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resurgance2001
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In QM, position is an operator, while in QFT, it is a label. Could someone help me understand what is meant by the term "label" - just in the simplest terms possible? Cheers
resurgance2001 said:In QM, position is an operator, while in QFT, it is a label. Could someone help me understand what is meant by the term "label" - just in the simplest terms possible? Cheers
This is what happens when you go from systems with a finite number of degrees of freedom to an infinite number of continuous degrees of freedom which is a field theory. This happens at the classical level before any kind of quantisation. The point is when you have a finite number of degrees of freedom, the associated coordinates are variables which encode the locations of particles and their variations represent different positions/configurations of the mechanical system in the usual sense. When you have an infinite number of continuous degrees of freedom such as a fluid, you consider your space positions to be fixed points in space which do not vary, in contrast to the previous situation where one takes the positions of the discrete system to be moving in space. In the case of a field, positions in space are fixed and do not move, instead it is the field value defined over these position labels which varies, giving rise to wave-like motion whose form depends on the kind of interactions one defines between the degrees of freedom. If you'd like an example of a field that would make this a bit more tangible, let us know!resurgance2001 said:In QM, position is an operator, while in QFT, it is a label. Could someone help me understand what is meant by the term "label" - just in the simplest terms possible? Cheers
A label is a piece of information attached to an object or entity that identifies and describes it. It can be used to categorize, organize, or give instructions about the object or entity.
QM stands for quantum mechanics, which is a branch of physics that studies the behavior of particles on a very small scale. QFT stands for quantum field theory, which is a theoretical framework that describes the behavior of particles and fields in quantum mechanics.
In quantum mechanics, labels are used to identify and describe particles and their properties. In quantum field theory, labels are used to identify and describe fields and their interactions with particles.
In quantum mechanics, a label could be the spin of a particle, which can be either "up" or "down". In quantum field theory, a label could be the charge of a particle, which can be positive or negative.
Labels play a crucial role in understanding the behavior of particles and fields in quantum mechanics and quantum field theory. They allow us to categorize and describe the properties of these entities, and ultimately help us make predictions and theories about the fundamental nature of the universe.