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rodsika
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How do Holonomies or ideas of closed-loops in Gauge Theory compare to the ordinary? What is its advantage and disadvantage? And how does it scale in the plausibility rating?
tom.stoer said:In (non-abelian) gauge theories closed Wilson loops have been introduced especially in lattice gauge theories. The advantage ist that these closed loops are gauge invariant by construction. They can be used as "canonical variables" defining the theory, but unfortunately they are uncountable and do not allow for separable Hilbert spaces. This can be fixed in gravity due to the diffeomorphsims invariance of the theory (but not in gauge theory, so Wilson loops are not used as fundamental objects).
Holonomies in gauge theory refer to the mathematical concept of parallel transport of a vector or tensor along a closed curve in curved space. In simpler terms, it describes how a quantity changes as it moves along a path in a curved space.
Holonomies are used in gauge theory to study the behavior of gauge fields, which are vector fields that describe the interactions between particles in a quantum field theory. They are also used to understand the behavior of gravity in general relativity.
Holonomies play a crucial role in understanding the geometry of space-time and the fundamental interactions between particles. They also provide a way to mathematically describe the curvature of space-time and the behavior of gauge fields.
Yes, the effects of holonomies can be observed and measured in experiments, particularly in cosmology and high-energy particle physics. For example, the cosmic microwave background radiation and the behavior of particles in accelerators can provide evidence for the existence of holonomies.
Yes, holonomies have applications in various fields of science, including quantum computing, condensed matter physics, and string theory. They also have potential applications in areas such as molecular dynamics simulations and machine learning.