Quantization of Gauge Systems (eBook)

Marc Henneaux, Claudio Teitelboim (Autoren)

eBook Download: PDF

2020
552 Seiten
Princeton University Press (Verlag)
978-0-691-21386-6 (ISBN)

Infos

This book is a systematic study of the classical and quantum theories of gauge systems. It starts with Dirac's analysis showing that gauge theories are constrained Hamiltonian systems. The classical foundations of BRST theory are then laid out with a review of the necessary concepts from homological algebra. Reducible gauge systems are discussed, and the relationship between BRST cohomology and gauge invariance is carefully explained. The authors then proceed to the canonical quantization of gauge systems, first without ghosts (reduced phase space quantization, Dirac method) and second in the BRST context (quantum BRST cohomology). The path integral is discussed next. The analysis covers indefinite metric systems, operator insertions, and Ward identities. The antifield formalism is also studied and its equivalence with canonical methods is derived. The examples of electromagnetism and abelian 2-form gauge fields are treated in detail. The book gives a general and unified treatment of the subject in a self-contained manner. Exercises are provided at the end of each chapter, and pedagogical examples are covered in the text.

Produkt-Details

• Erscheint lt. Verlag: 23.6.2020
• Zusatzinfo: 4 illus.
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Mechanik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
• Schlagworte: Abelian constraints • Action (physics) • antighost number • antisymmetric tensor • asymptotic expansion • auxiliary fields • Axiom • Basis (linear algebra) • Berezin integral • Boundary Operator • Boundary problem (spatial analysis) • Boundary value problem • BRST quantization • Canonical Hamiltonian • canonical quantization • Canonical transformation • Change of variables • classical electromagnetism • classical limit • coefficient • cohomology • commutative property • commutator • Configuration space • Conjugate variables • Constant of integration • Constraint algorithm • convolution • Correspondence rule • Critical dimension • Degrees of freedom (statistics) • derivations • Diagram (category theory) • Differential • differential form • Differential operator • Dimensional regularization • Dimension (vector space) • Dirac bracket • Dirac delta function • doublet • Effective action • Eigenfunction • Eigenvalues and Eigenvectors • energy level • Equation • Equations of motion • Expectation value (quantum mechanics) • extended action • exterior derivative • exterior product • Fermi–Dirac statistics • Fourier Transformation • Gauge anomaly • Gauge Fixing • gauge function • Gauge Theory • Gaussian average • Gaussian integral • gauss law • Gauss's Law • general covariance • G-Force • Global symmetry • Green functions • Hamiltonian constraint • hamiltonian mechanics • Hamiltonian vector field • Hamilton–Jacobi equation • harmonic states • Heisenberg algebra • hilbert space • Infinitesimal generator (stochastic processes) • Involution • Jacobian matrix and determinant • Jacobi identity • Klein–Gordon equation • Kunneth formula • Lagrange multiplier • Lagrange multipliers • Lagrangian (field theory) • left derivatives • linear differential equation • linear equation • Linear Independence • Linear map • local commutativity • Lorentz covariance • Minkowski space • Noether's second theorem • nontrivial cycle • Path integral formulation • Pauli matrices • Peierls bracket • perturbation theory • Perturbation theory (quantum mechanics) • Phase space • Phase space method • Poisson Bracket • Projection (linear algebra) • Quantum gauge theory • Quantum Master Equation • quantum mechanics • Quotient space (linear algebra) • Quotient space (topology) • Riemannian Geometry • rotational invariance • Scalar Field • Schrödinger equation • Schwinger–Dyson equation • Square-integrable function • Structure Function • submanifold • Supercommutative algebra • superdomain • Supertrace • Symmetry in Quantum Mechanics • Symplectic Geometry • tensor product • Theorem • theory • Total derivative • Unitarity (physics) • Variable (mathematics) • Variational Principle • wave function • Wave vector
• ISBN-10: 0-691-21386-0 / 0691213860
• ISBN-13: 978-0-691-21386-6 / 9780691213866