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1.
SYMMETRIES AND CONSERVED QUANTITIES FOR SYSTEMS OF GENERALIZED CLASSICAL MECHANICS 总被引:4,自引:0,他引:4 下载免费PDF全文
In this paper, the symmetries and the conserved quantities for systems of generalized classical mechanics are studied. First, the generalized Noether's theorem and the generalized Noether's inverse theorem of the systems are given, which are based upon the invariant properties of the canonical action with respect to the action of the infinitesimal transformation of r-parameter finite group of transformation; second, the Lie symmetries and conserved quantities of the systems are studied in accordance with the Lie's theory of the invariance of differential equations under the transformation of infinitesimal groups; and finally, the inner connection between the two kinds of symmetries of systems is discussed. 相似文献
2.
本文导出非不变性作用量系统的广义Noether恒等式并给出它的应用。
关键词: 相似文献
3.
The quantum theory of free fields is used with Noether's theorem to discuss the polarization features of vector and spinor fields in the QHGRE (generalized de Broglie group) from the viewpoint of local isomorphism of the QHGRE for the product of two ordinary groups (the groups of x
, t deformations and rotations). Estimates are made of the contributions to the polarization tensors for the corresponding fields. In both cases the spin tensors are induced by space and time generators of the generalized de Broglie group, and the rotational component of the QHGRE is responsible for the spin properties.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, Vol. 12, No. 1, pp. 32–36, January, 1969.We are indebted to D. D. Ivanenko for discussion of these topics. 相似文献
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6.
L. Martinez Alonso 《Letters in Mathematical Physics》1979,3(5):419-424
For a wide class of lagrangian systems we show rigorously that the conventional formulation of Noether's theorem provides a bijective map from the set of equivalence classes of Noether's symmetries onto the set of equivalence classes of conserved currents. We further discuss if Noether's theorem is generalized in a significant way by several formulations proposed in this decade.Partially supported by the Junta de Energia Nuclear, Madrid. 相似文献
7.
本文导出场论中用奇异拉氏量描述的系统正则形式的广义Noether第一定理(GNFT),导出无限连续群下变更性系统正则形式的广义Noether恒等式(GNI),讨论了它们在Dirac约束理论中的应用。给出一个新的反倒,说明Dirac猜想失效,指出某些变更性系统也具有Dirac约束,讨论了GNI在色动力学中的应用。
关键词: 相似文献
8.
N. Nissani 《International Journal of Theoretical Physics》1985,24(7):675-683
Noether's theorem is applied to Hilbert's Lagrangian written as a functional of spinorial variables. The associatedSL(2,C) conserved current is obtained, and its expression for the Tolman metric is given explicitly. 相似文献
9.
M. W. Evans 《Foundations of Physics Letters》1995,8(1):63-71
It is shown that the longitudinal, magnetic flux density,B
(3)
, of vacuum electromagnetic radiation can be accommodated rigorously within Noether's theorem, which relates fundamental spacetime symmetries to fundamental conservation laws. This demonstration linksB
(3)
to the canonical energy-momentum tensorT
µv that appears in Einstein's field equations of general relativity. Thus,B
(3)
provides a link between electromagnetism and gravitation which might eventually lead to an unified understanding of field theory. 相似文献
10.
Generalized Noether theorems in canonical formalism for field theories and their applications 总被引:1,自引:0,他引:1
Zi-ping Li 《International Journal of Theoretical Physics》1993,32(1):201-215
A generalization of Noether's first theorem in phase space for an invariant system with a singular Lagrangian in field theories is derived and a generalization of Noether's second theorem in phase space for a noninvariant system in field theories is deduced. A counterexample is given to show that Dirac's conjecture fails. Some preliminary applications of the generalized Noether second theorem to the gauge field theories are discussed. It is pointed out that for certain systems with a noninvariant Lagrangian in canonical variables for field theories there is also a Dirac constraint. Along the trajectory of motion for a gauge-invariant system some supplementary relations of canonical variables and Lagrange multipliers connected with secondary first-class constraints are obtained. 相似文献
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12.
