycki, Jedrzej. "Nonholonomic reduction for free and proper actions" Regular \& Chaotic Dynamics. International Scientific Journal 7.1 (2002): 61-72
Cushman, Richard and Sniatycki, Jedrzej. "Differential structure of orbit spaces" Canadian Journal of Mathematics. Journal Canadien de Math\'ematiques 53.4 (2001): 715-755
Sniatycki, Jedrzej. "Almost {P}oisson spaces and nonholonomic singular reduction" Rep. Math. Phys. 48.1-2 (2001): 235-248
Sniatycki, Jedrzej. "Regularity of constraints and reduction in the {M}inkowski space {Y}ang-{M}ills-{D}irac theory" Annales de l'Institut Henri Poincar\'e. Physique Th\'eorique 70.3 (1999): 277-293
Sniatycki, Jedrzej. "Geometry of the constraint sets for {Y}ang-{M}ills-{D}irac equations with inhomogeneous boundary conditions" Comm. Math. Phys. 203.3 (1999): 707-712
Cushman, Richard and Sniatycki, Jedrzej. "Hamiltonian mechanics on principal bundles" Comptes Rendus Math\'ematiques de l'Acad\'emie des Sciences. La Soci\'et\'e Royale du Canada. Mathematical Reports of the Academy of Science. The Royal Society of Canada 21.2 (1999): 60-64
Sniatycki, Jedrzej. "A {H}amiltonian analysis of {Y}ang-{M}ills equations" Rep. Math. Phys. 44.1-2 (1999): 205-214
Sniatycki, Jedrzej. "Nonholonomic {N}oether theorem and reduction of symmetries" Rep. Math. Phys. 42.1-2 (1998): 5-23
Cushman, Richard, Kemppainen, David and Sniatycki, Jedrzej. "A classical particle with spin realized by reduction of a nonlinear nonholonomic constraint" Rep. Math. Phys. 41.1 (1998): 133-142
Schwarz, G , Sniatycki, Jedrzej and Tafel, Jacek . "Yang-{M}ills and {D}irac fields with inhomogeneous boundary conditions" Comm. Math. Phys. 188.2 (1997): 439-448
Tafel, J. and Sniatycki, Jedrzej. "Nonlinear semigroups and the {Y}ang-{M}ills equations with the metallic boundary conditions" Communications in Partial Differential Equations 22.1-2 (1997): 49-69
Schwarz, G and Sniatycki, Jedrzej. "Gauge symmetries of an extended phase space for {Y}ang-{M}ills and {D}irac fields" Annales de l'Institut Henri Poincar\'e. Physique Th\'eorique 66.1 (1997): 109-136
Sniatycki, Jedrzej, Schwarz, G and Bates, Larry. "Yang-{M}ills and {D}irac fields in a bag, constraints and reduction" Comm. Math. Phys. 176.1 (1996): 95-115
Sniatycki, Jedrzej. "What can we learn from the classical theory of {Y}ang-{M}ills and {D}irac fields?" Jagellonian University. Institute of Physics and Polish Physical Society. Acta Physica Polonica B 27.10 (1996): 2497-2505
Schwarz, G. and Sniatycki, Jedrzej. "The {H}amiltonian evolution of {Y}ang-{M}ills fields in bounded domains" Jagellonian University. Institute of Physics and Polish Physical Society. Acta Physica Polonica B 27.4 (1996): 881-892
Cushman, Richard and Sniatycki, Jedrzej. "Local integrability of the mixmaster model" Rep. Math. Phys. 36.1 (1995): 75-89
Schwarz, G and Sniatycki, Jedrzej. "Yang-{M}ills and {D}irac fields in a bag, existence and uniqueness theorems" Comm. Math. Phys. 168.2 (1995): 441-453
Cushman, Richard, Kemppainen, David, Sniatycki, Jedrzej and Bates, Larry. "Geometry of nonholonomic constraints" Rep. Math. Phys. 36.2-3 (1995): 275-286
Sniatycki, Jedrzej and Schwartz, G . "An invariance argument for confinement" Rep. Math. Phys. 34.3 (1994): 311-324
Sniatycki, Jedrzej and Schwarz, G . "The existence and uniqueness of solutions of {Y}ang-{M}ills equations with bag boundary conditions" Comm. Math. Phys. 159.3 (1994): 593-604
Bates, Larry and Sniatycki, Jedrzej. "Nonholonomic reduction" Rep. Math. Phys. 32.1 (1993): 99-115
Bates, Larry and Sniatycki, Jedrzej. "On action-angle variables" Archive for Rational Mechanics and Analysis 120.4 (1992): 337-343
Bates, Larry and Sniatycki, Jedrzej. "On the period-energy relation" Proc. Amer. Math. Soc. 114.3 (1992): 877-878
