Non Polynomial Hamiltonian Constraint

Thread starter Quantizer
Start date Apr 25, 2014
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Constraint Hamiltonian Polynomial

In summary, a Non Polynomial Hamiltonian Constraint is a type of constraint used in Hamiltonian mechanics that cannot be expressed as a finite sum of terms with each term being a polynomial. It differs from a Polynomial Hamiltonian Constraint in that it involves more complex mathematical expressions and is often used to model nonlinear and chaotic physical systems. Non Polynomial Hamiltonian Constraints are significant in physics because they allow for a better understanding and prediction of these systems. They are commonly used in research and experimentation but can present challenges due to their difficulty in mathematical analysis and the unpredictable nature of systems with these constraints.

Apr 25, 2014

Quantizer

1. Is the root(det(q)) term in the Hamiltonian Constraint what makes it non polynomial
2. Is the motivation for Ashtekar Variables to remove the non polynomial terms by replacing the Hamiltonian with a densitised Hamiltonian

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Apr 26, 2014

Matterwave

Science Advisor

Gold Member

I suggest you try the "Beyond the standard model" forum for questions regarding loop quantum gravity.

Related to Non Polynomial Hamiltonian Constraint

What is a Non Polynomial Hamiltonian Constraint?

A Non Polynomial Hamiltonian Constraint refers to a type of constraint that is used in Hamiltonian mechanics, which is a mathematical framework for studying the dynamics of physical systems. The constraint is in the form of a non-polynomial function, which means that it cannot be expressed as a finite sum of terms with each term being a polynomial.

How is a Non Polynomial Hamiltonian Constraint different from a Polynomial Hamiltonian Constraint?

A Polynomial Hamiltonian Constraint can be expressed as a finite sum of terms, with each term being a polynomial. On the other hand, a Non Polynomial Hamiltonian Constraint cannot be expressed in this way and often involves more complex mathematical expressions. This makes it more challenging to analyze and solve problems with a Non Polynomial Hamiltonian Constraint.

What is the significance of Non Polynomial Hamiltonian Constraints in physics?

Non Polynomial Hamiltonian Constraints are used to model physical systems that have nonlinear dynamics, meaning that their behavior cannot be described by simple linear equations. They are particularly useful in studying complex systems such as chaotic systems, where small changes in initial conditions can lead to significantly different outcomes. Non Polynomial Hamiltonian Constraints allow scientists to better understand and predict the behavior of these types of systems.

How are Non Polynomial Hamiltonian Constraints used in research and experimentation?

Non Polynomial Hamiltonian Constraints are often used in computer simulations and numerical calculations to study the behavior of physical systems. They are also used in experiments, such as in particle accelerators, to model and analyze the behavior of particles and their interactions. By incorporating these constraints, scientists can gain a deeper understanding of the underlying principles and dynamics of these systems.

What are some challenges associated with Non Polynomial Hamiltonian Constraints?

One of the main challenges of Non Polynomial Hamiltonian Constraints is that they can be difficult to solve and analyze mathematically. This is because they involve complex functions and equations, which can be challenging to manipulate and solve. Additionally, the behavior of systems with Non Polynomial Hamiltonian Constraints can be unpredictable and sensitive to small changes in initial conditions, making it challenging to accurately predict their behavior.