A. E. Bernardini 《International Journal of Theoretical Physics》2008,47(4):971-976
We propose a generalized way to formally obtain the gauge invariance of the kinetic part of a field Lagrangian over which
a gauge transformation ruled by an SU(n)
U
⊗
SU(m)
V
coupling symmetry is applied. As an illustrative example, we employ such a formal construction for reproducing the standard
model Lagrangian. This generalized formulation is supposed to contribute for initiating the study of gauge transformation
applied to generalized SU(n)
U
⊗
SU(m)
V
symmetries as well as for complementing an introductory study of the standard model of elementary particles. 相似文献
13.
T. Kawai 《Foundations of Physics》1975,5(1):143-158
Schwinger's action principle is formulated for the quantum system which corresponds to the classical system described by the LagrangianL
c(
, x)=(M/2)gij(x)
i
j–v(x). It is sufficient for the purpose of deriving the laws of quantum mechanics to consider onlyc-number variations of coordinates and time. The Euler-Lagrange equation, the canonical commutation relations, and the canonical equations of motion are derived from this principle in a consistent manner. Further, it is shown that an arbitrary point transformation leaves the forms of the fundamental equations invariant. The judicious choice of the quantal Lagrangian is essential in our formulation. A quantum mechanical analog of Noether's theorem, which relates the invariance of the quantal action with a conservation law, is established. The ambiguities in the quantal Lagrangian are also discussed and it is pointed out that the requirement of invariance is not sufficient to determine uniquely the quantal Lagrangian and the Hamiltonian. 相似文献
14.
A theorem which forbids the existence of certain nontrivial static finite-energy classical solutions to Yang-Mills-Higgs equations in dependence on the spatial dimension is generalized to include fields with nonvanishing electric-like componentsF
0j
.Dedicated to 30th anniversary of the Joint Institute for Nuclear Research. 相似文献
15.
研究事件空间中Birkhoff系统的Noether对称性与Noether守恒量.首先,建立了事件空间中Birkhoff系统的参数方程;其次,基于Pfaff作用量在无限小变换下的不变性,给出了事件空间中Birkhoff系统的Noether定理及其逆定理;最后,举例说明结果的应用.
关键词:
事件空间
Birkhoff系统
Pfaff作用量
Noether对称性 相似文献
16.
C. D'Antoni S. Doplicher K. Fredenhagen R. Longo 《Communications in Mathematical Physics》1987,110(2):325-348
The local generators of symmetry transformations which have recently been constructed from a quantum field theoretical version of Noether's theorem are shown to converge to the global ones as the volume tends to the whole space. The proof relies on the continuous volume dependence of the universal localizing maps which are associated to the local splitW*-inclusions.Research supported by Ministero della Pubblica Istruzione and CNR-GNAFA 相似文献
17.
本文从约束系统的作用量和约束方程的普遍变换性质出发,得到了约束系统的推广Killing方程组,此方程组的解所生成的变换可产生经典Noether定理的守恒量。讨论了连续系统的时空变换和内禀变换,在变换保持约束方程不变时,指出此变换能导致守恒流的充要条件,给出了对不可压缩连续介质的应用,讨论了对广义力学和经典力学的应用,并给出了推广Killing方程组解的某些实例,将Poincare不变量推广到了受约束广义力学系统。
关键词: 相似文献
18.
从系统的作用量在普遍的定域和非定域变换下的性质出发,导出了含非定城变换的广义Noether恒等式.将其用于高阶微商杨—Mills场论,求出了有别于BRS荷的新PBRS守恒荷和非定域变换下的新守恒荷. 相似文献
19.
Joe Rosen 《International Journal of Theoretical Physics》1971,4(4):287-294
The role of invariance considerations in conventional formulations of Noether's theorem in classical field theory is investigated and found weaker than is usually supposed. It is shown how nonfulfilment of the conventional assumptions going into Noether's theorem brings about nonconservation. 相似文献
20.
H. Steudel 《Annalen der Physik》1975,487(6):459-465
Derivation of a Continuous Set of Conservation Laws for the Modified Korteweg-de Vries Equation by Noether's Theorem A method developed recently to derive a continuous set of conservation laws from extended Bäcklund transformations by means of Noether's theorem is applied to the modified Korteweg-de Vries (m. KdV) equation that describes Alfvén waves in a plasma. The corresponding conserved currents are equivalent to those found by WADATI , SANUKI and KONNO . It is shown that the extended Bäcklund transformation B?α for the m. KdV equation, which coincides with that for the sine-Gordon equation, by MIURA'S transformation becomes the extended Bäcklund transformation βx for the Korteweg-de Vries equation where x = 1/2α. 相似文献