{"product_id":"rigorous-time-slicing-approach-to-feynman-path-integrals-short-term","title":"Rigorous Time Slicing Approach to Feynman Path Integrals - Short-Term","description":"\u003cp\u003eIn this review of Rigorous Time Slicing Approach to Feynman Path Integrals the bottom line is clear: this is a specialist, mathematically rigorous treatment aimed at researchers and advanced graduate students who need a proof that Feynman path integrals converge to the Schrdinger fundamental solution in short time. The book delivers a careful, theorem-driven account showing convergence under smoothness and boundedness conditions on the potential and supplies a semi-classical asymptotic to the second term, so readers seeking precise estimates and a novel proof technique will find real value here.\u003c\/p\u003e\n\u003ch2\u003eKey Features\u003c\/h2\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cstrong\u003eRigorous convergence proof:\u003c\/strong\u003e Presents a detailed proof that Feynmandings original path integral definition converges to the fundamental solution of the Schrdinger equation for sufficiently smooth potentials in short time.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eRegularity conditions clarified:\u003c\/strong\u003e States explicit differentiability and boundedness conditions on the potential and its derivatives from order two onward, which guides applicability in research.\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 using a method distinct from Birkhoff, offering a fresh analytic approach.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eRemainder bounds provided:\u003c\/strong\u003e Supplies a bound on the remainder term in the asymptotic expansion, making the estimates usable in further mathematical work.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eLagrangian versus Hamiltonian context:\u003c\/strong\u003e Discusses the relationship between Feynmandings Lagrangian quantization and Schrdingers Hamiltonian method, emphasizing the partial state of equivalence proofs.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003ch2\u003eWho It's For\u003c\/h2\u003e\n\u003cp\u003eThis book is best for mathematicians, mathematical physicists, and advanced graduate students who already have a solid background in functional analysis and quantum mechanics and who need a rigorous account of path integral convergence. Researchers working on semi-classical analysis or precise error estimates in quantization will appreciate the novel proof techniques and remainder bounds.\u003c\/p\u003e\n\u003cp\u003eIt is not intended for casual readers, beginners in quantum mechanics, or those seeking broad physical intuition without technical proofs; readers looking for introductory or computational treatments of path integrals should look elsewhere.\u003c\/p\u003e\n\u003ch2\u003ePros \u0026amp; Cons\u003c\/h2\u003e\n\u003cp\u003e\u003cstrong\u003ePros\u003c\/strong\u003e\u003c\/p\u003e\n\u003cul\u003e\n\u003cli\u003eThorough, mathematically rigorous convergence proof for short-time Feynman path integrals.\u003c\/li\u003e\n\u003cli\u003eClear assumptions on potential regularity and bounded higher derivatives that make theorems applicable.\u003c\/li\u003e\n\u003cli\u003eAlternative method for semi-classical expansion that complements existing literature.\u003c\/li\u003e\n\u003cli\u003eExplicit remainder estimates that support further theoretical work.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003cp\u003e\u003cstrong\u003eCons\u003c\/strong\u003e\u003c\/p\u003e\n\u003cul\u003e\n\u003cli\u003eHighly technical presentation limits accessibility to specialists rather than general readers.\u003c\/li\u003e\n\u003cli\u003eFocus on short-time convergence means long-time behavior and full equivalence with Schrdinger methods remain outside the main results.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003ch2\u003eSpecifications\u003c\/h2\u003e\n\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\u003c\/td\u003e\n\u003ctd\u003eDaisuke Fujiwara\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eMain result\u003c\/td\u003e\n\u003ctd\u003eConvergence to Schrdinger fundamental solution in short time\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eAssumptions\u003c\/td\u003e\n\u003ctd\u003ePotential sufficiently differentiable; derivatives order \u0026gt;=2 bounded\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eSemi-classical result\u003c\/td\u003e\n\u003ctd\u003eAsymptotic formula up to second term with remainder bound\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e\n\u003ch2\u003eOur Verdict\u003c\/h2\u003e\n\u003cp\u003eFor specialists who require a rigorous demonstration that Feynmandings path integral matches the Schrdinger fundamental solution in short time, this book is a focused, authoritative choice and good value for research-level study. Those needing broader or more introductory treatments should consider different texts.\u003c\/p\u003e\n\u003ch2\u003eFrequently Asked Questions\u003c\/h2\u003e\n\u003cp\u003e\u003cstrong\u003eDoes the book prove full equivalence with Schrdinger quantization?\u003c\/strong\u003e\u003cbr\u003eThe book proves convergence in short time under specified regularity conditions but notes that full equivalence between the two quantization methods is not completely established.\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eWhat regularity is required for the potential?\u003c\/strong\u003e\u003cbr\u003eThe proofs assume the potential is differentiable sufficiently many times and that derivatives of order two and higher are bounded.\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eIs the semi-classical expansion practical for applications?\u003c\/strong\u003e\u003cbr\u003eThe work provides the expansion up to the second term and a bound on the remainder, making it useful for theoretical semi-classical estimates in research contexts.\u003c\/p\u003e","brand":"Daisuke Fujiwara","offers":[{"title":"Default Title","offer_id":48243048743131,"sku":"4431568182","price":129.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0724\/1043\/1707\/files\/61ReAPJxJBL._SL1254.jpg?v=1771009014","url":"https:\/\/gearmusthave.com\/products\/rigorous-time-slicing-approach-to-feynman-path-integrals-short-term","provider":"GearMustHave","version":"1.0","type":"link"}