PATH INTEGRAL OF A SYMMETRY SYSTEM WITH CONSTRAINTS

MA Qian-Cheng; RUAN Tu-Nan

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2024年10月30日

Chinese Physics C> 1985, Vol. 9> Issue(2) : 168-173

PATH INTEGRAL OF A SYMMETRY SYSTEM WITH CONSTRAINTS

MA Qian-Cheng ^, ,
RUAN Tu-Nan

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Abstract：
When constraints of a system form a function group, the path integral quantum amplitude can exactly be beduced without adding the restrictions {χ_i,χ_j}=0 which are imposed on the gauge conditions or the "weak" concept. It can be shown that the contraints produced by symmetry just form a function group. Most of the interesting systems in physics are such symmetrical systems.

References

[1]

P. A. M. Dirac, Can. J. Math., 2(1950) 129.[2] L. D. Faddeev, Theot. Mat. Fiz., 1(1969), 3. (Theot. Math. Phys. USSR l(1969)1.).[3] P. Senjanovic, Ann. Phys., 100(1976) 227.[4] S. Kaptanoglu Phys. Lett., 98B (1981) 77.[5] C. Caratheodory, Variationsrechnung und die Partidle Differential Gleichungen von Erster Ord-nung, (Teubner, Berlin, 1935). A. R. Forshty, Theory of Differential Equations, Vol. 5 4 , N. Y.1959.[6] P. G. Bergmann, Phys. Rev., 75(1949), 680.P. G. Bergnann and J. H. M. Brunings, Rev. Modern Phys., 21(1949) 480.J. L. Anderson and P. G. Bergmann, Phys. Rev., 83(1951) 1018.

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MA Qian-Cheng and RUAN Tu-Nan. PATH INTEGRAL OF A SYMMETRY SYSTEM WITH CONSTRAINTS[J]. Chinese Physics C, 1985, 9(2): 168-173.

MA Qian-Cheng and RUAN Tu-Nan. PATH INTEGRAL OF A SYMMETRY SYSTEM WITH CONSTRAINTS[J]. Chinese Physics C, 1985, 9(2): 168-173. shu

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Received: 1900-01-01
Revised: 1900-01-01

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沈阳化工大学材料科学与工程学院沈阳 110142

PATH INTEGRAL OF A SYMMETRY SYSTEM WITH CONSTRAINTS

MA Qian-Cheng ^,
RUAN Tu-Nan

Corresponding author: MA Qian-Cheng,

Received Date: 1900-01-01
Accepted Date: 1900-01-01
Available Online: 1985-04-05

Abstract: When constraints of a system form a function group, the path integral quantum amplitude can exactly be beduced without adding the restrictions {χ_i,χ_j}=0 which are imposed on the gauge conditions or the "weak" concept. It can be shown that the contraints produced by symmetry just form a function group. Most of the interesting systems in physics are such symmetrical systems.