Summary
The canonical and functional integral quantization of Yang-Mills theory is discussed. The gauge-fixing «weak» conditionsA 0a ≈0,A 3a ≈0 over phase space are found to be very convenient for any gauge group and in the presence of interactions. These conditions fix the gauge for arbitrary strong field and we obtain a description of Yang-Mills field in terms of physical degress of freedom only.
Riassunto
Si discute la quantizzazione canonica e dell’integrale funzionale della teoria di Yang e Mills. Si trova che le condizioni «deboli»A 0a ≈0,A 3a ≈0 che fissano la gauge sullo spazio delle fasi sono molto adatte per ogni gruppo di gauge e in presenza di interazioni. Queste condizioni fissano la gauge per campi forti arbitrari e otteniamo una descrizione dei campi di Yang e Mills in termini di gradi fisici di libertà solamente.
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P. A. M. Dirac:Lectures in Quantum Mechanics, Belfer Graduate School of Science, Yeshiva University, (New York, N. Y., 1964).
R. P. Feynman:Rev. Mod. Phys.,20, 367 (1948);Phys. Rev.,84, 108 (1951);80, 440 (1950);R. P. Feynman andA. R. Hibbs:Quantum Mechanics and Path Integral (New York, N. Y., 1965).
L. D. Faddeev andV. N. Popov:Phys. Lett. B,25, 29 (1967);L. D. Faddeev:Teor. Mat. Fiz.,1, 3 (1969); inMethods in Field Theory (Les Houches Lectures) (Amsterdam, 1976).
V. N. Gribov: preprint LI.yp-367, Leningrad (1977).
M. B. Halpern andJ. Koplik: preprint LBL-6189, Berkeley (1977);V. N. Popov: preprint CERN Ref. TH-2424 (1977);H. Abarbanell andJ. Bartels: preprint FERMILAB-PvB 77/104-Thy, Batavia;M. Daniel andG. M. Vialett: preprint PARLPTHE 78/4, Paris (1978).
J. Goldstone andR. Jackiw: preprint M.I.T., C.P.T. 696 (1978).
L. A. Faddeev, A. G. Izergin, V. E. Korepin andM. A. Semenov-Tian-Shansky: LOMI preprint E-4-78, Leningrad (1978);Teor. Mat. Fiz.,38, 3 (1979).
A. Hanson, T. Regge andC. Teitelboim:Constrained Hamiltonian System, Accademia Nazionale dei Lincei (Roma, 1976).
R. N. Mohapatra:Phys. Rev. D,4, 2215 (1971);R. Arnowitt andS. I. Fickler:Phys. Rev.,127, 1821 (1962).
P. P. Srivastava:Rev. Bras. Fis.,10, No. 8 (1980). See alsoCanonical and functional integral quantization of Yang-Mills theory, C.B.P.F. preprint A0024/79 (July 1979).
B. W. Lee: inMethods in Field Theory, edited byR. Balian andJ. Zinn-Justin (Amsterdam, 1976).
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Srivastava, P.P. On canonical and functional integral quantization of Yang-Mills theory. Nuov Cim A 64, 259–268 (1981). https://doi.org/10.1007/BF02812372
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DOI: https://doi.org/10.1007/BF02812372