Pubbl/distr/stampa	Providence, Rhode Island : , : American Mathematical Society, , [2007]
Descrizione fisica	1 online resource (272 p.)
Disciplina	530.14/3
Collana	Contemporary mathematics
Soggetto topico	Quantum field theory Algebraic topology Geometry, Algebraic
Soggetto genere / forma	Electronic books.
ISBN	0-8218-8113-2 0-8218-4062-2
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	eng
Nota di contenuto	""Contents""; ""Introduction""; ""List of participants""; ""Invited Lecturers""; ""Deformation Quantization: a Mini-Lecture""; ""Examples of noncommutative instantons""; ""1. Introduction""; ""2. Toric noncommutative manifolds""; ""3. Gauge theory on the sphere s4Î?""; ""4. SU(2)-instantons on S4Î?""; ""5. An instanton bundle over a symplectic quantum sphere S4q""; ""Appendix A. Connections on noncommutative vector bundles""; ""Appendix B. The Chern character of projections""; ""References""; ""Topological Quantum Field Theories, Strings and Orbifolds""; ""1. Group Actions""; ""2. Orbifolds""
Record Nr.	UNINA-9910479977003321

Pubbl/distr/stampa	Hackensack, N.J., : World Scientific, 2012
Descrizione fisica	1 online resource (362 p.)
Disciplina	516 530.14/3
Altri autori (Persone)	GoldmanWilliam SeriesCaroline TanSer Peow
Collana	Lecture notes series. Institute for Mathematical Sciences, National University of Singapore
Soggetto topico	Topology
Soggetto genere / forma	Electronic books.
ISBN	1-281-60367-8 9786613784360 981-4401-36-6
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	eng
Nota di contenuto	CONTENTS; Foreword; Preface; An Invitation to Elementary Hyperbolic Geometry Ying Zhang; Introduction; 1. Euclid's Elements, Book I and Neutral Plane Geometry; 1.1. A brief review of contents of Elements, Book I; 1.2. A useful lemma; 1.3. A gure-free proof of Proposition I.7; 1.4. More notes on Elements, Book I; 1.5. Playfair's axiom; 1.6. Neutral plane geometry; 1.7. Angle-sums of triangles and Legendre's Theorems; 1.8. Quadrilaterals with two consecutive right angles; 1.9. Saccheri and Lambert quadrilaterals; 1.10. Variation of triangles in a neutral plane 1.11. A midline configuration for triangles1.12. More theorems of neutral plane geometry; 1.13. Small angles; 2. Hyperbolic Plane Geometry; 2.1. Hyperbolic plane; 2.2. Asymptotic Parallelism; 2.3. Angle of parallelism; 2.4. The variation in the distance between two straight lines; 2.5. Some more theorems in hyperbolic plane geometry; 2.6. Construction of the common perpendicular to two ultra-parallel straight lines; 2.7. Construction of asymptotic parallels; 2.8. Ideal points; 2.9. Horocycles; 2.10. Construction of the straight line joining two given ideal points; 2.11. Ultra-ideal points 2.12. The projective plane associated to a hyperbolic plane2.13. Center-pencils of a hyperbolic triangle; 2.14. Equidistant curves; 2.15. Positions of proper points relative to an ideal point; 2.16. Hyperbolic areas via equivalence of triangles; 2.17. Metric relations of corresponding arcs in concentric horocycles; 3. Isometries of the Hyperbolic Plane; 3.1. Isometries and reections in straight lines; 3.2. Orientation preserving/reversing isometries; 3.3. Rotations; 3.4. Translations; 3.5. Isometries of parabolic type; 3.6. Redundancy of two reflections 3.7. Orientation reversing isometries as reflections and glide reflections3.8. Isometries as projective transformations; 3.9. Invariant projective lines of; 3.10. Composition of two orientation preserving isometries other than two translations; 3.11. Composition of two translations; 3.12. Conjugates of isometries; 