Definition of Poisson Bracket: {f,g}

Click For Summary
SUMMARY

The Poisson bracket is defined as either {f,g} = df/dp.dg/dq - df/dq.dg/dp or {f,g} = df/dq.dg/dp - df/dp.dg/dq. Both definitions are valid, with the choice depending on the author's preference. However, the second definition is more commonly accepted in literature and is recommended for use. Understanding this distinction is crucial for accurate application in Hamiltonian mechanics.

PREREQUISITES
  • Familiarity with Hamiltonian mechanics
  • Understanding of differential calculus
  • Knowledge of classical mechanics terminology
  • Experience with mathematical notation in physics
NEXT STEPS
  • Research the applications of Poisson brackets in Hamiltonian dynamics
  • Study the implications of different definitions in theoretical physics
  • Learn about symplectic geometry and its relation to Poisson brackets
  • Explore the role of Poisson brackets in statistical mechanics
USEFUL FOR

This discussion is beneficial for physicists, mathematicians, and students studying classical mechanics or Hamiltonian systems, particularly those interested in the mathematical foundations of physics.

Pyroadept
Messages
82
Reaction score
0



Hi, what is the correct definition for a Poisson bracket?
Some books say it is:

{f,g} = df/dp.dg/dq - df/dq.dg/dp

but others say it is:

{f,g} = df/dq.dg/dp - df/dp.dg/dq

One is the other multiplied by -1.
Which is the correct definition?


Thanks for any help.
 
Physics news on Phys.org
Pyroadept said:
Hi, what is the correct definition for a Poisson bracket?
Some books say it is:

{f,g} = df/dp.dg/dq - df/dq.dg/dp

but others say it is:

{f,g} = df/dq.dg/dp - df/dp.dg/dq

One is the other multiplied by -1.
Which is the correct definition?


Thanks for any help.

You CAN use either the first definition or the other one and this only depends on author's style though if I were you, I would take the second one for granted in being more common and true.

AB
 

Similar threads

Characterizing random processes
  • · Replies 8 ·
Replies
8
Views
1K
Graduate Recover Hamilton equation from 2-form defined on phase space
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Question on derivation of a property of Poisson brackets
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Invariance of the Poisson Bracket
  • · Replies 8 ·
Replies
8
Views
1K
Graduate Parallel transport on a symplectic space
  • · Replies 1 ·
Replies
1
Views
2K
Graduate What is the exact connection between Poisson brackets and commutators
  • · Replies 2 ·
Replies
2
Views
4K
Does the derivative df/dg of the function f(g) exist and what does this mean?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad On inverse function theorem in Spivak's CoM
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad The different generators of canonical transformations
  • · Replies 3 ·
Replies
3
Views
1K
Graduate What is the physical significance of Poisson brackets?
  • · Replies 3 ·
Replies
3
Views
5K