Tagged Questions
3
votes
2answers
208 views
primary constraints for constrained Hamiltonian systems
I would be most thankful if you could help me clarify the setting of primary constraints for constrained Hamiltonian systems. I am reading "Classical and quantum
dynamics of constrained Hamiltonian ...
6
votes
2answers
146 views
From Lagrangian to Hamiltonian in Fermionic Model
While going from a given Lagrangian to Hamiltonian for a fermionic field, we use the following formula. $$ H = \Sigma_{i} \pi_i \dot{\phi_i} - L$$ where $\pi_i = \dfrac{\partial L}{\partial ...
4
votes
0answers
40 views
The consistency conditions of constrained Hamiltonian systems
I am studying the Hamiltonian description of a constrained system. There are some questions puzzled me for days, which I have been stuck on it. From the lagrangian, we can obtain the primary ...
4
votes
2answers
108 views
Are Poisson brackets of second-class constraints independent of the canonical coordinates?
Say we have a constraint system with second-class constraints $\chi_N(q,p)=0$. To define Dirac brackets we need the Poisson brackets of these constraints: $C_{NM}=\{\chi_N(q,p),\chi_M(q,p)\}_P$ . Is ...
1
vote
2answers
77 views
Hamiltonian constraint in spherical Friedmann cosmology
I'm taking a GR course, in which the instructor discussed the 'Hamiltonian constraint' of spherical Friedmann cosmology action. I'm not quite clear about the definition of 'Hamiltonian constraint' ...
3
votes
3answers
201 views
Writing $\dot{q}$ in terms of $p$ in the Hamiltonian formulation
In the Hamiltonian formulation, we make a Legendre transformation of the Lagrangian and it should be written in terms of the coordinates $q$ and momentum $p$. Can we always write $dq/dt$ in terms of ...
8
votes
4answers
231 views
What makes an equation an 'equation of motion'?
Every now and then, I find myself reading papers/text talking about how this equation is a constraint but that equation is an equation of motion which satisfies this constraint.
For example, in the ...
2
votes
3answers
129 views
Quantizing first-class constraints for open algebras: can Hermiticity and noncommutativity coexist?
An open algebra for a collection of first-class constraints, $G_a$, $a=1,\cdots, r$, is given by the Poisson bracket $\{ G_a, G_b \} = {f_{ab}}^c[\phi] G_c$ classically, where the structure constants ...
2
votes
2answers
84 views
Commutation for constraints
Suppose from the Hamiltonian I got the Primary constraints $$(\Phi_m,\Phi)$$ And $\dot \Phi_m$ , $\dot \Phi$ leads to secondary constraints $$(\gamma_m,\gamma)$$ respectively. Now if the commutation ...
2
votes
2answers
215 views
Counting degrees of freedom in presence of constraints
In a $N$ dimensional phase space if I have $M$ 1st class and $S$ 2nd class constraints, then I have $N-2M-S$ degrees of freedom in phase space. How can I calculate the degrees of freedom in ...
3
votes
4answers
399 views
First class and second class constraints
Hello I am working on a project that involves the constraints. I checkout the paper of Dirac about the constraints as well as some other resources. But still confuse about the first class and second ...
7
votes
1answer
248 views
Relation between Dirac's generalized Hamiltonian dynamics method and path integral method to deal with constraints
What is the relation between path integral methods for dealing with constraints (constrained Hamiltonian dynamics involving non-singular Lagrangian) and Dirac's method of dealing with such systems ...
3
votes
2answers
155 views
Elimination of velocities from momenta equations for singular Lagrangian
this doubt is related to Generalized Hamiltonian Dynamics paper by Dirac.
Consider the set of $n$ equations : $p_i$ = $∂L/∂v_i$,
(where $v_i$ is $q_i$(dot) = $dq_i/dt$, or time derivative of ...
