Difference betw mathematical and physics definition of fields

In summary, the person is a computer science student who is confused about the definition of 'field' in the context of Markov Random Field. They found both mathematical and physics definitions of 'field' but are unsure which one is correct. They also found a relation between the two definitions while searching online, but are still confused. The expert clarifies that the word 'field' is used in neither of these contexts in the Markov Random Field concept and provides a relevant Wikipedia link for further information.
  • #1
zerok
2
0
Hi,
I'm a computer science guy. I was searching the definition of 'Field' in the context of 'Markov Random Field' for my project work. I found mathematical ( http://en.wikipedia.org/wiki/Field_theory_(mathematics ) ) and physics ( http://en.wikipedia.org/wiki/Field_(physics ) )definition of field. Though I am certain that physics definition is the correct one in the context of Markov Random Field. But somehow I find something related between these two definitions by searching over internet. I'm confused. Kindly clarify these things to me.

Thanks,
 
Last edited by a moderator:
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  • #2
links are broken.
 
  • #3
granpa said:
links are broken.

Add ')' at the end of links.
 
  • #4
you add them. click on the 'edit' button below your post.
 
  • #6
There is no relation between the algebraic meaning of "field" (the first Wikipedia citation) and the physics meaning of "field". The "vector field" is an abstraction of the physics meaning of "field".

But neither of those has anything to do with "Markov random field". I googled on that and got
http://en.wikipedia.org/wiki/Markov_network
 

1. What is the mathematical definition of fields?

The mathematical definition of fields refers to a mathematical concept that describes a region in space or a mathematical space where a numerical value is assigned to every point in that space. This numerical value can represent various physical quantities, such as temperature, electric or magnetic fields, or gravitational potential.

2. What is the physics definition of fields?

In physics, fields refer to physical quantities that have a value at every point in space and can affect other objects or particles. These fields can be classified into various types, such as electric, magnetic, gravitational, and more, depending on the type of interaction they have with other objects.

3. How do mathematical and physics definitions of fields differ?

The main difference between the mathematical and physics definitions of fields lies in their approach. While the mathematical definition focuses on describing the properties of a field in a mathematical space, the physics definition focuses on understanding the physical interactions of these fields with other objects or particles.

4. What are some examples of fields in both mathematics and physics?

In mathematics, fields can refer to vector fields, scalar fields, or tensor fields. In physics, some examples of fields include the electric field surrounding a charged particle, the magnetic field around a magnet, or the gravitational field around a massive object like a planet or star.

5. How are fields used in scientific research and applications?

Fields are essential in various scientific fields, including mathematics, physics, engineering, and more. They are used to model and understand the behavior of natural phenomena, such as electricity and magnetism, gravity, and fluid dynamics. Fields also have numerous practical applications, such as in technology, medicine, and energy production.

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