{"product_id":"rigorous-time-slicing-approach-to-feynman-path-integrals","title":"Rigorous Time Slicing Approach to Feynman Path Integrals","description":"\u003cp\u003eIn this review of Rigorous Time Slicing Approach to Feynman Path Integrals the bottom line is clear: this is a specialist mathematical text for readers who need a rigorous bridge between path integral intuition and the Schrodinger equation. The book's single biggest reason to buy is that it provides a proved convergence of Feynman's original path integral to the fundamental solution of the Schrodinger equation under clearly stated regularity conditions, making it valuable for graduate students and researchers seeking a mathematically rigorous treatment rather than heuristic arguments.\u003c\/p\u003e\u003ch2\u003eKey Features\u003c\/h2\u003e\u003cul\u003e\n\u003cli\u003e\n\u003cstrong\u003eRigorous convergence proof:\u003c\/strong\u003e Demonstrates that Feynman's original definition of the path integral converges to the fundamental solution of the Schrodinger equation in the short term, providing a firm mathematical foundation for the method.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eRegularity conditions clarified:\u003c\/strong\u003e Specifies that the potential must be differentiable sufficiently many times and that derivatives of order two and higher are bounded, which helps readers understand the precise applicability.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eSemi-classical asymptotics:\u003c\/strong\u003e Proves the semi-classical asymptotic formula up to the second term of the fundamental solution by a method distinct from Birkhoff's, useful for those studying asymptotic expansions.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eRemainder bound:\u003c\/strong\u003e Provides a bound on the remainder term in the asymptotic expansion, giving users a sense of quantitative control over approximations.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eComparative quantization perspective:\u003c\/strong\u003e Discusses the relationship between Lagrangian path integral quantization and Hamiltonian Schrodinger quantization, framing the open mathematical issues about equivalence.\u003c\/li\u003e\n\u003c\/ul\u003e\u003ch2\u003eWho It's For\u003c\/h2\u003e\u003cp\u003eGraduate students in mathematical physics and applied mathematicians who need a rigorous, theorem-driven account will find this book directly useful. It is suited to readers comfortable with functional analysis and PDE methods who want to see convergence results and controlled asymptotics rather than physics-level heuristics.\u003c\/p\u003e\u003cp\u003eResearchers focused primarily on physical intuition or those seeking introductory treatments of path integrals should look elsewhere; this is not a pedagogical primer or a popular exposition, and it assumes familiarity with advanced mathematical tools.\u003c\/p\u003e\u003ch2\u003ePros \u0026amp; Cons\u003c\/h2\u003e\u003cp\u003e\u003cstrong\u003ePros\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eProvides a clear, rigorous convergence proof tying path integrals to the Schrodinger fundamental solution.\u003c\/li\u003e\n\u003cli\u003eStates practical regularity and boundedness conditions that clarify where the results apply.\u003c\/li\u003e\n\u003cli\u003eIncludes a semi-classical asymptotic expansion and a proved bound on the remainder, offering useful quantitative results.\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003e\u003cstrong\u003eCons\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eSpecialist level and terse presentation make it unsuitable for readers without substantial mathematical background.\u003c\/li\u003e\n\u003cli\u003eFocus on short-term convergence means long-time behavior and more general potentials are not the primary concern.\u003c\/li\u003e\n\u003c\/ul\u003e\u003ch2\u003eSpecifications\u003c\/h2\u003e\u003ctable\u003e\n\u003ctr\u003e\n\u003ctd\u003eTitle\u003c\/td\u003e\n\u003ctd\u003eRigorous Time Slicing Approach to Feynman Path Integrals\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eSeries\u003c\/td\u003e\n\u003ctd\u003eMathematical Physics Studies\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eAuthor \/ Brand\u003c\/td\u003e\n\u003ctd\u003eFujiwara\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eMain result\u003c\/td\u003e\n\u003ctd\u003eConvergence of Feynman path integral to Schrodinger fundamental solution\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eAssumptions\u003c\/td\u003e\n\u003ctd\u003ePotential differentiable sufficiently many times with bounded derivatives of order \u0026gt;= 2\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eAdditional results\u003c\/td\u003e\n\u003ctd\u003eSemi-classical asymptotic formula up to second term with remainder bound\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e\u003ch2\u003eOur Verdict\u003c\/h2\u003e\u003cp\u003eThis book is recommended for advanced students and researchers who require a rigorous demonstration that time-sliced Feynman path integrals converge to the Schrodinger fundamental solution under explicit regularity conditions. It offers good value as a specialist reference because of its proved asymptotic expansion and remainder estimates, but it is not intended as an introductory or physics-first treatment.\u003c\/p\u003e\u003ch2\u003eFrequently Asked Questions\u003c\/h2\u003e\u003cp\u003e\u003cstrong\u003eDoes the book prove path integral convergence?\u003c\/strong\u003e\u003cbr\u003eYes. It proves convergence of Feynman's original path integral to the fundamental solution in the short term under stated differentiability and boundedness conditions.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eWhat assumptions are needed on the potential?\u003c\/strong\u003e\u003cbr\u003eThe potential must be differentiable sufficiently many times and have bounded derivatives of order two and higher.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eIs this suitable for beginners?\u003c\/strong\u003e\u003cbr\u003eNo. The treatment is rigorous and technical, aimed at readers with background in PDEs and functional analysis.\u003c\/p\u003e","brand":"Fujiwara","offers":[{"title":"Default Title","offer_id":48639540527323,"sku":"4431565515","price":109.85,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0724\/1043\/1707\/files\/614ooov9faL._SL1245.jpg?v=1778611203","url":"https:\/\/gearmusthave.com\/products\/rigorous-time-slicing-approach-to-feynman-path-integrals","provider":"GearMustHave","version":"1.0","type":"link"}