See the last examples. Predict the preceding dialog. DIALOG:
What is the difference between a hamiltonian and a gaussian?
- In the presence of such constraints, the total Hamiltonian formula_36 is obtained from the Lagrangian formula_37 by adding to the Legendre Hamiltonian formula_38 the sum of the constraints times an appropriate set of Lagrange multipliers formula_39.
- Are there any other interesting aspects about this article?
- This total Hamiltonian is traditionally called the Dirac Hamiltonian.
- Why is it called that?
- Constraints arise naturally from parameter invariant actions of the form In the case of four vector and Lorentz scalar interactions for a single particle the Lagrangian is The canonical momentum is  and by squaring leads to the generalized mass shell condition or generalized mass shell constraint Since, in this case, the Legendre Hamiltonian vanishes the Dirac Hamiltonian is simply the generalized mass constraint (with no interactions it would simply be the ordinary mass shell constraint) One then postulates that for two bodies the Dirac Hamiltonian is the sum of two such mass shell constraints,  that is  and that each constraint formula_50 be constant in the proper time associated with formula_36 Here the weak equality means that the Poisson bracket could result in terms proportional one of the constraints, the classical Poisson brackets for the relativistic two-body system being defined by  To see the consequences of having each constraint be a constant of the motion, take, for example Since formula_55 and formula_56 and formula_57 one has  The simplest solution to this is  which leads to (note the equality in this case is not a weak one in that no constraint need be imposed after the Poisson bracket is worked out) (see Todorov, and Wong and Crater ) with the same formula_61 defined above.
- Is there anything else noteable about the dirac equations?
- 
Preceding conversation: DIALOG:
What is the difference between a hamiltonian and a gaussian?
- In the presence of such constraints, the total Hamiltonian formula_36 is obtained from the Lagrangian formula_37 by adding to the Legendre Hamiltonian formula_38 the sum of the constraints times an appropriate set of Lagrange multipliers formula_39.
- Are there any other interesting aspects about this article?
- This total Hamiltonian is traditionally called the Dirac Hamiltonian.
- Why is it called that?
- Constraints arise naturally from parameter invariant actions of the form In the case of four vector and Lorentz scalar interactions for a single particle the Lagrangian is The canonical momentum is  and by squaring leads to the generalized mass shell condition or generalized mass shell constraint Since, in this case, the Legendre Hamiltonian vanishes the Dirac Hamiltonian is simply the generalized mass constraint (with no interactions it would simply be the ordinary mass shell constraint) One then postulates that for two bodies the Dirac Hamiltonian is the sum of two such mass shell constraints,  that is  and that each constraint formula_50 be constant in the proper time associated with formula_36 Here the weak equality means that the Poisson bracket could result in terms proportional one of the constraints, the classical Poisson brackets for the relativistic two-body system being defined by  To see the consequences of having each constraint be a constant of the motion, take, for example Since formula_55 and formula_56 and formula_57 one has  The simplest solution to this is  which leads to (note the equality in this case is not a weak one in that no constraint need be imposed after the Poisson bracket is worked out) (see Todorov, and Wong and Crater ) with the same formula_61 defined above.
- Is there anything else noteable about the dirac equations?
- 


See the last examples. Predict the preceding dialog. DIALOG:
What is the result of the Inter-Governmental Philatelic Corporation's (IGPC) activities?
- Thematic stamp shows have been sponsored in the United States in support of one of IGPC's key markets and in 2007 the company provided 12 vehicles to the new Liberian post office.
- What else did you find interesting?
- 
Preceding conversation: DIALOG:
What is the result of the Inter-Governmental Philatelic Corporation's (IGPC) activities?
- Thematic stamp shows have been sponsored in the United States in support of one of IGPC's key markets and in 2007 the company provided 12 vehicles to the new Liberian post office.
- What else did you find interesting?
- 


See the last examples. Predict the preceding dialog. DIALOG:
What are some examples of his best known Art Nouveau work?
- His best known Art Nouveau work is the poster for "La Maison Moderne", a shop of Art Nouveau interior design which competed with that of Samuel Bing, which combined a dozen aspects of Art Nouveau into a single illustration.
- What are some of his other works?
- Orazi also made illustrations of Sarah Berhnardt. poster of Sarah Bernhardt as the Byzantine Empress Theodora, surrounded by mosaic patterns.
- Are there any other interesting aspects about this article?
- The first Art Nouveau architecture had appeared in Belgium in 1893, and Belgian graphic artists were quick to use the style.
- Did he work with any other artists?
- The most prominent was Henri Privat-Livemont, a member of the symbolist movement, who made his reputation as a member of the Circle of Artists of Schaerbeek, a group of artists in that neighborhood of Brussels.
- What other symbolist movements was he known for?
- 
Preceding conversation:
DIALOG:
What are some examples of his best known Art Nouveau work?
- His best known Art Nouveau work is the poster for "La Maison Moderne", a shop of Art Nouveau interior design which competed with that of Samuel Bing, which combined a dozen aspects of Art Nouveau into a single illustration.
- What are some of his other works?
- Orazi also made illustrations of Sarah Berhnardt. poster of Sarah Bernhardt as the Byzantine Empress Theodora, surrounded by mosaic patterns.
- Are there any other interesting aspects about this article?
- The first Art Nouveau architecture had appeared in Belgium in 1893, and Belgian graphic artists were quick to use the style.
- Did he work with any other artists?
- The most prominent was Henri Privat-Livemont, a member of the symbolist movement, who made his reputation as a member of the Circle of Artists of Schaerbeek, a group of artists in that neighborhood of Brussels.
- What other symbolist movements was he known for?
-