3.13. The orthic triangle; 4. Hyperbolic Trigonometry Derived from Isometries; 4.1. Some identities of isometries of a neutral plane; 4.2. Some trigonometric formulas in H2(k); 4.3. Upper half-plane model U2 for hyperbolic plane H2(1); 4.4. Matrices of certain isometries of U2 4.5. Trigonometric laws via identities of isometries4.6. Suggested further readings; Acknowledgments; References; Hyperbolic Structures on Surfaces Javier Aramayona; 1. Introduction; 2. Plane Hyperbolic Geometry; 2.1. Mobius transformations; 2.1.1. Classification in terms of trace and fixed points; 2.2. Models for hyperbolic geometry; 2.2.1. Hyperbolic distance; 2.2.2. Mobius transformations act by isometries; 2.2.3. The Cayley transformation; 2.2.4. Hyperbolic geodesics; 2.2.5. The boundary at infinity; 2.2.6. The full isometry group; 2.2.7. Dynamics of elements of Isom+(H) 2.3. Fuchsian groups and fundamental domains
Record Nr.	UNINA-9910462554303321

Edizione	[1st ed.]
Pubbl/distr/stampa	Hackensack, N.J., : World Scientific, 2012
Descrizione fisica	1 online resource (362 p.)
Disciplina	516 530.14/3
Altri autori (Persone)	GoldmanWilliam SeriesCaroline TanSer Peow
Collana	Lecture notes series. Institute for Mathematical Sciences, National University of Singapore
Soggetto topico	Topology
ISBN	1-281-60367-8 9786613784360 981-4401-36-6
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	eng
Nota di contenuto	CONTENTS; Foreword; Preface; An Invitation to Elementary Hyperbolic Geometry Ying Zhang; Introduction; 1. Euclid's Elements, Book I and Neutral Plane Geometry; 1.1. A brief review of contents of Elements, Book I; 1.2. A useful lemma; 1.3. A gure-free proof of Proposition I.7; 1.4. More notes on Elements, Book I; 1.5. Playfair's axiom; 1.6. Neutral plane geometry; 1.7. Angle-sums of triangles and Legendre's Theorems; 1.8. Quadrilaterals with two consecutive right angles; 1.9. Saccheri and Lambert quadrilaterals; 1.10. Variation of triangles in a neutral plane 1.11. A midline configuration for triangles1.12. More theorems of neutral plane geometry; 1.13. Small angles; 2. Hyperbolic Plane Geometry; 2.1. Hyperbolic plane; 2.2. Asymptotic Parallelism; 2.3. Angle of parallelism; 2.4. The variation in the distance between two straight lines; 2.5. Some more theorems in hyperbolic plane geometry; 2.6. Construction of the common perpendicular to two ultra-parallel straight lines; 2.7. Construction of asymptotic parallels; 2.8. Ideal points; 2.9. Horocycles; 2.10. Construction of the straight line joining two given ideal points; 2.11. Ultra-ideal points 2.12. The projective plane associated to a hyperbolic plane2.13. Center-pencils of a hyperbolic triangle; 2.14. Equidistant curves; 2.15. Positions of proper points relative to an ideal point; 2.16. Hyperbolic areas via equivalence of triangles; 2.17. Metric relations of corresponding arcs in concentric horocycles; 3. Isometries of the Hyperbolic Plane; 3.1. Isometries and reections in straight lines; 3.2. Orientation preserving/reversing isometries; 3.3. Rotations; 3.4. Translations; 3.5. Isometries of parabolic type; 3.6. Redundancy of two reflections 3.7. Orientation reversing isometries as reflections and glide reflections3.8. Isometries as projective transformations; 3.9. Invariant projective lines of; 3.10. Composition of two orientation preserving isometries other than two translations; 3.11. Composition of two translations; 3.12. Conjugates of isometries; 3.13. The orthic triangle; 4. Hyperbolic Trigonometry Derived from Isometries; 4.1. Some identities of isometries of a neutral plane; 