Maxwell equations are not electromagnetic characteristics, but geometric ones.

[Ginhak Kim]

To prove this, I define dot product between r-blades in geometric algebra and define newly curl and divergence also.

this book is short, 13 pages. After reading, if you are satisfied, please pass this on to others.

[Peeter Joot]

This group is moderated by default, so new authors must be patient, waiting for a moderator to approve their post and their userid for future posts.  Moderating this group was done to prevent spam, and has proved effective, at least for a low-volume group like this.

I've approved your (first) post to this group, as it is on topic, but not the second (duplicate) and third (test) posts.

As for your attached PDF, I personally, do not find your intent very clear.  If there something new that you are attempting to demonstrate, it is hard to see, among all the other derivations included.  There are other things that make the paper hard to read.  For example, you introduce a new notation for wedge:

 [a b c... d] = a \wedge b \wedge c ... \wedge d.  

It's not clear why you do this, and requires the reader to mentally map the new notation that you (and only you) are using, to familiar notation, making the paper harder to read.  It's hard to scan it, looking for intent, when notational choices require work to read.

Also, if you are trying to write significant mathematical content, I'd strongly encourage that you use LaTeX to format your equations, as Microsoft word equations are harder to read than LaTeX.  I would guess that many potential readers will be discouraged by the format itself.  If you are trying to convey new ideas, make it easy on those that you are trying to communicate to.

Peeter

[Ginhak Kim]

Thank you for your advice.

abbreviation of wedge(∧) is from similar notation pqr=p×q×r.

In my book, I use only anticommutative characteristic of  r-blade.

That is the basic difference with existing geometric algebra.

for example)

existing geometric algebra: e₁∧e₂∧e₁=-e₁∧e₁∧e₂=-e₂

but in my book: e₁∧e₂∧e₁=(ε₃₂₁)e₁∧e₂∧e₁=-e₁∧e₂∧e₁=0

I hope to hear your thoughts on curl.

Ginac

2023년 9월 4일 월요일 오후 11시 32분 37초 UTC+9에 Peeter Joot님이 작성:

[Ginhak Kim]

sorry. I will correct what I wrote incorrectly.

for example)

existing geometric algebra: e₁e₂e₁=-e₁e₁e₂=-e₂

but in my book: [e₁e₂e₁]=e₁∧e₂∧e₁=0=(ε₃₂₁)[e₁e₂e₁]=-[e₁e₂e₁]

2023년 9월 5일 화요일 오후 3시 37분 54초 UTC+9에 Ginhak Kim님이 작성:

[Peeter Joot]

Hi Ginac,

If you are only using the wedge, it doesn't sound like what you have done is significantly different than the differential forms approach (except for putting the wedges on the basis vectors instead of the differentials) -- I admit that I like that better too, but that's the approach used in existing geometric calculus formulations of Maxwell's equations.

In geometric algebra, e₁∧e₂∧e₁=0 too, so again, it's not clear to me what the value of your special commutator notation is.

Notational differences aside, can you outline what you are trying to accomplish in your paper?

Peeter

[Ginhak Kim]

Hi Peeter

English is difficult for me. I will explain one thing at a time. but I'll do my best.
and It's easier for me to explain with examples.

'In calculus, it doesn't matter which basis you choose.'
that is what I want to say, this time.

An example is included in the attached file.

Ginac

2023년 9월 6일 수요일 오전 2시 4분 27초 UTC+9에 Peeter Joot님이 작성:

[Ginhak Kim]

Hi Peeter

English is difficult for me. I will explain one thing at a time. but I'll do my best.
and It's easier for me to explain with examples.

'In calculus, it doesn't matter which basis you choose.'
that is what I want to say, this time.

An example is included in the attached file.

Ginac

2023년 9월 6일 수요일 오전 2시 4분 27초 UTC+9에 Peeter Joot님이 작성:

Hi Ginac,

[Ginhak Kim]

The following information is omitted from the example.

vector A is 1-vector, curl(A) is 2-vector 

2023년 9월 6일 수요일 오후 5시 43분 30초 UTC+9에 Ginhak Kim님이 작성:

[Peeter Joot]

Hi Ginhak,

I can see that you are defining a bivector curl and expressing it in terms of the reciprocal frame, so that it applies to any chosen parameterization.  Nothing there looks unreasonable, with the exception of a sign error in this identity in your Exam1.pdf:

(𝑎 ∧ 𝑏) ⋅ (𝑐 ∧ 𝑑) = (𝑎 ⋅ 𝑐)(𝑏 ⋅ 𝑑) − (𝑎 ⋅ 𝑑)(𝑏 ⋅ 𝑐)

which has the sign reversed.  It should be:

(𝑎 ∧ 𝑏) ⋅ (𝑐 ∧ 𝑑) = ((𝑎 ∧ 𝑏) ⋅ 𝑐) ⋅ 𝑑 = (𝑎 ⋅ 𝑑)(𝑏 ⋅ 𝑐) - (𝑎 ⋅ 𝑐)(𝑏 ⋅ 𝑑) 

Peeter

[Ginhak Kim]

Hi Peeter

My definition of the dot product of r-vectors follows the commutative law,  is different existing dot product.
In summary, I only use r-vectors and commutative dot product.
examples are included in the attached file.

next time, I will explain about infinitesimal volume [dX] and the border of  [dX].

Ginac

2023년 9월 7일 목요일 오전 3시 34분 11초 UTC+9에 Peeter Joot님이 작성:

[Ginhak Kim]

Hi Peeter

From your questions and advice, I learned that my book is difficult to read and understand. It was a book that made me understand myself. I will rewrite the first part of the book to make it easier for others to understand.

I'll be back when it's completed.
Thank you.

Ginac

2023년 9월 7일 목요일 오후 5시 32분 8초 UTC+9에 Ginhak Kim님이 작성:

[Ginhak Kim]

Hi Peeter

I rewrote the first part of the book, but it's still an ms-word file.
Please read the entire book.
Thank you.

Ginac

2023년 9월 8일 금요일 오후 1시 43분 4초 UTC+9에 Ginhak Kim님이 작성: