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Why is a covariant formalism preferred over a canonical formalism in loop quantum gravity, in simple layman terms
Covariant formalism is a mathematical framework used to describe the dynamics of a physical system in terms of geometric objects. It is based on the principles of general relativity and uses the concept of tensors to represent physical quantities. On the other hand, canonical formalism is a mathematical framework used to describe the dynamics of a physical system in terms of canonical variables, which are pairs of position and momentum variables. It is based on the principles of classical mechanics and uses the Hamiltonian formalism to describe the dynamics of a system.
Both covariant and canonical formalism are used in different areas of physics. Covariant formalism is commonly used in the field of general relativity and cosmology, while canonical formalism is used in classical mechanics and quantum mechanics. The choice of formalism depends on the specific problem being studied and the preferred mathematical approach of the scientist.
Covariant formalism is advantageous because it allows for a more elegant and concise mathematical description of physical systems. It also has the advantage of being covariant, meaning it is independent of the choice of coordinates and is therefore applicable to a wide range of physical systems. Additionally, it is well-suited for describing systems with symmetries, such as those found in general relativity.
Canonical formalism is advantageous because it provides a clear physical interpretation of the mathematical equations, making it easier to understand the behavior of a system. It also allows for a direct connection to classical mechanics, making it useful for studying a wide range of physical systems. Furthermore, it is well-suited for quantization, which is the process of describing a classical system in terms of quantum mechanics.
Yes, it is possible to use both covariant and canonical formalism together in certain cases. For example, in general relativity, the covariant formalism is used to describe the dynamics of spacetime, while the canonical formalism is used to describe the dynamics of matter within spacetime. This combination allows for a more complete description of physical systems and has led to important advancements in our understanding of the universe.