Dimensions of Hilbert Spaces confusion

In summary: I'm not sure what that means.The tensor product of two Hilbert spaces is a Hilbert space that is the product of the two original Hilbert spaces.
  • #36
tom.stoer said:
With gauge-invariant regularization these Schwinger terms do vanish for gauge currents. (I don't know whether this works for chiral gauge theories)

I think, I said that the anomalies come from the source current not the gauge field current.


I don't see why the local color gauge algebra shall be able to do that.

That is a very long story. See any paper by E. Leader on the “proton angular momentum controversy”. Or read page 49-51 in the above mentioned review by Lavelle & McMullan.
 
<h2>What is a Hilbert Space?</h2><p>A Hilbert Space is a mathematical concept that represents an infinite-dimensional vector space. It is a generalization of Euclidean space, where the concept of length and angles can be extended to an infinite number of dimensions.</p><h2>What are the dimensions of a Hilbert Space?</h2><p>The dimensions of a Hilbert Space can vary from finite to infinite. In a finite-dimensional Hilbert Space, the number of dimensions is a finite positive integer. In an infinite-dimensional Hilbert Space, the number of dimensions is infinite.</p><h2>What is the confusion surrounding Dimensions of Hilbert Spaces?</h2><p>The confusion surrounding Dimensions of Hilbert Spaces arises from the fact that the concept of dimensions in a Hilbert Space is different from the dimensions in a Euclidean Space. In a Hilbert Space, the dimensions refer to the number of basis vectors needed to span the space, whereas in a Euclidean Space, the dimensions refer to the number of coordinates needed to locate a point.</p><h2>How do you calculate the dimensions of a Hilbert Space?</h2><p>The dimensions of a Hilbert Space can be calculated by finding the number of linearly independent basis vectors that span the space. This can be done by using techniques such as Gram-Schmidt orthogonalization or finding the null space of a linear transformation.</p><h2>What are some real-world applications of Hilbert Spaces?</h2><p>Hilbert Spaces have various applications in physics, engineering, and mathematics. They are used in quantum mechanics, signal processing, and control theory. They are also used in image and sound processing, as well as in data compression algorithms.</p>

FAQ: Dimensions of Hilbert Spaces confusion

What is a Hilbert Space?

A Hilbert Space is a mathematical concept that represents an infinite-dimensional vector space. It is a generalization of Euclidean space, where the concept of length and angles can be extended to an infinite number of dimensions.

What are the dimensions of a Hilbert Space?

The dimensions of a Hilbert Space can vary from finite to infinite. In a finite-dimensional Hilbert Space, the number of dimensions is a finite positive integer. In an infinite-dimensional Hilbert Space, the number of dimensions is infinite.

What is the confusion surrounding Dimensions of Hilbert Spaces?

The confusion surrounding Dimensions of Hilbert Spaces arises from the fact that the concept of dimensions in a Hilbert Space is different from the dimensions in a Euclidean Space. In a Hilbert Space, the dimensions refer to the number of basis vectors needed to span the space, whereas in a Euclidean Space, the dimensions refer to the number of coordinates needed to locate a point.

How do you calculate the dimensions of a Hilbert Space?

The dimensions of a Hilbert Space can be calculated by finding the number of linearly independent basis vectors that span the space. This can be done by using techniques such as Gram-Schmidt orthogonalization or finding the null space of a linear transformation.

What are some real-world applications of Hilbert Spaces?

Hilbert Spaces have various applications in physics, engineering, and mathematics. They are used in quantum mechanics, signal processing, and control theory. They are also used in image and sound processing, as well as in data compression algorithms.

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