View Item 

Show simple item record

Foundations for relativistic quantum theory. I. Feynman’s operator calculus and the Dyson conjectures

dc.contributor.authorGill, Tepper L.en_US
dc.contributor.authorZachary, W. W.en_US
dc.date.accessioned2010-05-06T21:53:56Z
dc.date.available2010-05-06T21:53:56Z
dc.date.issued2002-01en_US
dc.identifier.citationGill, Tepper L.; Zachary, W. W. (2002). "Foundations for relativistic quantum theory. I. Feynman’s operator calculus and the Dyson conjectures." Journal of Mathematical Physics 43(1): 69-93. <http://hdl.handle.net/2027.42/70270>en_US
dc.identifier.urihttps://hdl.handle.net/2027.42/70270
dc.description.abstractIn this paper, we provide a representation theory for the Feynman operator calculus. This allows us to solve the general initial-value problem and construct the Dyson series. We show that the series is asymptotic, thus proving Dyson’s second conjecture for quantum electrodynamics. In addition, we show that the expansion may be considered exact to any finite order by producing the remainder term. This implies that every nonperturbative solution has a perturbative expansion. Using a physical analysis of information from experiment versus that implied by our models, we reformulate our theory as a sum over paths. This allows us to relate our theory to Feynman’s path integral, and to prove Dyson’s first conjecture that the divergences are in part due to a violation of Heisenberg’s uncertainly relations. © 2002 American Institute of Physics.en_US
dc.format.extent3102 bytes
dc.format.extent208528 bytes
dc.format.mimetypetext/plain
dc.format.mimetypeapplication/pdf
dc.publisherThe American Institute of Physicsen_US
dc.rights© The American Institute of Physicsen_US
dc.titleFoundations for relativistic quantum theory. I. Feynman’s operator calculus and the Dyson conjecturesen_US
dc.typeArticleen_US
dc.subject.hlbsecondlevelPhysicsen_US
dc.subject.hlbtoplevelScienceen_US
dc.description.peerreviewedPeer Revieweden_US
dc.contributor.affiliationumDepartment of Physics, University of Michigan, Ann Arbor, Michigan 48109en_US
dc.contributor.affiliationotherDepartment of Mathematics and Electrical Engineering, Howard University, Washington, DC 20059en_US
dc.contributor.affiliationotherDepartment of Electrical Engineering, Howard University, Washington, DC 20059en_US
dc.contributor.affiliationotherDepartment of Mathematics and Statistics, University of Maryland University College, College Park, Maryland 20742en_US
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/70270/2/JMAPAQ-43-1-69-1.pdf
dc.identifier.doi10.1063/1.1425080en_US
dc.identifier.sourceJournal of Mathematical Physicsen_US
dc.identifier.citedreferenceP. A. M. Dirac, Proc. R. Soc. London, Ser. A PRLAAZ114, 243 (1927).en_US
dc.identifier.citedreferenceP. A. M. Dirac, Proc. R. Soc. London, Ser. A PRLAAZ117, 610 (1928).en_US
dc.identifier.citedreferenceW. Heisenberg and W. Pauli, Z. Phys. ZEPYAA56, 1 (1929).en_US
dc.identifier.citedreferenceW. Heisenberg and W. Pauli, Z. Phys. ZEPYAA59, 168 (1930).en_US
dc.identifier.citedreferenceA. I. Miller, Early Quantum Electrodynamics (Cambridge University Press, Cambridge, 1994).en_US
dc.identifier.citedreferenceS. S. Schweber, QED and the Men Who Made It: Dyson, Feynman, Schwinger, and Tomonaga (Princeton University Press, Princeton, NJ, 1994).en_US
dc.identifier.citedreferenceJ. R. Oppenheimer, Phys. Rev. PHRVAO35, 461 (1930).en_US
dc.identifier.citedreferenceP. A. M. Dirac, Proc. R. Soc. London, Ser. A PRLAAZ167, 148 (1938).en_US
