{"product_id":"9789814365260","title":"Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets","description":"\u003cp\u003eThis is the fifth, expanded edition of the comprehensive textbook published in 1990 on the theory and applications of path integrals. It is the first book to explicitly solve path integrals of a wide variety of nontrivial quantum-mechanical systems, in particular the hydrogen atom. The solutions have been made possible by two major advances. The first is a \u003ci\u003enew euclidean path integral formula\u003c\/i\u003e which increases the restricted range of applicability of Feynman's time-sliced formula to include singular attractive 1\/\u003ci\u003er\u003c\/i\u003e- and 1\/\u003ci\u003er\u003c\/i\u003e\u003csup\u003e2\u003c\/sup\u003e-potentials. The second is a \u003ci\u003enew nonholonomic mapping principle\u003c\/i\u003e carrying physical laws in flat spacetime to spacetimes with curvature and torsion, which leads to time-sliced path integrals that are manifestly invariant under coordinate transformations.\u003c\/p\u003e\u003cp\u003eIn addition to the time-sliced definition, the author gives a perturbative, coordinate-independent definition of path integrals, which makes them invariant under coordinate transformations. A consistent implementation of this property leads to an extension of the theory of generalized functions by defining uniquely products of distributions.\u003c\/p\u003e\u003cp\u003eThe powerful Feynman-Kleinert variational approach is explained and developed systematically into a \u003ci\u003evariational perturbation theory\u003c\/i\u003e which, in contrast to ordinary perturbation theory, produces convergent results. The convergence is uniform from weak to strong couplings, opening a way to precise evaluations of analytically unsolvable path integrals in the strong-coupling regime where they describe critical phenomena.\u003c\/p\u003e\u003cp\u003eTunneling processes are treated in detail, with applications to the lifetimes of supercurrents, the stability of metastable thermodynamic phases, and the large-order behavior of perturbation expansions. A variational treatment extends the range of validity to small barriers. A corresponding extension of the large-order perturbation theory now also applies to small orders.\u003c\/p\u003e\u003cp\u003eSpecial attention is devoted to path integrals with topological restrictions needed to understand the statistical properties of elementary particles and the entanglement phenomena in polymer physics and biophysics. The Chern–Simons theory of particles with fractional statistics \u003ci\u003e(anyons)\u003c\/i\u003e is introduced and applied to explain the fractional quantum Hall effect.\u003c\/p\u003e\u003cp\u003eThe relevance of path integrals to financial markets is discussed, and improvements of the famous Black–Scholes formula for option prices are developed which account for the fact, recently experienced in the world markets, that large fluctuations occur much more frequently than in Gaussian distributions.\u003c\/p\u003e\u003cb\u003eContents:\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eFundamentals\u003c\/li\u003e\n\u003cli\u003ePath Integrals — Elementary Properties and Simple Solutions\u003c\/li\u003e\n\u003cli\u003eExternal Sources, Correlations, and Perturbation Theory\u003c\/li\u003e\n\u003cli\u003eSemiclassical Time Evolution Amplitude\u003c\/li\u003e\n\u003cli\u003eVariational Perturbation Theory\u003c\/li\u003e\n\u003cli\u003ePath Integrals with Topological Constraints\u003c\/li\u003e\n\u003cli\u003eMany Particle Orbits — Statistics and Second Quantization\u003c\/li\u003e\n\u003cli\u003ePath Integrals in Polar and Spherical Coordinates\u003c\/li\u003e\n\u003cli\u003eWave Functions\u003c\/li\u003e\n\u003cli\u003eSpaces with Curvature and Torsion\u003c\/li\u003e\n\u003cli\u003eSchrödinger Equation in General Metric-Affine Spaces\u003c\/li\u003e\n\u003cli\u003eNew Path Integral Formula for Singular Potentials\u003c\/li\u003e\n\u003cli\u003ePath Integral of Coulomb System\u003c\/li\u003e\n\u003cli\u003eSolution of Further Path Integrals by Duru-Kleinert Method\u003c\/li\u003e\n\u003cli\u003ePath Integrals in Polymer Physics\u003c\/li\u003e\n\u003cli\u003ePolymers and Particle Orbits in Multiply Connected Spaces\u003c\/li\u003e\n\u003cli\u003eTunneling\u003c\/li\u003e\n\u003cli\u003eNonequilibrium Quantum Statistics\u003c\/li\u003e\n\u003cli\u003eRelativistic Particle Orbits\u003c\/li\u003e\n\u003cli\u003ePath Integrals and Financial Markets\u003c\/li\u003e\n\u003c\/ul\u003e\u003cbr\u003e\u003cb\u003eReadership:\u003c\/b\u003e Students and researchers in theoretical physics.\u003cbr\u003e","brand":"World Scientific Publishing Company, Incorporated","offers":[{"title":"Default Title","offer_id":47185350459632,"sku":"9789814365260","price":38.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/9789814365260_p0.jpg?v=1763691277","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9789814365260","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}