4.2. Some trigonometric formulas in H2(k); 4.3. Upper half-plane model U2 for hyperbolic plane H2(1); 4.4. Matrices of certain isometries of U2 4.5. Trigonometric laws via identities of isometries4.6. Suggested further readings; Acknowledgments; References; Hyperbolic Structures on Surfaces Javier Aramayona; 1. Introduction; 2. Plane Hyperbolic Geometry; 2.1. Mobius transformations; 2.1.1. Classification in terms of trace and fixed points; 2.2. Models for hyperbolic geometry; 2.2.1. Hyperbolic distance; 2.2.2. Mobius transformations act by isometries; 2.2.3. The Cayley transformation; 2.2.4. Hyperbolic geodesics; 2.2.5. The boundary at infinity; 2.2.6. The full isometry group; 2.2.7. Dynamics of elements of Isom+(H) 2.3. Fuchsian groups and fundamental domains
Record Nr.	UNINA-9910815267803321

Autore	Avramidi Ivan G
Edizione	[1st ed. 2000.]
Pubbl/distr/stampa	Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2000
Descrizione fisica	1 online resource (X, 152 p.)
Disciplina	530.14/3
Collana	Lecture Notes in Physics Monographs
Soggetto topico	Quantum field theory String theory Physics Gravitation Quantum Field Theories, String Theory Mathematical Methods in Physics Classical and Quantum Gravitation, Relativity Theory
ISBN	3-540-46523-5
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	eng
Nota di contenuto	Background Field Method in Quantum Field Theory -- Technique for Calculation of De Witt Coefficients -- Partial Summation of Schwinger-De Witt Expansion -- Higher-Derivative Quantum Gravity -- Conclusion.
Record Nr.	UNINA-9910257424103321

Autore	Smit Jan <1943->
Pubbl/distr/stampa	Cambridge : , : Cambridge University Press, , 2002
Descrizione fisica	1 online resource (xii, 271 pages) : digital, PDF file(s)
Disciplina	530.14/3
Collana	Cambridge lecture notes in physics
Soggetto topico	Quantum field theory Lattice theory
ISBN	9780511020783 0-511-14814-3 0-511-58397-4 0-511-02078-3
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	eng
Nota di contenuto	QED, QCD, and confinement -- Scalar field -- Path-integral and lattice regularization -- Path integral in quantum mechanics -- Regularization by discretization -- Analytic continuation to imaginary time -- Spectrum of the transfer operator -- Latticization of the scalar field -- Transfer operator for the scalar field -- Fourier transformation on the lattice -- Free scalar field -- Particle interpretation -- Back to real time -- O(n) models -- Goldstone bosons -- O(n) models as spin models -- Phase diagram and critical line -- Weak-coupling expansion -- Renormalization -- Renormalization-group beta functions -- Hopping expansion -- Luscher-Weisz solution -- Numerical simulation -- Real-space renormalization group and universality -- Universality at weak coupling -- Triviality and the Standard Model -- Gauge field on the lattice -- QED action -- QCD action -- Lattice gauge field -- Gauge-invariant lattice path integral -- Compact and non-compact Abelian gauge theory -- Hilbert space and transfer operator -- The kinetic-energy operator -- Hamiltonian for continuous time -- Wilson loop and Polyakov line -- U(1) and SU(n) gauge theory -- Potential at weak coupling -- Asymptotic freedom -- Strong-coupling expansion -- Potential at strong coupling -- Confinement versus screening -- Glueballs -- Coulomb phase, confinement phase -- Mechanisms of confinement -- Scaling and asymptotic scaling, numerical results -- Fermions on the lattice -- Naive discretization of the Dirac action -- Species doubling -- Wilson's fermion method.
Record Nr.	UNINA-9910455630803321