Assistant Director, Pacific Institute for the Mathematical Sciences, UBC

Professor, University of Hawai`i (Retired);

Editor, JDGA

 

Pacific Institute for the Mathematical Sciences University of British Columbia 200 - 1933 West Mall Vancouver, BC V6T 1Z2 Canada
		Email: gotay@pims.math.ca

 

CV

Selected Publications

 

• QUANTIZATION VIA DEFORMATION OF PREQUANTIZATION (2011)
  
  
  
• COVARIANTIZING CLASSICAL FIELD THEORIES (2011)
  
  
  
• MULTIMOMENTUM MAPS and CLASSICAL FIELD THEORY: Lectures at the 14th International Summer School on Global Analysis and Mathematical Physics (Olomouc, Czech Republic, 2009)
  
  Lecture 1: Introduction
  
  Lecture 2: Covariant Field Theory
  
  Lecture 3: Canonical Field Theory
  
  Lectures 4 & 5: Gauge Symmetries and Initial Value Constraints
  
  
• PARAMETRIZATION AND STRESS-ENERGY-MOMENTUM TENSORS IN METRIC FIELD THEORIES (2008)
  MR ZMATH
  
  
• CONCATENATING VARIATIONAL PRINCIPLES AND THE KINETIC STRESS-ENERGY-MOMENTUM TENSOR (2008)
  
  
  
• MOMENTUM MAPS AND CLASSICAL FIELDS, PART III: GAUGE SYMMETRIES AND INITIAL VALUE CONSTRAINTS (GiMmsy III, 2006)
  
  
  
• MOMENTUM MAPS AND CLASSICAL FIELDS, PART II: CANONICAL ANALYSIS OF FIELD THEORIES (GiMmsy II, 2003)
  
  
  
• ON QUANTIZING NON-NILPOTENT COADJOINT ORBITS OF SEMISIMPLE LIE GROUPS (2002)
  Slides MR
  
  
• POLYNOMIAL ALGEBRAS ON COADJOINT ORBITS OF SEMISIMPLE LIE GROUPS (2002)
  MR
  
  
• ON QUANTIZING SEMISIMPLE BASIC ALGEBRAS, I: sl(2,R) (2002)
  MR
  
  
• ON QUANTIZING NILPOTENT AND SOLVABLE BASIC ALGEBRAS (2001)
  MR
  
  
• OBSTRUCTIONS TO QUANTIZATION (2000)
  
  
  
• NONEXISTENCE OF FINITE-DIMENSIONAL QUANTIZATIONS OF A NONCOMPACT SYMPLECTIC MANIFOLD (1999)
  MR ZMATH
  
  
• ON THE GROENEWOLD-VAN HOVE PROBLEM FOR R^{2n} (1999)
  MR
  
  
• AN OBSTRUCTION TO QUANTIZING COMPACT SYMPLECTIC MANIFOLDS (1999)
  Addendum MR
  
  
• SYMPLECTIC GEOMETRY (1998)
  Abstract (Order Full Issue) MR
  
  
• SOME REMARKS ON SINGULARITIES IN QUANTUM COSMOLOGY (1997)
  MR
  
  
• ON QUANTIZING T*S^1 (1997)
  MR
  
  
• MOMENTUM MAPS AND CLASSICAL FIELDS, PART I: COVARIANT FIELD THEORY (GiMmsy I, 1997)
  
  
  
• OBSTRUCTION RESULTS IN QUANTIZATION THEORY (1996)
  MR ZMATH
  
  
• A GROENEWOLD-VAN HOVE THEOREM FOR S^2 (1996)
  MR
  
  
• ON A FULL QUANTIZATION OF THE TORUS (1995)
  MR
  
  
• ON SYMPLECTIC SUBMANIFOLDS OF COTANGENT BUNDLES (1993)
  MR ZMATH
  
  
• MATHEMATICAL ASPECTS OF CLASSICAL FIELD THEORY (1992)
  Abstract (Order Book) MR
  
  
• LA SYMPLECTIFICATION DE LA SCIENCE (1992)
  English French MR ZMATH
  
  
• STRESS-ENERGY-MOMENTUM TENSORS AND THE BELINFANTE-ROSENFELD FORMULA (1992)
  Beamer MR
  
  
• A MULTISYMPLECTIFIC FRAMEWORK FOR CLASSICAL FIELD THEORY AND THE CALCULUS OF VARIATIONS II: SPACE + TIME DECOMPOSITION (1991)
  MR
  
  
• A UNIVERSAL REDUCTION PROCEDURE FOR HAMILTONIAN GROUP ACTIONS (1991)
  MR ZMATH
  
  
• AN EXTERIOR DIFFERENTIAL SYSTEMS APPROACH TO THE CARTAN FORM (1991)
  MR ZMATH
  
  
• A MULTISYMPLECTIFIC FRAMEWORK FOR CLASSICAL FIELD THEORY AND THE CALCULUS OF VARIATIONS I: COVARIANT HAMILTONIAN FORMALISM (1991)
  MR ZMATH
  
  
• QUANTIZATION AND BOSONIC BRST THEORY (1991)
  
  
  