dc.identifier.citedreferenceJ. R. Oppenheimer, Rapports du 8e8e Conseil de Physique, Solvay, 1950, p. 269.en_US
dc.identifier.citedreferenceS. Tomonaga, Prog. Theor. Phys. PTPKAV1, 27 (1949).en_US
dc.identifier.citedreferenceJ. Schwinger, Phys. Rev. PHRVAO73, 416 (1948).en_US
dc.identifier.citedreferenceR. P. Feynman, Phys. Rev. PHRVAO76, 749 (1949); 76, 769 (1949).en_US
dc.identifier.citedreferenceR. P. Feynman, Phys. Rev. PHRVAO80, 440 (1950).en_US
dc.identifier.citedreferenceJ. Schwinger, Selected Papers on Quantum Electrodynamics (Dover, New York, 1958).en_US
dc.identifier.citedreferenceF. J. Dyson, Phys. Rev. PHRVAO75, 486 (1949); 75, 1736 (1949).en_US
dc.identifier.citedreferenceF. J. Dyson, Phys. Rev. PHRVAO85, 631 (1952).en_US
dc.identifier.citedreferenceR. P. Feynman, Phys. Rev. PHRVAO81, 108 (1951).en_US
dc.identifier.citedreferenceP. A. M. Dirac, in The Birth of Particle Physics, edited by L. M. Brown and L. Hodderson (Cambridge University Press, Cambridge, 1983), p. 39.en_US
dc.identifier.citedreferenceS. Sakata, Prog. Theor. Phys. PTPKAV16, 686 (1956).en_US
dc.identifier.citedreferenceJ. Schwinger, in The Birth of Particle Physics, edited by L. M. Brown and L. Hodderson (Cambridge University Press, Cambridge, 1983), p. 329.en_US
dc.identifier.citedreferenceA. S. Wightman, Phys. Rev. PHRVAO101, 860 (1956).en_US
dc.identifier.citedreferenceH. Lehmann, K. Symanzik, and W. Zimmermann, Nuovo Cimento NUCIAD1, 205 (1955).en_US
dc.identifier.citedreferenceH. Lehmann, K. Symanzik, and W. Zimmermann, Nuovo Cimento NUCIAD6, 319 (1957).en_US
dc.identifier.citedreferenceA. S. Wightman, Fortschr. Phys. FPYKA644, 143 (1996).en_US
dc.identifier.citedreferenceW. Heisenberg, Sitzungberichte der Sächsischen Academíe der Wissenschaft Math. Phys. Klasse ZZZZZZ83, 3 (1931).en_US
dc.identifier.citedreferenceR. Jost, The General Theory of Quantized Fields (American Mathematical Society, Providence, RI, 1965).en_US
dc.identifier.citedreferenceR. F. Streater and A. S. Wightman, PCT, Spin and Statistics and All That (Benjamin, New York, 1964).en_US
dc.identifier.citedreferenceN. N. Bogolubov and D. V. Shirkov, Introduction to the Theory of Quantized Fields (Interscience, London, 1958).en_US
dc.identifier.citedreferenceR. Haag, Local Quantum Physics, 2nd ed. (Springer, New York, 1996).en_US
dc.identifier.citedreferenceN. N. Bogolubov, A. A. Logunov, and I. T. Todorov, Introduction to Axiomatic Quantum Field Theory (Benjamin, New York, 1975).en_US
dc.identifier.citedreferenceD. Buchholz, hep-th/9811233 (1998).en_US
dc.identifier.citedreferenceConstructive Quantum Field Theory, edited by G. Velo and A. S. Wightman Lect. Notes Phys. 25, 331 (1974).en_US
dc.identifier.citedreferenceConstructive Quantum Field Theory II, edited by G. Velo and A. S. Wightman NATO ASI Ser., Ser. B 234, 344 (1990).en_US
dc.identifier.citedreferenceO. I. Zavialov, Renormalized Quantum Field Theory (Kluwer, Dordrecht, 1990).en_US
dc.identifier.citedreferenceJ. Glimm and A. Jaffe, Quantum Physics. A Functional Integral Point of View (Springer, New York, 1987).en_US
dc.identifier.citedreferenceB. Simon, Functional Integration and Quantum Physics (Academic, New York, 1979).en_US
dc.identifier.citedreferenceA. D. Sokal, Ann. Inst. Henri Poincare, Sect. A AHPAAO37, 13 (1982).en_US
dc.identifier.citedreferenceM. Aizenman and R. Graham, Nucl. Phys. B NUPBBO225, 261 (1983).en_US
dc.identifier.citedreferenceJ. Fröhlich, Nucl. Phys. B NUPBBO200, 281 (1982).en_US
dc.identifier.citedreferenceK. Gawedzki and A. Kupiainen, Commun. Math. Phys. CMPHAY102, 1 (1985).en_US
dc.identifier.citedreferenceG. Gallavotti, Rev. Mod. Phys. RMPHAT57, 471 (1985).en_US
