A REVIEW OF SYMMETRIES, CONSERVED QUANTITIES AND INVARIANCE PROPERTIES
DOI:
https://doi.org/10.53808/KUS.2006.7.1.0546-PSKeywords:
Physical laws, Lagrangian systems, Neother constant, manifolds, Lie GroupsAbstract
Symmetries, conserved quantities and invariance properties are studied. In the case of Lagrangian systems the connection between conserved quantities and dynamical symmetries is not too direct, for instance, there always exists an infinite number of linearly independent dynamical symmetries which have no associated Neother constant of the motion but for general systems dynamical symmetries always possesses associated conserved quantities which are invariants of the symmetry group itself. Now a days symmetry properties are crucial for renormalizability of a theory under consideration which helps in characterizing the above mentioned features of the micro world and is a tool for exploration of further possibility. In this study we have made an attempt to discuss the relationship among symmetry, conserved quantity and invariance property with their applications.
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References
Anderson, R.L.; Davison, S.M. and Wulfman, C.E. 1976. The Lie group of Newton's and Lagrange's equations for the harmonic oscillator. Journal of Physics A: Mathematical General, 9: 507-518.
Chohen, A. 1931. An Introduction to the Lie Theory of One-Parameter Groups. Stechert, New York.
Cracknell, A.P. 1968. Applied Group Theory. Pergamon Press Ltd., New York.
Emmerson, J.M. 1972. Symmetry Principle in Particle Physics. Oxford University Press, London.
Gibson, W.M. and Pollard, B.R.1980. Symmetry Principle in Elementary Particle Physics. Cambridge University Press, London.
Goldstein, H. 1950. Classical Mechanics. Addition-Wesley Publisher Co. Inc., London.
Greiner, W. and Müller, B. 1994. Quantum Mechanics – Symmetries. 2nd edn., Springer-Verlag, New York.
Inui, T.; Tanbe, Y. and Onodera, Y. 1996. Group Theory and its Applications in Physics. 2nd printing, Springer-Verlag, New York.
Jablan, S.V. 1995. Theory of Symmetry and Ornament. Mathematical Institute, Belgrade, Yugoslavia.
Katz, A. 1965. Classical Mechanics, Quantum Mechanics, Field Theory. Academic Press, New York.
Lie, S. 1967. Differentialgleichungen. Chelsea, New York.
Ludwig, W. and Falter, C. 1996. Symmetries in Physics. 2nd edn., Springer-Verlag, New York.
Lutzky, M. 1978. Noether's theorem and the time-dependent harmonic oscillator. Journal of Physics A: Mathematical General, 68: 3-4.
Neother, E. 1918a. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, pp. 200-235 (in German).
Neother, E. 1918b. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, pp. 235-257 (in German).
Ovsjannikov, L.V. 1969. Gruppovye svoystva differentsialny uravneni (Novosobirsk). Group Properties of Differential Equations. Translated by G.B. Vancouver, University of British Columbia (in French).
Rosen, J. 1981. Resource letter SP-2, symmetry and group theory in physics. American Journal of Physics, 49(4): 304-319.
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