• A SYMPLECTIC ANALOGUE OF THE MOSTOW-PALAIS THEOREM (1991)
  MR ZMATH
  
  
• NON-UNIMODULARITY AND THE QUANTIZATION OF THE PSEUDO-RIGID BODY (1990)
  MR
  
  
• GEOMETRIC AND ALGEBRAIC REDUCTION FOR SINGULAR MOMENTUM MAPPINGS (1990)
  MR
  
  
• REDUCTION OF HOMOGENEOUS YANG-MILLS FIELDS (1989)
  MR
  
  
• R^{2n} IS A UNIVERSAL SYMPLECTIC MANIFOLD FOR REDUCTION (1989)
  MR
  
  
• ZERO LEVELS OF MOMENTUM MAPPINGS FOR COTANGENT ACTIONS (1989)
  MR
  
  
• A MULTISYMPLECTIC APPROACH TO THE KdV EQUATION (1988)
  MR
  
  
• COMPACT PARALLELIZABLE FOUR DIMENSIONAL SYMPLECTIC AND COMPLEX MANIFOLDS (1988)
  MR ZMATH
  
  
• FORMAL QUANTIZATION OF QUADRATIC MOMENTUM OBSERVABLES (1987)
  MR
  
  
• A CLASS OF NON-POLARIZABLE SYMPLECTIC MANIFOLDS (1987)
  MR
  
  
• SINGULAR ANGULAR MOMENTUM MAPPINGS (1986)
  MR
  
  
• NEGATIVE ENERGY STATES IN QUANTUM GRAVITY? (1986)
  MR
  
  
• CONSTRAINTS, REDUCTION AND QUANTIZATION (1986)
  MR ZMATH
  
  
• REDUCED CANONICAL FORMALISM FOR A PARTICLE WITH ZERO ANGULAR MOMENTUM (1984)
  MR
  
  
• TIME AND SINGULARITY (1984)
  Honorable Mention Essay, 1983 Gravity Research Foundation Competition
  
  
• APARTHEID IN THE DIRAC THEORY OF CONSTRAINTS (1984)
  MR
  
  
• POISSON REDUCTION AND QUANTIZATION FOR THE n+1 PHOTON (1984)
  MR
  
  
• CLOSED FORMS ON SYMPLECTIC FIBRE BUNDLES (1983)
  MR
  
  
• QUANTUM COSMOLOGICAL SINGULARITIES (1983)
  MR
  
  
• ON THE VALIDITY OF DIRAC'S CONJECTURE REGARDING FIRST CLASS SECONDARY CONSTRAINTS (1983)
  MR
  
  
• ON COISOTROPIC IMBEDDINGS OF PRESYMPLECTIC MANIFOLDS (1982)
  MR
  
  
• COISOTROPIC IMBEDDINGS, DIRAC BRACKETS AND QUANTIZATION (1981)
  
  
  
• QUANTUM COSMOLOGY AND GEOMETRIC QUANTIZATION (1981)
  MR
  
  
• GEOMETRIC QUANTIZATION (1981)
  Abstract
  
  
• ON THE QUANTIZATION OF PRESYMPLECTIC DYNAMICAL SYSTEMS VIA COISOTROPIC IMBEDDINGS (1981)
  MR
  
  
• GEOMETRIC QUANTIZATION (1981)
  Abstract
  
  
• PRESYMPLECTIC LAGRANGIAN SYSTEMS II: THE SECOND ORDER EQUATION PROBLEM (1980)
  MR
  
  
• CAN QUANTUM EFFECTS PREVENT SPACETIME COLLAPSE? (1980)
  
  
  
• GENERALIZED CONSTRAINT ALGORITHM AND SPECIAL PRESYMPLECTIC MANIFOLDS (1980)
  MR
  
  
• FUNCTORIAL GEOMETRIC QUANTIZATION AND VAN HOVE'S THEOREM (1980)
  MR
  
  
• GEOMETRIC QUANTIZATION AND GRAVITATIONAL COLLAPSE (1980)
  MR
  
  
• PRESYMPLECTIC HAMILTON AND LAGRANGE SYSTEMS, GAUGE TRANSFORMATIONS AND THE DIRAC THEORY OF CONSTRAINTS (1979)
  
  
• PRESYMPLECTIC LAGRANGIAN SYSTEMS I: THE CONSTRAINT ALGORITHM AND THE EQUIVALENCE THEOREM (1979)
  MR
  
  
• PRESYMPLECTIC MANIFOLDS, GEOMETRIC CONSTRAINT THEORY AND THE DIRAC-BERGMANN THEORY OF CONSTRAINTS (1979)
  
  
  
• KOSTANT-SOURIAU QUANTIZATION OF ROBERTSON-WALKER COSMOLOGIES WITH A SCALAR FIELD (1979)
  
  
  
• PRESYMPLECTIC MANIFOLDS AND THE DIRAC-BERGMANN THEORY OF CONSTRAINTS (1978)
  MR
  
  
• EXISTENCE OF INSTANTANEOUS CAUCHY SURFACES (1978)
  
  
  

  The files that will be downloaded are usually .pdf files. If you need a reader for them, you can download Acrobat Reader from Adobe for free. If you prefer, I can email you the files or send reprints the old-fashioned way; contact me at: gotay@pims.math.ca.