dc.identifier.citedreferenceA. S. Wightman, in Renormalization Theory, edited by G. Velo and A. S. Wightman [NATO Adv. Study Inst. Ser. C NASCD623, 1 (1976)].en_US
dc.identifier.citedreferenceJ. M. Jauch and F. Rohrlich, The Theory of Photons and Electrons (Addison–Wesley, Reading, MA, 1955).en_US
dc.identifier.citedreferenceK. Hepp, Commun. Math. Phys. CMPHAY2, 301 (1966).en_US
dc.identifier.citedreferenceJ. Feldman, T. Hurd, L. Rosen, and J. Wright, QED: A Proof of Renormalizability, Springer Lecture Notes in Physics Vol. 312 (Springer, New York, 1988).en_US
dc.identifier.citedreferenceK. G. Wilson, Phys. Rev. D PRVDAQ6, 419 (1972).en_US
dc.identifier.citedreferenceJ. Lowenstein and E. Speer, Commun. Math. Phys. CMPHAY47, 4 (1976).en_US
dc.identifier.citedreferenceI. E. Segal, in Lectures in Modern Analysis and Applications II, edited by G. T. Taam [Lect. Notes Math. LNMAA2140, 30 (1970)].en_US
dc.identifier.citedreferenceW. L. Miranker and B. Weiss, SIAM Rev. SIREAD6, 104 (1966).en_US
dc.identifier.citedreferenceE. Nelson, in Functional Analysis and Related Fields, edited by F. Browder (Springer, New York, 1970).en_US
dc.identifier.citedreferenceH. Araki, Ann. Sci. Ecole Norm. Sup. ZZZZZZ6, 67 (1973).en_US
dc.identifier.citedreferenceI. Fujiwara, Prog. Theor. Phys. PTPKAV7, 433 (1952).en_US
dc.identifier.citedreferenceV. P. Maslov, Operational Methods (Mir, Moscow, 1976).en_US
dc.identifier.citedreferenceG. W. Johnson and M. L. Lapidus, Mem. Am. Math. Soc. MAMCAU62, 1 (1986).en_US
dc.identifier.citedreferenceG. W. Johnson and M. L. Lapidus, J. Funct. Anal. JFUAAW81, 74 (1988).en_US
dc.identifier.citedreferenceG. W. Johnson and M. L. Lapidus, The Feynman Integral and Feynman’s Operational Calculus (Oxford University Press, New York, 2000).en_US
dc.identifier.citedreferenceG. W. Johnson, M. L. Lapidus, and B. DeFacio, in Stochastics Processes: A Festschrift in Honour of Gopinath Kallianpur, edited by S. Cambanis, J. K. Ghosh, R. L. Karandikar, and P. K. Sen (Springer, New York, 1993).en_US
dc.identifier.citedreferenceA. Salam, Phys. Rev. ZZZZZZ84, 426 (1951).en_US
dc.identifier.citedreferenceJ. Ward, Proc. Phys. Soc. London, Sec. A PPSAAMA64, 54 (1951).en_US
dc.identifier.citedreferenceR. L. Mills and C. N. Yang, Suppl. Prog. Theor. Phys. PTPSAL37, 507 (1966).en_US
dc.identifier.citedreferenceK. Hepp, Théorie de la Rénormalization, Springer Lecture Notes in Physics Vol. 2 (Springer, New York, 1969).en_US
dc.identifier.citedreferenceS. Weinberg, Phys. Rev. PHRVAO118, 838 (1960).en_US
dc.identifier.citedreferenceT. L. Gill, Trans. Am. Math. Soc. TAMTAM266, 161 (1981).en_US
dc.identifier.citedreferenceT. L. Gill, Trans. Am. Math. Soc. TAMTAM279, 617 (1983).en_US
dc.identifier.citedreferenceT. L. Gill and W. W. Zachary, J. Math. Phys. JMAPAQ28, 1459 (1987).en_US
dc.identifier.citedreferenceR. Henstock, Theory of Integration (Butterworth, London, 1963).en_US
dc.identifier.citedreferenceJ. Kurzweil, Czech. Math. J. ZZZZZZ7, 418 (1957).en_US
dc.identifier.citedreferenceR. Henstock, Proc. London Math. Soc. PLMTAL27, 317 (1973).en_US
dc.identifier.citedreferenceP. Muldowney, A General Theory of Integration in Function Spaces, Pitman Research Notes in Mathematics (Wiley, New York, 1987).en_US
dc.identifier.citedreferenceJ. A. Goldstein, Semigroups of Linear Operators and Applications (Oxford University Press, New York, 1985).en_US
dc.identifier.citedreferenceA. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Applied Mathematical Science Vol. 44 (Springer, New York, 1983).en_US