Kerbrat, Yvan , Kerbrat-Lunc, H and Sniatycki, Jedrzej. "Geometry of minisuperspace in examples" Rep. Math. Phys. 31.2 (1992): 205-215
Epstein, Marcelo and Sniatycki, Jedrzej. "Fermat's principle in elastodynamics" Journal of Elasticity. The Physical and Mathematical Science of Solids 27.1 (1992): 45-56
Sniatycki, Jedrzej. "Regularity of constraints in the {M}inkowski space {Y}ang-{M}ills theory" Comm. Math. Phys. 141.3 (1991): 593-597
Kerbrat, Yvan , Kerbrat-Lunc, H and Sniatycki, Jedrzej. "Generalized gauge fields" Journal of Mathematical Physics 32.7 (1991): 1750-1754
Duval, C. , Elhadad, J. , Gotay, M. J., Sniatycki, Jedrzej and Tuynman, G. M. "Quantization and bosonic {BRST} theory" Annals of Physics 206.1 (1991): 1-26
Elzanowski, Marek, Epstein, Marcelo and Sniatycki, Jedrzej. "{$G$}-structures and material homogeneity" Journal of Elasticity. The Physical and Mathematical Science of Solids 23.2-3 (1990): 167-180
Kerbrat, Y. , Kerbrat-Lunc, H. and Sniatycki, Jedrzej. "A geometric interpretation of symmetry breaking in electroweak interactions" Rep. Math. Phys. 28.2 (1989): 201-212
Kerbrat, Y. , Kerbrat-Lunc, H. and Sniatycki, Jedrzej. "How to get masses from {K}aluza-{K}lein theory" Journal of Geometry and Physics 6.2 (1989): 311-329
Sniatycki, Jedrzej. "Gauge invariance, boundary conditions, and charges" Rep. Math. Phys. 25.3 (1988): 291-303
Sniatycki, Jedrzej. On the role of boundary conditions in conservation laws in field theory (1987): 154-161
Binz, Ernst and Sniatycki, Jedrzej. "Conservation laws in spacetimes with boundary" Classical and Quantum Gravity 3.6, North-Holland Publishing Co. (1986): 1191-1197
Sniatycki, Jedrzej. "Geometric quantization and constraints in field theory" Journal of Geometry and Physics 2.2, North-Holland Publishing Co. (1985): 1-21
Sniatycki, Jedrzej. "The {C}auchy data space formulation of classical field theory" Rep. Math. Phys. 19.3 (1984): 407-422
Gotay, Mark J., Lashof, Richard , Sniatycki, Jedrzej and Weinstein, Alan . "Closed forms on symplectic fibre bundles" Comment. Math. Helv. 58.4 (1983): 617-621
Sniatycki, Jedrzej. "On gauge invariance and confinement" Hadronic Journal 6.6 (1983): 1509-1517
Sniatycki, Jedrzej and Weinstein, Alan . "Reduction and quantization for singular momentum mappings" Letters in Mathematical Physics. A Journal for the Rapid Dissemination of Short Contributions in the Field of Mathematical Physics 7.2 (1983): 155-161
Gotay, Mark J. and Sniatycki, Jedrzej. "On the quantization of presymplectic dynamical systems via coisotropic imbeddings" Comm. Math. Phys. 82.3 (1981/82): 377-389
Sniatycki, Jedrzej. "On particles with gauge degrees of freedom" Hadronic Journal 4.3 (1980/81): 844-878
Sniatycki, Jedrzej. "Kinematics of particles with isotopic spin" Hadronic Journal 3.2 (1979/80): 743-764
Sniatycki, Jedrzej. "On {H}amiltonian dynamics of particles with gauge degrees of freedom" Hadronic Journal 2.3 (1979): 642-656
Sniatycki, Jedrzej and Toporowski, Stanley . "On representation spaces in geometric quantization" International Journal of Theoretical Physics 16.8 (1977): 615-633
Lawruk, B. , Sniatycki, Jedrzej and Tulczyjew, W. M. "Special symplectic spaces" J. Differential Equations 17, Springer-Verlag (1975): 477-497
Sniatycki, Jedrzej. "Wave functions relative to a real polarization" International Journal of Theoretical Physics 14.4 (1975): 277-288
Sniatycki, Jedrzej. "Bohr-{S}ommerfeld conditions in geometric quantization" Rep. Mathematical Phys. 7.2 (1975): 303-311
Sniatycki, Jedrzej. "Dirac brackets in geometric dynamics" Ann. Inst. H. Poincar\'e Sect. A (N.S.) 20 (1974): 365-372
Sniatycki, Jedrzej. "Prequantization of charge" J. Mathematical Phys. 15 (1974): 619-620
