References for Hamiltonian field theory and Dirac Brackets

In summary, Hamiltonian field theory is a mathematical framework based on classical mechanics, used to describe the dynamics of continuous systems. Dirac brackets, introduced by physicist Paul Dirac, are essential for treating constraints in Hamiltonian systems. They have a wide range of applications in theoretical physics, but also have limitations and challenges, such as difficulties with singularities and gauge symmetries.
  • #1
andresB
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I'm looking for complete and detailed references on constrained Hamiltonian systems and Dirac brackets. While my main interest is electrodynamics, I would prefer a complete exposition of the theory from the ground up.

So far, my knowledge about the topic comes from books in QFT, like Weinberg. But those books just want to get over with it quickly and go to QED, so it is somewhat unsatisfactory.

So, any good reference out there?
 
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  • #2
Absolutely, it is the "bible" Henneaux, M., Teitelboim, C. "Quantization of Gauge Theories", or Sundermayer, K. "Constrained Dynamics".
 
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1. What is Hamiltonian field theory?

Hamiltonian field theory is a framework used in theoretical physics to describe the dynamics of systems with an infinite number of degrees of freedom. It is based on the Hamiltonian formalism, which uses a set of equations to determine the evolution of a system over time.

2. What are Dirac brackets in Hamiltonian field theory?

Dirac brackets are a mathematical tool used in Hamiltonian field theory to handle the constraints that arise when working with systems with an infinite number of degrees of freedom. They are a generalization of the Poisson brackets used in classical mechanics.

3. How are Dirac brackets different from Poisson brackets?

Dirac brackets take into account the constraints of a system, while Poisson brackets do not. This allows for a more accurate description of the dynamics of systems with constraints, such as those found in field theory. Additionally, Dirac brackets are defined in terms of the constraints, while Poisson brackets are defined in terms of the canonical variables of the system.

4. What is the significance of references in Hamiltonian field theory and Dirac brackets?

References are important in Hamiltonian field theory and Dirac brackets because they provide a way to validate and build upon existing theories and techniques. They also allow for a better understanding of the historical development of these concepts and their applications.

5. How are Hamiltonian field theory and Dirac brackets used in practical applications?

Hamiltonian field theory and Dirac brackets have many practical applications in theoretical physics, including in the study of quantum field theory, general relativity, and string theory. They are also used in engineering and other fields to model and analyze complex systems with an infinite number of degrees of freedom.

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