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Path integral formulation
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== Bibliography == {{divcol}} * {{cite book |last=Ahmad |first=Ishfaq |author-link=Ishfaq Ahmad |title=Mathematical Integrals in Quantum Nature |series=The Nucleus |year=1971 |pages=189–209}} * {{cite book |last1=Albeverio |first1=S. |last2=Hoegh-Krohn |first2=R. |last3=Mazzucchi |first3=S |name-list-style=amp |title=Mathematical Theory of Feynman Path Integrals |series=Lecture Notes in Mathematics 523 |publisher=Springer-Verlag |year=2008 |isbn=9783540769569}} * {{cite journal |first1=A. O. |last1=Caldeira |author-link1=Amir Caldeira |first2=A. J. |last2=Leggett |author-link2=Anthony James Leggett |title=Quantum tunnelling in a dissipative system |journal=Annals of Physics |volume=149 |year=1983 |issue=2 |pages=374–456 |doi=10.1016/0003-4916(83)90202-6 |bibcode=1983AnPhy.149..374C}} * {{cite journal |last1=Cartier |first1=P. C. |author-link=Pierre Cartier (mathematician) |last2=DeWitt-Morette |first2=Cécile |title=A new perspective on Functional Integration |journal=Journal of Mathematical Physics |volume=36 |year=1995 |issue=5 |pages=2137–2340 |doi=10.1063/1.531039 |arxiv=funct-an/9602005 |bibcode=1995JMP....36.2237C |s2cid=119581543}} * {{cite book |title=Path Integrals in Physics Volume 1: Stochastic Process & Quantum Mechanics |chapter-url=https://books.google.com/books?id=-XDP-8mrmQYC&pg=PA1 |chapter=Introduction |page=1ff |isbn=978-0-7503-0801-4 |year=2001 |publisher=Taylor & Francis |first1=M. |last1=Chaichian |first2=A. P. |last2=Demichev}} * {{cite journal |author-link=Cécile DeWitt-Morette |last=DeWitt-Morette |first=C. |title=Feynman's path integral: Definition without limiting procedure |journal=Communications in Mathematical Physics |volume=28 |issue=1 |year=1972 |pages=47–67 |mr=0309456 |doi=10.1007/BF02099371 |bibcode=1972CMaPh..28...47D |s2cid=119669964}} * {{cite journal |last=Dirac |first=Paul A. M. |author-link=Paul Dirac |year=1933 |title=The Lagrangian in Quantum Mechanics |journal=Physikalische Zeitschrift der Sowjetunion |volume=3 |pages=64–72 |url=http://www.hep.anl.gov/czachos/soysoy/Dirac33.pdf}} * {{cite journal |first1=İ. H. |last1=Duru |author-link1=İsmail Hakkı Duru |first2=Hagen |last2=Kleinert |author-link2=Hagen Kleinert |title=Solution of the path integral for the H-atom |year=1979 |journal=Physics Letters |volume=84B |issue=2 |pages=185–188 |url=http://www.physik.fu-berlin.de/~kleinert/kleiner_re65/65.pdf |access-date=2007-11-25 |bibcode=1979PhLB...84..185D |doi=10.1016/0370-2693(79)90280-6}} * {{cite web |last=Etingof |first=P. |author-link=Pavel Etingof |title=Geometry and Quantum Field Theory |publisher=MIT OpenCourseWare |year=2002 |url=http://ocw.mit.edu/courses/mathematics/18-238-geometry-and-quantum-field-theory-fall-2002/index.htm}} <small>This course, designed for mathematicians, is a rigorous introduction to perturbative quantum field theory, using the language of functional integrals.</small> * {{cite book |last=Feynman |first=R. P. |author-link=Richard Feynman |editor-last=Brown |editor-first=L. M. |title=Feynman's Thesis — A New Approach to Quantum Theory |year=2005 |orig-year=1942/1948 |publisher=World Scientific |doi=10.1142/5852 |bibcode=2005ftna.book.....B |url=https://cds.cern.ch/record/910611 |isbn=978-981-256-366-8}} <small>The 1942 thesis. Also includes Dirac's 1933 paper and Feynman's 1948 publication.