Non-local Quantal Noether Identities and Their Applications

LI Zi-Ping

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2024年10月30日

Chinese Physics C> 2002, Vol. 26> Issue(12) : 1214-1222

Non-local Quantal Noether Identities and Their Applications

LI Zi-Ping ^,

College of Applied Science,Beijing Polytechnic University,Beijing 100022,China

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Abstract：
Based on the phase-space generating functional for a system with a singular higher-order Lagrangian,the quantal canonical Noether identities under the local and non-local transformation in phase space for such system have been derived. For a gauge-invariant system with a higher-order Lagrangian,the quantal Noether identities under the local and non-local transformation in configuration space have also been derived. It has been pointed out that in certain cases the quantal Noether identities may be converted to the conservation laws at the quantum level. This algorithm to derive the quantal conservation laws is significantly different from the first quantal Noether theorem. The applications to the non-Abelian CS theories with higher-order derivatives are given. The conserved quantities at the quantum level for some local and non-local transformation are found respectively.

References

[1]

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LI Zi-Ping. Non-local Quantal Noether Identities and Their Applications[J]. Chinese Physics C, 2002, 26(12): 1214-1222.

LI Zi-Ping. Non-local Quantal Noether Identities and Their Applications[J]. Chinese Physics C, 2002, 26(12): 1214-1222. shu

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Received: 2002-01-29
Revised: 1900-01-01

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Non-local Quantal Noether Identities and Their Applications

LI Zi-Ping ^,

Corresponding author: LI Zi-Ping,

College of Applied Science,Beijing Polytechnic University,Beijing 100022,China

Received Date: 2002-01-29
Accepted Date: 1900-01-01
Available Online: 2002-12-05

Abstract: Based on the phase-space generating functional for a system with a singular higher-order Lagrangian,the quantal canonical Noether identities under the local and non-local transformation in phase space for such system have been derived. For a gauge-invariant system with a higher-order Lagrangian,the quantal Noether identities under the local and non-local transformation in configuration space have also been derived. It has been pointed out that in certain cases the quantal Noether identities may be converted to the conservation laws at the quantum level. This algorithm to derive the quantal conservation laws is significantly different from the first quantal Noether theorem. The applications to the non-Abelian CS theories with higher-order derivatives are given. The conserved quantities at the quantum level for some local and non-local transformation are found respectively.