Understanding the Hermitian Form in Velo-Zwanzinger's Article

in summary, the hermitian form contains the original form, but there's an extra term, the hermitian conjugated from the anterior form. if you add the conjugated to the original, you have the hermitian form.
  • #1
Renattus
2
0
hi, i don't have the expression, but my problem is this: in the article of Velo-Zwanzinger appears a step... passing from a equation to other which they call the hermitian form. i going to explain it... this form contains the original form...but appear an extra term..i suppose that it's the hermitian conjugated from the anterior form..so if add the conjugated to the original...i have the hermitian form...is that true??
 
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  • #2
Renattus said:
hi, i don't have the expression, but my problem is this: in the article of Velo-Zwanzinger appears a step... passing from a equation to other which they call the hermitian form. i going to explain it... this form contains the original form...but appear an extra term..i suppose that it's the hermitian conjugated from the anterior form..so if add the conjugated to the original...i have the hermitian form...is that true??

Since you're new here, you should probably read the posting guidelines first.
You're more likely to get a useful answer if you:

(a) cite specific references,

(b) include more context in your question (including some formulas or equations in latex if you're asking about some math),

(c) Use complete English sentences. (Even though you're apparently not a native English speaker, I think you could compose your question better than the above.)
 
  • #3
well...i'm new here..and I'm not a native english speaker..so i just want to tell me about hermitian form... how can i put into hermitian form a motion equation... i think i don't have to include the equation ('cause it's large)..just explain me (if you can, course)...
i'm studying the rarita-schwinger equation for particles with s=3/2... when i consider an interaction with an electromagnetic field... (velo-zwanzinger problem) the expression changes to a complicated form...i don't have my eq. but ..can you explain me...why do i have to put into hermitian form a motion equation?.
sorry for my english...i'm not a very good writer..
 

What is a Hermitian form?

A Hermitian form is a mathematical concept used in linear algebra and functional analysis. It is a generalization of the notion of an inner product on a complex vector space, and is defined as a function that takes two vectors as inputs and produces a complex number as output. It has certain properties, such as symmetry and linearity, that make it useful in mathematical analysis.

Why is the Hermitian form important in Velo-Zwanzinger's article?

In Velo-Zwanzinger's article, the Hermitian form is used to study the properties of quark and gluon interactions in quantum chromodynamics, a theory that describes the strong nuclear force. The Hermitian form is a crucial mathematical tool in this analysis, as it helps to understand the structure and behavior of quarks and gluons in high-energy collisions.

What is the difference between a Hermitian form and an inner product?

While both concepts are related, there are some key differences between a Hermitian form and an inner product. A Hermitian form is defined on a complex vector space, whereas an inner product is defined on a real vector space. Additionally, a Hermitian form has certain properties, such as linearity and symmetry, that may not hold for an inner product in a complex vector space.

How is the Hermitian form used in quantum chromodynamics?

In quantum chromodynamics, the Hermitian form is used to study the properties of quarks and gluons, such as their interactions and behavior in high-energy collisions. It is also used to analyze the quantum states of these particles and to derive important equations and predictions in the theory.

What are some applications of understanding the Hermitian form?

Understanding the Hermitian form has many applications in mathematics and physics. It is used in quantum mechanics, functional analysis, and differential geometry, among other fields. In addition, it has practical applications in areas such as signal processing, image recognition, and machine learning.

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