By Andrew Hanson, Tuilio Regge, Claudio Teitelboim
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Extra resources for Constrained Hamiltonian Systems
I 2) becomes the usual equation v == w Xx. If we now take the 7-deri vati ve of Eq. (3. I), \\"e discover the generalized angular velocity which has SIX independent components and reduces to (Jij == u/i j\'P'v is a pure rotation. Let us also define an angular change by oOp·v == (3. J. J. \;vhen ~(f[l·. LV ( ai ~ or <:Pi, ~ ai ) ~ a~i, or Compatibility \vith Eq. [3 g vc< . Using Eqs. (3. 18) and (3. 19), one can sho\v that (3. 24). Equation (3. ie algebra (Racah, 1965). • l' '1' XO\V the Lagrangian depends on CPi only through i\J\ === j\crJ\.
T -- pi H d x jOt · d~ W . t WO x,' Xi +W '0 J Xo ( ) t . -:t. 36). 3. t. \. RELATIVISTIC SPINNING PARTICLE REVIE\V OF LAGRANGIAN ApPROACH TO Top We next consider the Lagrangian approach to classical relati vistic spinning particles developed by Hanson and Regge (1974). The treatment gi \'en here will be slightly n10re general than that in the original paper, \vhich dealt only with spherical tops. In order to ensure Poincare-inyariance, unphysical degrees of freedon1 are introduced into the Lagrangian.
LV ( ai ~ or <:Pi, ~ ai ) ~ a~i, or Compatibility \vith Eq. [3 g vc< . Using Eqs. (3. 18) and (3. 19), one can sho\v that (3. 24). Equation (3. ie algebra (Racah, 1965). • l' '1' XO\V the Lagrangian depends on CPi only through i\J\ === j\crJ\. l'hus if vVC define ,ve 111a y ,vri te Tl 1-1"'ro111 I~q. J.. J.. ')' (3. 19), \ve ha ve also sIt') is thus a con1hination of canonical coordinates and canonical 1110111cnta son1c\\"hat sin1ilar to the spinless Lorentz group generator p') _ XV p'l . l;sing l~qs.