</small> * {{cite journal |last=Feynman |first=R. P. |title=Space-Time Approach to Non-Relativistic Quantum Mechanics |journal=Reviews of Modern Physics |volume=20 |issue=2 |pages=367–387 |year=1948 |doi=10.1103/RevModPhys.20.367 |bibcode=1948RvMP...20..367F |url=https://authors.library.caltech.edu/47756/1/FEYrmp48.pdf}} * {{cite book |last1=Feynman |first1=R. P. |last2=Hibbs |first2=A. R. |year=1965 |title=Quantum Mechanics and Path Integrals |place=New York |publisher=McGraw-Hill |isbn=978-0-07-020650-2 |url-access=registration |url=https://archive.org/details/quantummechanics0000feyn }} <small>The historical reference written by the inventor of the path integral formulation himself and one of his students.</small> * {{cite book |last1=Feynman |first1=R. P. |last2=Hibbs |first2=A. R. |author-link2=Albert Hibbs |last3=Styer |first3=D. F. |author-link3=Daniel F. Styer |title=Quantum Mechanics and Path Integrals |year=2010 |publisher=Dover Publications |location=Mineola, NY |isbn=978-0-486-47722-0 |pages=29–31}} * {{cite book |contribution=Most of the Good Stuff |title=Memories Of Richard Feynman |editor1-first=Laurie M. |editor1-last=Brown |editor2-first=John S. |editor2-last=Rigden |publisher=American Institute of Physics |first=Murray |last=Gell-Mann |author-link=Murray Gell-Mann |isbn=978-0883188705 |year=1993}} * {{cite book |last1=Glimm |first1=J. |last2=Jaffe |first2=A. |name-list-style=amp |title=Quantum Physics: A Functional Integral Point of View |url=https://archive.org/details/quantumphysicsfu0000glim |url-access=registration |place=New York |publisher=Springer-Verlag |year=1981 |isbn=978-0-387-90562-4}} * {{cite book |last1=Grosche |first1= Christian |last2=Steiner |first2= Frank |name-list-style=amp |year=1998 |title=Handbook of Feynman Path Integrals |series=Springer Tracts in Modern Physics 145 |publisher=Springer-Verlag |isbn=978-3-540-57135-3}} * {{cite arXiv |last=Grosche |first=Christian |title=An Introduction into the Feynman Path Integral |year=1992 |eprint=hep-th/9302097}} * {{cite book |last=Hall |first=Brian C. |year=2013 |title=Quantum Theory for Mathematicians |series=Graduate Texts in Mathematics |volume=267 |publisher=Springer |isbn=978-1-4614-7115-8 |doi=10.1007/978-1-4614-7116-5 |bibcode=2013qtm..book.....H |s2cid=117837329 }} * {{cite book |last1=Inomata |first1= Akira |last2= Kuratsuji |first2= Hiroshi |last3= Gerry |first3= Christopher |title=Path Integrals and Coherent States of SU(2) and SU(1,1) |place=Singapore |publisher=World Scientific |year=1992 |isbn=978-981-02-0656-7}} * {{cite book |editor-last1=Janke |editor-first1=W. |editor-last2=Pelster |editor-first2=Axel |title=Path Integrals--New Trends And Perspectives |year=2008 |series=Proceedings Of The 9Th International Conference |publisher=World Scientific Publishing |isbn=978-981-283-726-4}} * {{cite book |first1=Gerald W. |last1=Johnson |first2=Michel L. |last2= Lapidus |title=The Feynman Integral and Feynman's Operational Calculus |series=Oxford Mathematical Monographs |publisher=Oxford University Press |year=2002 |isbn=978-0-19-851572-2}} * {{cite book |author-link=John R. Klauder |last=Klauder |first=John R. |title=A Modern Approach to Functional Integration |place=New York |publisher=Birkhäuser |year=2010 |isbn=978-0-8176-4790-2}} * {{cite book |author-link=Hagen Kleinert |last=Kleinert |first=Hagen |year=2004 |title=Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets |edition=4th |place=Singapore |publisher=World Scientific |isbn=978-981-238-107-1 |url=http://www.physik.fu-berlin.de/~kleinert/b5}} * {{cite arXiv |last=MacKenzie |first=Richard |year=2000 |title=Path Integral Methods and Applications |eprint=quant-ph/0004090}} * {{cite book |last= Mazzucchi |first= S. |title=Mathematical Feynman path integrals and their applications |publisher=World Scientific |year=2009 |isbn=978-981-283-690-8}} * {{cite book |first=Harald J. W. |last=Müller-Kirsten |year=2012 |title=Introduction to Quantum Mechanics: Schrödinger Equation and Path Integral |edition=2nd |place=Singapore |publisher=World Scientific}} * {{cite book |last=Rivers |first= R. J. |title=Path Integrals Methods in Quantum Field Theory |publisher=Cambridge University Press |year=1987 |isbn=978-0-521-25979-8}} * {{cite book |last=Ryder |first= Lewis H. |title=Quantum Field Theory |url=https://archive.org/details/quantumfieldtheo0000ryde |url-access=registration |publisher=Cambridge University Press |year=1985 |isbn=978-0-521-33859-2}} Highly readable textbook; introduction to relativistic QFT for particle physics. * {{cite book |last=Schulman |first= L S. |year=1981 |title=Techniques & Applications of Path Integration |place=New York |publisher=John Wiley & Sons |isbn=978-0-486-44528-1}} * {{cite book |author-link=Barry Simon |last=Simon |first=B. |title=Functional Integration and Quantum Physics |place=New York |publisher=Academic Press |year=1979 |isbn=978-0-8218-6941-3}} * {{cite journal |first1=Sukanya |last1=Sinha |first2=Rafael D. |last2=Sorkin |title=A Sum-over-histories Account of an EPR(B) Experiment |journal=Foundations of Physics Letters |volume=4 |issue=4 |pages=303–335 |year=1991 |doi=10.1007/BF00665892 |url=https://www.perimeterinstitute.ca/personal/rsorkin/some.papers/63.eprb.pdf |bibcode=1991FoPhL...4..303S |s2cid=121370426 }} * {{cite book |last=Tomé |first=W. A. |author-link= Wolfgang A. Tomé |year=1998 |title=Path Integrals on Group Manifolds |place=Singapore |publisher=World Scientific |isbn=978-981-02-3355-6}} Discusses the definition of Path Integrals for systems whose kinematical variables are the generators of a real separable, connected Lie group with irreducible, square integrable representations. * {{cite journal |last=Van Vleck |first=J. H. |author-link=John Hasbrouck Van Vleck |title=The correspondence principle in the statistical interpretation of quantum mechanics |journal=Proceedings of the National Academy of Sciences of the United States of America |volume=14 |issue=2 |pages=178–188 |year=1928 |doi=10.1073/pnas.14.2.178 |pmid=16577107 |pmc=1085402 |bibcode=1928PNAS...14..178V |doi-access=free}} * {{citation |last=Weinberg |first=S. |year=2002 |orig-year=1995 |title=Foundations |series=The Quantum Theory of Fields |volume=1 |isbn=978-0-521-55001-7 |author-link=Steven Weinberg |location=Cambridge |publisher=[[Cambridge University Press]] |url-access=registration |url=https://archive.org/details/quantumtheoryoff00stev}} * {{cite book |last=Zee |first=A. |author-link=Anthony Zee |title=Quantum Field Theory in a Nutshell |edition=Second |publisher=Princeton University Press |isbn=978-0-691-14034-6 |date=2010-02-21 |url-access=registration |url=https://archive.org/details/isbn_9780691140346 }} A great introduction to Path Integrals (Chapter 1) and QFT in general. * {{cite book |last=Zinn Justin |first= J. |author-link=Jean Zinn-Justin |year=2004 |title=Path Integrals in Quantum Mechanics |publisher=Oxford University Press |isbn=978-0-19-856674-8}} * {{cite book |last=Deshmukh |first= P. C. |author-link=Pranawachandra Deshmukh |year=2023 |title=Quantum Mechanics Formalism, Methodologies, and Applications |publisher=Cambridge University Press |isbn=978-1316512258}} {{divcol end}}
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