dc.identifier.citedreferenceJ. von Neumann, Compos. Math. CMPMAF6, 1 (1938).en_US
dc.identifier.citedreferenceT. L. Gill, J. Funct. Anal. JFUAAW30, 17 (1978).en_US
dc.identifier.citedreferenceE. Hille, and R. S. Phillips, Functional Analysis and Semigroups, American Mathematical Society Colloquium Publication No. 31 (American Mathematical Society, Providence, RI, 1957).en_US
dc.identifier.citedreferenceC. A. Hurst, Proc. Cambridge Philos. Soc. PCPSA448, 625 (1952).en_US
dc.identifier.citedreferenceW. Thirring, Helv. Phys. Acta HPACAK26, 33 (1953).en_US
dc.identifier.citedreferenceA. Petermann, Helv. Phys. Acta HPACAK26, 291 (1953).en_US
dc.identifier.citedreferenceA. Jaffe, Commun. Math. Phys. CMPHAY1, 127 (1965).en_US
dc.identifier.citedreferenceF. Dyson, Selected Papers of Freeman Dyson with Commentary (American Mathematical Society, Providence, RI, 1996).en_US
dc.identifier.citedreferenceS. S. Schweber, An Introduction to Relativistic Quantum Field Theory (Harper & Row, New York, 1961).en_US
dc.identifier.citedreferenceA. S. Wightman, in The Lesson of Quantum Theory, edited by J. de Boer, E. Dal, and O. Ulfbeck (Elsevier, Amsterdam, 1986), p. 201.en_US
dc.identifier.citedreferenceJ. Zinn-Justin, Quantum Field Theory and Critical Phenomena, 2nd ed. (Clarendon, Oxford, 1993).en_US
dc.identifier.citedreferenceJ. D. Dollard and C. N. Friedman, Product Integration with Applications to Differential Equations, Encyclopedia of Mathematics Vol. 10 (Addison–Wesley, Reading, MA 1979).en_US
dc.identifier.citedreferenceT. Tang and Z. Li, Lett. Math. Phys. LMPHDY43, 55 (1998).en_US
dc.identifier.citedreferenceK.-J. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Graduate Texts in Mathematics (Springer, New York, 2000).en_US
dc.identifier.citedreferenceA. Einstein, Ann. Phys. (Leipzig) ANPYA217, 549 (1905).en_US
dc.identifier.citedreferenceN. Wiener, A. Siegel, B. Rankin, and W. T. Martin, Differential Space, Quantum Systems, and Prediction (MIT, Cambridge, MA, 1966).en_US
dc.identifier.citedreferenceL. S. Ornstein and G. E. Uhlenbeck, Phys. Rev. PHRVAO36, 1103 (1930).en_US
dc.identifier.citedreferenceJ. L. Doob, Ann. Math. ANMAAH43, 62 (1954).en_US
dc.identifier.citedreferenceS. M. Ross, Introduction to Probability Models, 4th ed. (Academic, New York, 1989).en_US
dc.identifier.citedreferenceR. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw–Hill, New York, 1965).en_US
dc.identifier.citedreferenceN. F. Mott and H. S. Massey, Theory of Atomic Collisions (Clarendon, Oxford, 1965).en_US
dc.identifier.citedreferenceH. D. Dahmen, B. Scholz, and F. Steiner, Nucl. Phys. B NUPBBO202, 365 (1982).en_US
dc.identifier.citedreferenceW. Heisenberg, Ann. Phys. (Leipzig) ANPYA232, 20 (1938).en_US
dc.identifier.citedreferenceT. D. Lee, in The Lesson of Quantum Theory, edited by J. de Boer, E. Dal, and O. Ulfbeck (Elsevier, Amsterdam, 1986), p. 181.en_US
dc.owningcollnamePhysics, Department of


Files in this item

Name:
JMAPAQ-43-1-69-1.pdf
Size:
203.6KB
Format:
PDF
View/Open

Show simple item record

Remediation of Harmful Language

The University of Michigan Library aims to describe library materials in a way that respects the people and communities who create, use, and are represented in our collections. Report harmful or offensive language in catalog records, finding aids, or elsewhere in our collections anonymously through our metadata feedback form. More information at Remediation of Harmful Language.

Accessibility

If you are unable to use this file in its current format, please select the Contact Us link and we can modify it to make it more accessible to you.