# Tag Info

### Hamiltonian of a complex scalar quantum field

Where did I go wrong? Seems like probably there are a number of different places you could have gone wrong. Since this is a homework-like question, I will answer in terms of classical field theory, ...
• 19.8k
Accepted

### Why do we need a Poisson bracket structure?

The simplest way to motivate the Dirac bracket is to consider a situation where two second-class constraints $f_1,f_2$ have constant non-zero Poisson bracket $\{f_1,f_2\} = c \neq 0$, e.g. when we ...
• 125k
Accepted

• 71.7k
1 vote
Accepted

### Why $q,p,Q,P$ are Independent Variables when Using Generating Functions?

In Hamiltonian formalism, specifically generating functions, why do the variables $q, p, Q, P$ are treated as independent when finding the equations that arise from the generating function? Let us ...
• 19.8k
1 vote

### Why $q,p,Q,P$ are Independent Variables when Using Generating Functions?

As QMechanic described in his answer to the related post, the generating functions are defined on a $4n$ dimensional manifold. By definition you have $4n$ independent coordinates to describe a point ...
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1 vote

• 202k
1 vote
Accepted

### Constrained Hamiltonian problems

This is a quite broad question. Briefly speaking, starting from the non-degenerate canonical Poisson bracket structure, according to the Dirac-Bergmann analysis, the constraints can in principle (...
• 202k
1 vote

### Regarding varying the coefficients of constraints in the pre-extended Hamiltonian in Dirac method

The short answer is that at this point in Ref. 1 $u^m$ are new independent variables; not functions of $q$ and $p$. Equivalently, $u^m$ are Lagrange undetermined multipliers. It is possibly helpful to ...
• 202k
1 vote

### What is Phase Space Formulation of QM and does it explain use of complex variables in QM?

I feel like the other two answers are not satisfying from a mathematical point of view, respectively due to their brevity or dogmatic nature. I will describe two ways in which the complex numbers are ...

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