Sniatycki, Jedrzej and Tulczyjew, W. M. "Generating forms of {L}agrangian submanifolds" Indiana University Mathematics Journal 22, Springer-Verlag (1972/73): 267-275
Sniatycki, Jedrzej. Lagrangian systems, canonical systems and {L}egendre transformation (1972): 125-143
Sniatycki, Jedrzej and Tulczyjew, W. M. "Canonical formulation of {N}ewtonian dynamics" Ann. Inst. H. Poincar\'e Sect. A (N.S.) 16 (1972): 23-27
Sniatycki, Jedrzej and Tulczyjew, W. M. "Canonical dynamics of relativistic charged particles" Ann. Inst. H. Poincar\'e Sect. A (N.S.) 15 (1971): 177-187
Sniatycki, Jedrzej. "On the geometric structure of classical field theory in {L}agrangian formulation" Proc. Cambridge Philos. Soc. 68 (1970): 475-484
Bia{\l}ynicki-Birula, I. , Sniatycki, Jedrzej and Tatur, S. . "Functional methods in the {T}hirring model" Bull. Acad. Polon. Sci. S\'er. Sci. Math. Astronom. Phys. 11 (1963): 479-482
Preprint
Sniatycki, Jedrzej. Orbits of Families of Vector Fields on Subcartesian (2003)
Sniatycki, Jedrzej. Singular Multisymplestic Reduction (2002)
Sniatycki, Jedrzej. The Momentum Equation and Second Order Differential Equation Condition. (2001)
Sniatycki, Jedrzej and Cushman, Richard. Differential Structure of Orbit Spaces. (2000)
Sniatycki, Jedrzej and Cushman, Richard. Lifted Action and the Local Geometry of Orbit Spaaces (2000)
Sniatycki, Jedrzej. Almost Poisson Spaces and Non-holomic Singular Reduction. (2000)
Sniatycki, Jedrzej. Spaces of sufficiently smooth solutions of the Yang-Mills equations (1998)
Sniatycki, Jedrzej. Regular Multisymplectic Reduction (1970)
Book
Sniatycki, Jedrzej. Quantization of {Y}ang-{M}ills fields commutes with reduction World Sci. Publishing (2000): 68-75
Sniatycki, Jedrzej. Classical {Y}ang-{M}ills and {D}irac fields in the {M}inkowski space and in a bag Plenum (1995): 109-118
Sniatycki, Jedrzej. Geometry of minisuperspace World Sci. Publishing (1991): 91-97
Sniatycki, Jedrzej. On boundary conditions for {Y}ang-{M}ills fields in spatially bounded domains 379, Springer (1991): 43-53
Sniatycki, Jedrzej. Hamiltonian constraints, the {J}acobi principle and gravity 99, Birkh\"auser Boston (1991): 433-441
Sniatycki, Jedrzej. On reduction of almost regular momentum maps Univ. Montr\'eal (1990): 229-233
Elzanowski, Marek, Epstein, Marcelo and Sniatycki, Jedrzej. Geometry of uniform bodies World Sci. Publishing (1989): 134-151
Binz, Ernst , Sniatycki, Jedrzej and Fischer, Hans . "Geometry of classical fields" Rep. Math. Phys., 154, North-Holland Publishing Co. (1988): xviii+450
Sniatycki, Jedrzej. On quantization of {Y}ang-{M}ills fields 76, Teubner (1985): 351-363
Epstein, Marcelo , Elzanowski, Marek and Sniatycki, Jedrzej. Locality and uniformity in global elasticity 1139, Springer (1985): 300-310
Sniatycki, Jedrzej. On quantization of systems with constraints 6, Reidel (1984): 207-211
Sniatycki, Jedrzej. Constraints and quantization 1037, Springer (1983): 301-334
Sniatycki, Jedrzej. Further applications of geometric quantization 139, Springer (1981): 36-37
Sniatycki, Jedrzej. "Geometric quantization and quantum mechanics" Comm. Math. Phys., 30, Springer-Verlag (1980): ix+230
Sniatycki, Jedrzej. Application of geometric quantization in quantum mechanics 676, Springer (1978): 357-367
Sniatycki, Jedrzej. On geometric quantization of classical systems Academic Press (1978): 287-297
Sniatycki, Jedrzej. On cohomology groups appearing in geometric quantization Springer (1977): 46-66. Lecture Notes in Math., Vol. 570
Sniatycki, Jedrzej. On wave functions in geometric quantization Springer (1976): 194-198. Lecture Notes in Phys., Vol. 50
Sniatycki, Jedrzej. Bohr-{S}ommerfeld quantum systems Centre Nat. Recherche Sci., Centre Phys. Theor., Marseille (1974): 42-51

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